LEADER 08397nam 2201885 450 001 9910786748903321 005 20200520144314.0 010 $a0-691-05094-5 010 $a1-4008-3250-0 024 7 $a10.1515/9781400832507 035 $a(CKB)3710000000222321 035 $a(EBL)1756199 035 $a(OCoLC)888348995 035 $a(SSID)ssj0001385064 035 $a(PQKBManifestationID)12615837 035 $a(PQKBTitleCode)TC0001385064 035 $a(PQKBWorkID)11339225 035 $a(PQKB)10218695 035 $a(DE-B1597)447398 035 $a(OCoLC)891400514 035 $a(OCoLC)979745250 035 $a(DE-B1597)9781400832507 035 $a(Au-PeEL)EBL1756199 035 $a(CaPaEBR)ebr10910135 035 $a(CaONFJC)MIL637577 035 $a(MiAaPQ)EBC1756199 035 $a(EXLCZ)993710000000222321 100 $a20140829h20022002 uy 0 101 0 $aeng 135 $aur|nu---|u||u 181 $ctxt 182 $cc 183 $acr 200 10$aChaotic transitions in deterministic and stochastic dynamical systems $eapplications of Melnikov processes in engineering, physics, and neuroscience /$fEmil Simiu 210 1$aPrinceton, New Jersey :$cPrinceton University Press,$d2002. 210 4$dİ2002 215 $a1 online resource (244 p.) 225 1 $aPrinceton Series in Applied Mathematics 300 $aDescription based upon print version of record. 311 $a1-322-06326-5 311 $a0-691-14434-6 320 $aIncludes bibliographical references and index. 327 $tFront matter --$tContents --$tPreface --$tChapter 1. Introduction --$tPART 1. FUNDAMENTALS --$tChapter 2. Transitions in Deterministic Systems and the Melnikov Function --$tChapter 3. Chaos in Deterministic Systems and the Melnikov Function --$tChapter 4. Stochastic Processes --$tChapter 5. Chaotic Transitions in Stochastic Dynamical Systems and the Melnikov Process --$tPART 2. APPLICATIONS --$tChapter 6. Vessel Capsizing --$tChapter 7. Open-Loop Control of Escapes in Stochastically Excited Systems --$tChapter 8. Stochastic Resonance --$tChapter 9. Cutoff Frequency of Experimentally Generated Noise for a First-Order Dynamical System --$tChapter 10. Snap-Through of Transversely Excited Buckled Column --$tChapter 11. Wind-Induced Along-Shore Currents over a Corrugated Ocean Floor --$tChapter 12. The Auditory Nerve Fiber as a Chaotic Dynamical System --$tAppendix A1 Derivation of Expression for the Melnikov Function --$tAppendix A2 Construction of Phase Space Slice through Stable and Unstable Manifolds --$tAppendix A3 Topological Conjugacy --$tAppendix A4 Properties of Space ?2 --$tAppendix A5 Elements of Probability Theory --$tAppendix A6 Mean Upcrossing Rate ?u-1 for Gaussian Processes --$tAppendix A7 Mean Escape Rate ??-1 for Systems Excited by White Noise --$tReferences --$tIndex 330 $aThe classical Melnikov method provides information on the behavior of deterministic planar systems that may exhibit transitions, i.e. escapes from and captures into preferred regions of phase space. This book develops a unified treatment of deterministic and stochastic systems that extends the applicability of the Melnikov method to physically realizable stochastic planar systems with additive, state-dependent, white, colored, or dichotomous noise. The extended Melnikov method yields the novel result that motions with transitions are chaotic regardless of whether the excitation is deterministic or stochastic. It explains the role in the occurrence of transitions of the characteristics of the system and its deterministic or stochastic excitation, and is a powerful modeling and identification tool. The book is designed primarily for readers interested in applications. The level of preparation required corresponds to the equivalent of a first-year graduate course in applied mathematics. No previous exposure to dynamical systems theory or the theory of stochastic processes is required. The theoretical prerequisites and developments are presented in the first part of the book. The second part of the book is devoted to applications, ranging from physics to mechanical engineering, naval architecture, oceanography, nonlinear control, stochastic resonance, and neurophysiology. 410 0$aPrinceton series in applied mathematics. 606 $aDifferentiable dynamical systems 606 $aChaotic behavior in systems 606 $aStochastic systems 610 $aAffine transformation. 610 $aAmplitude. 610 $aArbitrarily large. 610 $aAttractor. 610 $aAutocovariance. 610 $aBig O notation. 610 $aCentral limit theorem. 610 $aChange of variables. 610 $aChaos theory. 610 $aCoefficient of variation. 610 $aCompound Probability. 610 $aComputational problem. 610 $aControl theory. 610 $aConvolution. 610 $aCoriolis force. 610 $aCorrelation coefficient. 610 $aCovariance function. 610 $aCross-covariance. 610 $aCumulative distribution function. 610 $aCutoff frequency. 610 $aDeformation (mechanics). 610 $aDerivative. 610 $aDeterministic system. 610 $aDiagram (category theory). 610 $aDiffeomorphism. 610 $aDifferential equation. 610 $aDirac delta function. 610 $aDiscriminant. 610 $aDissipation. 610 $aDissipative system. 610 $aDynamical system. 610 $aEigenvalues and eigenvectors. 610 $aEquations of motion. 610 $aEven and odd functions. 610 $aExcitation (magnetic). 610 $aExponential decay. 610 $aExtreme value theory. 610 $aFlow velocity. 610 $aFluid dynamics. 610 $aForcing (recursion theory). 610 $aFourier series. 610 $aFourier transform. 610 $aFractal dimension. 610 $aFrequency domain. 610 $aGaussian noise. 610 $aGaussian process. 610 $aHarmonic analysis. 610 $aHarmonic function. 610 $aHeteroclinic orbit. 610 $aHomeomorphism. 610 $aHomoclinic orbit. 610 $aHyperbolic point. 610 $aInference. 610 $aInitial condition. 610 $aInstability. 610 $aIntegrable system. 610 $aInvariant manifold. 610 $aIteration. 610 $aJoint probability distribution. 610 $aLTI system theory. 610 $aLimit cycle. 610 $aLinear differential equation. 610 $aLogistic map. 610 $aMarginal distribution. 610 $aModuli (physics). 610 $aMultiplicative noise. 610 $aNoise (electronics). 610 $aNonlinear control. 610 $aNonlinear system. 610 $aOrnstein?Uhlenbeck process. 610 $aOscillation. 610 $aParameter space. 610 $aParameter. 610 $aPartial differential equation. 610 $aPerturbation function. 610 $aPhase plane. 610 $aPhase space. 610 $aPoisson distribution. 610 $aProbability density function. 610 $aProbability distribution. 610 $aProbability theory. 610 $aProbability. 610 $aProduction?possibility frontier. 610 $aRelative velocity. 610 $aScale factor. 610 $aShear stress. 610 $aSpectral density. 610 $aSpectral gap. 610 $aStandard deviation. 610 $aStochastic process. 610 $aStochastic resonance. 610 $aStochastic. 610 $aStream function. 610 $aSurface stress. 610 $aSymbolic dynamics. 610 $aThe Signal and the Noise. 610 $aTopological conjugacy. 610 $aTransfer function. 610 $aVariance. 610 $aVorticity. 615 0$aDifferentiable dynamical systems. 615 0$aChaotic behavior in systems. 615 0$aStochastic systems. 676 $a515/.352 700 $aSimiu$b Emil$043582 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910786748903321 996 $aChaotic transitions in deterministic and stochastic dynamical systems$91427554 997 $aUNINA