Chaotic Transitions in Deterministic and Stochastic Dynamical Systems : : Applications of Melnikov Processes in Engineering, Physics, and Neuroscience / / Emil Simiu.
The classical Melnikov method provides information on the behavior of deterministic planar systems that may exhibit transitions, i.e. escapes from and captures into preferred regions of phase space. This book develops a unified treatment of deterministic and stochastic systems that extends the appli...
Saved in:
Superior document: | Title is part of eBook package: De Gruyter Princeton Series in Applied Mathematics eBook-Package |
---|---|
VerfasserIn: | |
Place / Publishing House: | Princeton, NJ : : Princeton University Press, , [2014] ©2002 |
Year of Publication: | 2014 |
Language: | English |
Series: | Princeton Series in Applied Mathematics ;
51 |
Online Access: | |
Physical Description: | 1 online resource (240 p.) :; 94 line illus. |
Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
id |
9781400832507 |
---|---|
ctrlnum |
(DE-B1597)447398 (OCoLC)891400514 |
collection |
bib_alma |
record_format |
marc |
spelling |
Simiu, Emil, author. aut http://id.loc.gov/vocabulary/relators/aut Chaotic Transitions in Deterministic and Stochastic Dynamical Systems : Applications of Melnikov Processes in Engineering, Physics, and Neuroscience / Emil Simiu. Princeton, NJ : Princeton University Press, [2014] ©2002 1 online resource (240 p.) : 94 line illus. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Princeton Series in Applied Mathematics ; 51 Frontmatter -- Contents -- Preface -- Chapter 1. Introduction -- PART 1. FUNDAMENTALS -- Chapter 2. Transitions in Deterministic Systems and the Melnikov Function -- Chapter 3. Chaos in Deterministic Systems and the Melnikov Function -- Chapter 4. Stochastic Processes -- Chapter 5. Chaotic Transitions in Stochastic Dynamical Systems and the Melnikov Process -- PART 2. APPLICATIONS -- Chapter 6. Vessel Capsizing -- Chapter 7. Open-Loop Control of Escapes in Stochastically Excited Systems -- Chapter 8. Stochastic Resonance -- Chapter 9. Cutoff Frequency of Experimentally Generated Noise for a First-Order Dynamical System -- Chapter 10. Snap-Through of Transversely Excited Buckled Column -- Chapter 11. Wind-Induced Along-Shore Currents over a Corrugated Ocean Floor -- Chapter 12. The Auditory Nerve Fiber as a Chaotic Dynamical System -- Appendix A1 Derivation of Expression for the Melnikov Function -- Appendix A2 Construction of Phase Space Slice through Stable and Unstable Manifolds -- Appendix A3 Topological Conjugacy -- Appendix A4 Properties of Space ∑2 -- Appendix A5 Elements of Probability Theory -- Appendix A6 Mean Upcrossing Rate τu-1 for Gaussian Processes -- Appendix A7 Mean Escape Rate τ∊-1 for Systems Excited by White Noise -- References -- Index restricted access http://purl.org/coar/access_right/c_16ec online access with authorization star The classical Melnikov method provides information on the behavior of deterministic planar systems that may exhibit transitions, i.e. escapes from and captures into preferred regions of phase space. This book develops a unified treatment of deterministic and stochastic systems that extends the applicability of the Melnikov method to physically realizable stochastic planar systems with additive, state-dependent, white, colored, or dichotomous noise. The extended Melnikov method yields the novel result that motions with transitions are chaotic regardless of whether the excitation is deterministic or stochastic. It explains the role in the occurrence of transitions of the characteristics of the system and its deterministic or stochastic excitation, and is a powerful modeling and identification tool. The book is designed primarily for readers interested in applications. The level of preparation required corresponds to the equivalent of a first-year graduate course in applied mathematics. No previous exposure to dynamical systems theory or the theory of stochastic processes is required. The theoretical prerequisites and developments are presented in the first part of the book. The second part of the book is devoted to applications, ranging from physics to mechanical engineering, naval architecture, oceanography, nonlinear control, stochastic resonance, and neurophysiology. Issued also in print. Mode of access: Internet via World Wide Web. In English. Description based on online resource; title from PDF title page (publisher's Web site, viewed 31. Jan 2022) Chaotic behavior in systems. Differentiable dynamical systems. Stochastic systems. MATHEMATICS / Applied. bisacsh Affine transformation. Amplitude. Arbitrarily large. Attractor. Autocovariance. Big O notation. Central limit theorem. Change of variables. Chaos theory. Coefficient of variation. Compound Probability. Computational problem. Control theory. Convolution. Coriolis force. Correlation coefficient. Covariance function. Cross-covariance. Cumulative distribution function. Cutoff frequency. Deformation (mechanics). Derivative. Deterministic system. Diagram (category theory). Diffeomorphism. Differential equation. Dirac delta function. Discriminant. Dissipation. Dissipative system. Dynamical system. Eigenvalues and eigenvectors. Equations of motion. Even and odd functions. Excitation (magnetic). Exponential decay. Extreme value theory. Flow velocity. Fluid dynamics. Forcing (recursion theory). Fourier series. Fourier transform. Fractal dimension. Frequency domain. Gaussian noise. Gaussian process. Harmonic analysis. Harmonic function. Heteroclinic orbit. Homeomorphism. Homoclinic orbit. Hyperbolic point. Inference. Initial condition. Instability. Integrable system. Invariant manifold. Iteration. Joint probability distribution. LTI system theory. Limit cycle. Linear differential equation. Logistic map. Marginal distribution. Moduli (physics). Multiplicative noise. Noise (electronics). Nonlinear control. Nonlinear system. Ornstein-Uhlenbeck process. Oscillation. Parameter space. Parameter. Partial differential equation. Perturbation function. Phase plane. Phase space. Poisson distribution. Probability density function. Probability distribution. Probability theory. Probability. Production-possibility frontier. Relative velocity. Scale factor. Shear stress. Spectral density. Spectral gap. Standard deviation. Stochastic process. Stochastic resonance. Stochastic. Stream function. Surface stress. Symbolic dynamics. The Signal and the Noise. Topological conjugacy. Transfer function. Variance. Vorticity. Title is part of eBook package: De Gruyter Princeton Series in Applied Mathematics eBook-Package 9783110515831 ZDB-23-PAM Title is part of eBook package: De Gruyter Princeton University Press eBook-Package Backlist 2000-2013 9783110442502 print 9780691144344 https://doi.org/10.1515/9781400832507 https://www.degruyter.com/isbn/9781400832507 Cover https://www.degruyter.com/document/cover/isbn/9781400832507/original |
language |
English |
format |
eBook |
author |
Simiu, Emil, Simiu, Emil, |
spellingShingle |
Simiu, Emil, Simiu, Emil, Chaotic Transitions in Deterministic and Stochastic Dynamical Systems : Applications of Melnikov Processes in Engineering, Physics, and Neuroscience / Princeton Series in Applied Mathematics ; Frontmatter -- Contents -- Preface -- Chapter 1. Introduction -- PART 1. FUNDAMENTALS -- Chapter 2. Transitions in Deterministic Systems and the Melnikov Function -- Chapter 3. Chaos in Deterministic Systems and the Melnikov Function -- Chapter 4. Stochastic Processes -- Chapter 5. Chaotic Transitions in Stochastic Dynamical Systems and the Melnikov Process -- PART 2. APPLICATIONS -- Chapter 6. Vessel Capsizing -- Chapter 7. Open-Loop Control of Escapes in Stochastically Excited Systems -- Chapter 8. Stochastic Resonance -- Chapter 9. Cutoff Frequency of Experimentally Generated Noise for a First-Order Dynamical System -- Chapter 10. Snap-Through of Transversely Excited Buckled Column -- Chapter 11. Wind-Induced Along-Shore Currents over a Corrugated Ocean Floor -- Chapter 12. The Auditory Nerve Fiber as a Chaotic Dynamical System -- Appendix A1 Derivation of Expression for the Melnikov Function -- Appendix A2 Construction of Phase Space Slice through Stable and Unstable Manifolds -- Appendix A3 Topological Conjugacy -- Appendix A4 Properties of Space ∑2 -- Appendix A5 Elements of Probability Theory -- Appendix A6 Mean Upcrossing Rate τu-1 for Gaussian Processes -- Appendix A7 Mean Escape Rate τ∊-1 for Systems Excited by White Noise -- References -- Index |
author_facet |
Simiu, Emil, Simiu, Emil, |
author_variant |
e s es e s es |
author_role |
VerfasserIn VerfasserIn |
author_sort |
Simiu, Emil, |
title |
Chaotic Transitions in Deterministic and Stochastic Dynamical Systems : Applications of Melnikov Processes in Engineering, Physics, and Neuroscience / |
title_sub |
Applications of Melnikov Processes in Engineering, Physics, and Neuroscience / |
title_full |
Chaotic Transitions in Deterministic and Stochastic Dynamical Systems : Applications of Melnikov Processes in Engineering, Physics, and Neuroscience / Emil Simiu. |
title_fullStr |
Chaotic Transitions in Deterministic and Stochastic Dynamical Systems : Applications of Melnikov Processes in Engineering, Physics, and Neuroscience / Emil Simiu. |
title_full_unstemmed |
Chaotic Transitions in Deterministic and Stochastic Dynamical Systems : Applications of Melnikov Processes in Engineering, Physics, and Neuroscience / Emil Simiu. |
title_auth |
Chaotic Transitions in Deterministic and Stochastic Dynamical Systems : Applications of Melnikov Processes in Engineering, Physics, and Neuroscience / |
title_alt |
Frontmatter -- Contents -- Preface -- Chapter 1. Introduction -- PART 1. FUNDAMENTALS -- Chapter 2. Transitions in Deterministic Systems and the Melnikov Function -- Chapter 3. Chaos in Deterministic Systems and the Melnikov Function -- Chapter 4. Stochastic Processes -- Chapter 5. Chaotic Transitions in Stochastic Dynamical Systems and the Melnikov Process -- PART 2. APPLICATIONS -- Chapter 6. Vessel Capsizing -- Chapter 7. Open-Loop Control of Escapes in Stochastically Excited Systems -- Chapter 8. Stochastic Resonance -- Chapter 9. Cutoff Frequency of Experimentally Generated Noise for a First-Order Dynamical System -- Chapter 10. Snap-Through of Transversely Excited Buckled Column -- Chapter 11. Wind-Induced Along-Shore Currents over a Corrugated Ocean Floor -- Chapter 12. The Auditory Nerve Fiber as a Chaotic Dynamical System -- Appendix A1 Derivation of Expression for the Melnikov Function -- Appendix A2 Construction of Phase Space Slice through Stable and Unstable Manifolds -- Appendix A3 Topological Conjugacy -- Appendix A4 Properties of Space ∑2 -- Appendix A5 Elements of Probability Theory -- Appendix A6 Mean Upcrossing Rate τu-1 for Gaussian Processes -- Appendix A7 Mean Escape Rate τ∊-1 for Systems Excited by White Noise -- References -- Index |
title_new |
Chaotic Transitions in Deterministic and Stochastic Dynamical Systems : |
title_sort |
chaotic transitions in deterministic and stochastic dynamical systems : applications of melnikov processes in engineering, physics, and neuroscience / |
series |
Princeton Series in Applied Mathematics ; |
series2 |
Princeton Series in Applied Mathematics ; |
publisher |
Princeton University Press, |
publishDate |
2014 |
physical |
1 online resource (240 p.) : 94 line illus. Issued also in print. |
contents |
Frontmatter -- Contents -- Preface -- Chapter 1. Introduction -- PART 1. FUNDAMENTALS -- Chapter 2. Transitions in Deterministic Systems and the Melnikov Function -- Chapter 3. Chaos in Deterministic Systems and the Melnikov Function -- Chapter 4. Stochastic Processes -- Chapter 5. Chaotic Transitions in Stochastic Dynamical Systems and the Melnikov Process -- PART 2. APPLICATIONS -- Chapter 6. Vessel Capsizing -- Chapter 7. Open-Loop Control of Escapes in Stochastically Excited Systems -- Chapter 8. Stochastic Resonance -- Chapter 9. Cutoff Frequency of Experimentally Generated Noise for a First-Order Dynamical System -- Chapter 10. Snap-Through of Transversely Excited Buckled Column -- Chapter 11. Wind-Induced Along-Shore Currents over a Corrugated Ocean Floor -- Chapter 12. The Auditory Nerve Fiber as a Chaotic Dynamical System -- Appendix A1 Derivation of Expression for the Melnikov Function -- Appendix A2 Construction of Phase Space Slice through Stable and Unstable Manifolds -- Appendix A3 Topological Conjugacy -- Appendix A4 Properties of Space ∑2 -- Appendix A5 Elements of Probability Theory -- Appendix A6 Mean Upcrossing Rate τu-1 for Gaussian Processes -- Appendix A7 Mean Escape Rate τ∊-1 for Systems Excited by White Noise -- References -- Index |
isbn |
9781400832507 9783110515831 9783110442502 9780691144344 |
callnumber-first |
Q - Science |
callnumber-subject |
QA - Mathematics |
callnumber-label |
QA614 |
callnumber-sort |
QA 3614.8 S55 42014 |
url |
https://doi.org/10.1515/9781400832507 https://www.degruyter.com/isbn/9781400832507 https://www.degruyter.com/document/cover/isbn/9781400832507/original |
illustrated |
Illustrated |
dewey-hundreds |
500 - Science |
dewey-tens |
510 - Mathematics |
dewey-ones |
515 - Analysis |
dewey-full |
515.352 |
dewey-sort |
3515.352 |
dewey-raw |
515.352 |
dewey-search |
515.352 |
doi_str_mv |
10.1515/9781400832507 |
oclc_num |
891400514 |
work_keys_str_mv |
AT simiuemil chaotictransitionsindeterministicandstochasticdynamicalsystemsapplicationsofmelnikovprocessesinengineeringphysicsandneuroscience |
status_str |
n |
ids_txt_mv |
(DE-B1597)447398 (OCoLC)891400514 |
carrierType_str_mv |
cr |
hierarchy_parent_title |
Title is part of eBook package: De Gruyter Princeton Series in Applied Mathematics eBook-Package Title is part of eBook package: De Gruyter Princeton University Press eBook-Package Backlist 2000-2013 |
is_hierarchy_title |
Chaotic Transitions in Deterministic and Stochastic Dynamical Systems : Applications of Melnikov Processes in Engineering, Physics, and Neuroscience / |
container_title |
Title is part of eBook package: De Gruyter Princeton Series in Applied Mathematics eBook-Package |
_version_ |
1770176644974116864 |
fullrecord |
<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>09081nam a22019455i 4500</leader><controlfield tag="001">9781400832507</controlfield><controlfield tag="003">DE-B1597</controlfield><controlfield tag="005">20220131112047.0</controlfield><controlfield tag="006">m|||||o||d||||||||</controlfield><controlfield tag="007">cr || ||||||||</controlfield><controlfield tag="008">220131t20142002nju fo d z eng d</controlfield><datafield tag="019" ind1=" " ind2=" "><subfield code="a">(OCoLC)979745250</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781400832507</subfield></datafield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1515/9781400832507</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-B1597)447398</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)891400514</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-B1597</subfield><subfield code="b">eng</subfield><subfield code="c">DE-B1597</subfield><subfield code="e">rda</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="044" ind1=" " ind2=" "><subfield code="a">nju</subfield><subfield code="c">US-NJ</subfield></datafield><datafield tag="050" ind1=" " ind2="4"><subfield code="a">QA614.8 .S55 2014</subfield></datafield><datafield tag="072" ind1=" " ind2="7"><subfield code="a">MAT003000</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">515.352</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Simiu, Emil, </subfield><subfield code="e">author.</subfield><subfield code="4">aut</subfield><subfield code="4">http://id.loc.gov/vocabulary/relators/aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Chaotic Transitions in Deterministic and Stochastic Dynamical Systems :</subfield><subfield code="b">Applications of Melnikov Processes in Engineering, Physics, and Neuroscience /</subfield><subfield code="c">Emil Simiu.</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Princeton, NJ : </subfield><subfield code="b">Princeton University Press, </subfield><subfield code="c">[2014]</subfield></datafield><datafield tag="264" ind1=" " ind2="4"><subfield code="c">©2002</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 online resource (240 p.) :</subfield><subfield code="b">94 line illus.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">computer</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">online resource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="347" ind1=" " ind2=" "><subfield code="a">text file</subfield><subfield code="b">PDF</subfield><subfield code="2">rda</subfield></datafield><datafield tag="490" ind1="0" ind2=" "><subfield code="a">Princeton Series in Applied Mathematics ;</subfield><subfield code="v">51</subfield></datafield><datafield tag="505" ind1="0" ind2="0"><subfield code="t">Frontmatter -- </subfield><subfield code="t">Contents -- </subfield><subfield code="t">Preface -- </subfield><subfield code="t">Chapter 1. Introduction -- </subfield><subfield code="t">PART 1. FUNDAMENTALS -- </subfield><subfield code="t">Chapter 2. Transitions in Deterministic Systems and the Melnikov Function -- </subfield><subfield code="t">Chapter 3. Chaos in Deterministic Systems and the Melnikov Function -- </subfield><subfield code="t">Chapter 4. Stochastic Processes -- </subfield><subfield code="t">Chapter 5. Chaotic Transitions in Stochastic Dynamical Systems and the Melnikov Process -- </subfield><subfield code="t">PART 2. APPLICATIONS -- </subfield><subfield code="t">Chapter 6. Vessel Capsizing -- </subfield><subfield code="t">Chapter 7. Open-Loop Control of Escapes in Stochastically Excited Systems -- </subfield><subfield code="t">Chapter 8. Stochastic Resonance -- </subfield><subfield code="t">Chapter 9. Cutoff Frequency of Experimentally Generated Noise for a First-Order Dynamical System -- </subfield><subfield code="t">Chapter 10. Snap-Through of Transversely Excited Buckled Column -- </subfield><subfield code="t">Chapter 11. Wind-Induced Along-Shore Currents over a Corrugated Ocean Floor -- </subfield><subfield code="t">Chapter 12. The Auditory Nerve Fiber as a Chaotic Dynamical System -- </subfield><subfield code="t">Appendix A1 Derivation of Expression for the Melnikov Function -- </subfield><subfield code="t">Appendix A2 Construction of Phase Space Slice through Stable and Unstable Manifolds -- </subfield><subfield code="t">Appendix A3 Topological Conjugacy -- </subfield><subfield code="t">Appendix A4 Properties of Space ∑2 -- </subfield><subfield code="t">Appendix A5 Elements of Probability Theory -- </subfield><subfield code="t">Appendix A6 Mean Upcrossing Rate τu-1 for Gaussian Processes -- </subfield><subfield code="t">Appendix A7 Mean Escape Rate τ∊-1 for Systems Excited by White Noise -- </subfield><subfield code="t">References -- </subfield><subfield code="t">Index</subfield></datafield><datafield tag="506" ind1="0" ind2=" "><subfield code="a">restricted access</subfield><subfield code="u">http://purl.org/coar/access_right/c_16ec</subfield><subfield code="f">online access with authorization</subfield><subfield code="2">star</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">The classical Melnikov method provides information on the behavior of deterministic planar systems that may exhibit transitions, i.e. escapes from and captures into preferred regions of phase space. This book develops a unified treatment of deterministic and stochastic systems that extends the applicability of the Melnikov method to physically realizable stochastic planar systems with additive, state-dependent, white, colored, or dichotomous noise. The extended Melnikov method yields the novel result that motions with transitions are chaotic regardless of whether the excitation is deterministic or stochastic. It explains the role in the occurrence of transitions of the characteristics of the system and its deterministic or stochastic excitation, and is a powerful modeling and identification tool. The book is designed primarily for readers interested in applications. The level of preparation required corresponds to the equivalent of a first-year graduate course in applied mathematics. No previous exposure to dynamical systems theory or the theory of stochastic processes is required. The theoretical prerequisites and developments are presented in the first part of the book. The second part of the book is devoted to applications, ranging from physics to mechanical engineering, naval architecture, oceanography, nonlinear control, stochastic resonance, and neurophysiology.</subfield></datafield><datafield tag="530" ind1=" " ind2=" "><subfield code="a">Issued also in print.</subfield></datafield><datafield tag="538" ind1=" " ind2=" "><subfield code="a">Mode of access: Internet via World Wide Web.</subfield></datafield><datafield tag="546" ind1=" " ind2=" "><subfield code="a">In English.</subfield></datafield><datafield tag="588" ind1="0" ind2=" "><subfield code="a">Description based on online resource; title from PDF title page (publisher's Web site, viewed 31. Jan 2022)</subfield></datafield><datafield tag="650" ind1=" " ind2="0"><subfield code="a">Chaotic behavior in systems.</subfield></datafield><datafield tag="650" ind1=" " ind2="0"><subfield code="a">Differentiable dynamical systems.</subfield></datafield><datafield tag="650" ind1=" " ind2="0"><subfield code="a">Stochastic systems.</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">MATHEMATICS / Applied.</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Affine transformation.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Amplitude.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Arbitrarily large.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Attractor.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Autocovariance.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Big O notation.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Central limit theorem.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Change of variables.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Chaos theory.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Coefficient of variation.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Compound Probability.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Computational problem.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Control theory.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Convolution.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Coriolis force.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Correlation coefficient.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Covariance function.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Cross-covariance.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Cumulative distribution function.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Cutoff frequency.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Deformation (mechanics).</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Derivative.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Deterministic system.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Diagram (category theory).</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Diffeomorphism.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Differential equation.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Dirac delta function.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Discriminant.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Dissipation.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Dissipative system.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Dynamical system.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Eigenvalues and eigenvectors.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Equations of motion.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Even and odd functions.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Excitation (magnetic).</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Exponential decay.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Extreme value theory.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Flow velocity.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Fluid dynamics.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Forcing (recursion theory).</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Fourier series.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Fourier transform.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Fractal dimension.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Frequency domain.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Gaussian noise.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Gaussian process.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Harmonic analysis.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Harmonic function.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Heteroclinic orbit.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Homeomorphism.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Homoclinic orbit.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Hyperbolic point.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Inference.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Initial condition.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Instability.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Integrable system.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Invariant manifold.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Iteration.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Joint probability distribution.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">LTI system theory.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Limit cycle.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Linear differential equation.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Logistic map.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Marginal distribution.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Moduli (physics).</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Multiplicative noise.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Noise (electronics).</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Nonlinear control.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Nonlinear system.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Ornstein-Uhlenbeck process.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Oscillation.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Parameter space.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Parameter.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Partial differential equation.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Perturbation function.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Phase plane.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Phase space.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Poisson distribution.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Probability density function.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Probability distribution.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Probability theory.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Probability.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Production-possibility frontier.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Relative velocity.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Scale factor.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Shear stress.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Spectral density.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Spectral gap.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Standard deviation.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Stochastic process.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Stochastic resonance.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Stochastic.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Stream function.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Surface stress.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Symbolic dynamics.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">The Signal and the Noise.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Topological conjugacy.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Transfer function.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Variance.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Vorticity.</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Title is part of eBook package:</subfield><subfield code="d">De Gruyter</subfield><subfield code="t">Princeton Series in Applied Mathematics eBook-Package</subfield><subfield code="z">9783110515831</subfield><subfield code="o">ZDB-23-PAM</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Title is part of eBook package:</subfield><subfield code="d">De Gruyter</subfield><subfield code="t">Princeton University Press eBook-Package Backlist 2000-2013</subfield><subfield code="z">9783110442502</subfield></datafield><datafield tag="776" ind1="0" ind2=" "><subfield code="c">print</subfield><subfield code="z">9780691144344</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1515/9781400832507</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://www.degruyter.com/isbn/9781400832507</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="3">Cover</subfield><subfield code="u">https://www.degruyter.com/document/cover/isbn/9781400832507/original</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">978-3-11-044250-2 Princeton University Press eBook-Package Backlist 2000-2013</subfield><subfield code="c">2000</subfield><subfield code="d">2013</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">EBA_BACKALL</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">EBA_CL_MTPY</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">EBA_EBACKALL</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">EBA_EBKALL</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">EBA_ECL_MTPY</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">EBA_EEBKALL</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">EBA_ESTMALL</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">EBA_PPALL</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">EBA_STMALL</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV-deGruyter-alles</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">PDA12STME</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">PDA13ENGE</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">PDA18STMEE</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">PDA5EBK</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-23-PAM</subfield></datafield></record></collection> |