Chaotic Transitions in Deterministic and Stochastic Dynamical Systems
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A01=Emil Simiu
Amplitude
Arbitrarily large
Attractor
Author_Emil Simiu
Autocovariance
Category=PBW
Central limit theorem
Change of variables
Chaos theory
Coefficient of variation
Computational problem
Convolution
Correlation coefficient
Covariance function
Cross-covariance
Cutoff frequency
Derivative
Deterministic system
Diffeomorphism
Dirac delta function
Discriminant
Dissipation
Dissipative system
Dynamical system
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
Equations of motion
Even and odd functions
Excitation (magnetic)
Extreme value theory
Flow velocity
Fluid dynamics
Forcing (recursion theory)
Fractal dimension
Gaussian noise
Gaussian process
Harmonic analysis
Heteroclinic orbit
Homeomorphism
Homoclinic orbit
Hyperbolic point
Initial condition
Instability
Integrable system
Joint probability distribution
Limit cycle
Linear differential equation
Multiplicative noise
Nonlinear control
Nonlinear system
Oscillation
Parameter
Perturbation function
Phase plane
Phase space
Probability
Probability density function
Probability distribution
Production-possibility frontier
Relative velocity
Scale factor
Shear stress
Spectral density
Spectral gap
Standard deviation
Stochastic
Stochastic process
Stochastic resonance
Surface stress
Symbolic dynamics
The Signal and the Noise
Transfer function
Variance
Vorticity
Product details
- ISBN 9780691144344
- Weight: 340g
- Dimensions: 152 x 235mm
- Publication Date: 28 Jun 2009
- Publisher: Princeton University Press
- Publication City/Country: US
- Product Form: Paperback
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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.
Emil Simiu is a NIST Fellow, National Institute of Standards and Technology, and Research Professor, Whiting School of Engineering, The Johns Hopkins University. A specialist in flow-structure interaction, he is the coauthor of "Wind Effects on Structures" and was the 1984 recipient of the Federal Engineer of the Year award.
