Chaos in Systems with Noise

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World Scientific, 1990 - Science - 232 pages
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As in the first edition, the influence of random noise on the chaotic behavior of dissipative dynamical systems is investigated. Problems are illustrated by mechanical examples. This revised and updated edition contains new sections on the summary of probability theory, homoclinic chaos, Melnikov method, routes to chaos, stabilization of period-doubling, and Hopf bifurcation by noise. Some chapters have been rewritten and new examples have been added.
 

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Contents

Preface to the second edition
1
Chaotic and Stochastic Processes
19
Noisy Dynamical Systems
25
FokkerPlanckKolmogorov Equation
33
MultiMaxima Probability Density Functions
42
Random Lyapunov Exponents
53
Poincare Maps for Noisy Systems
65
Regular and Chaotic Stochastic Processes
76
Stochastic Sensitivity Functions and Chaos
95
Examples
117
Mechanical Machine
135
Noisy Routes to Chaos
154
References
219
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Page ix - Assume that we are tossing a fair coin three times. The possible outcomes of this experiment are HHH, HHT. HTH, THH. HTT, THT, TTH and TTT , where H denotes heads and T denotes tails. Each possible outcome of the experiment is called an elementary event. Thus, there are eight elementary events and it is by definition that the probability of obtaining for example HHT is 1/8, but we cannot obtain HHT repeatedly. Each event H or T occurs 'at random...

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