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Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields
01 Aug 1983-
TL;DR: In this article, the authors introduce differential equations and dynamical systems, including hyperbolic sets, Sympolic Dynamics, and Strange Attractors, and global bifurcations.
Abstract: Contents: Introduction: Differential Equations and Dynamical Systems.- An Introduction to Chaos: Four Examples.- Local Bifurcations.- Averaging and Perturbation from a Geometric Viewpoint.- Hyperbolic Sets, Sympolic Dynamics, and Strange Attractors.- Global Bifurcations.- Local Codimension Two Bifurcations of Flows.- Appendix: Suggestions for Further Reading. Postscript Added at Second Printing. Glossary. References. Index.
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TL;DR: Synchronization of chaos refers to a process where two chaotic systems adjust a given property of their motion to a common behavior due to a coupling or to a forcing (periodical or noisy) as discussed by the authors.
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2,116 citations
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Cites background from "Nonlinear Oscillations, Dynamical S..."
...…exponents, ordered as j 1 5j 2 525j n , each measuring the average expansion or contraction along an orbit in the different directions; for a formal definition of LCEs and theoretical background, see, e.g. Eckmann and Ruelle (1985), Guckenheimer and Holmes (1983), (pp. 283—288) or Brock (1986)....
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...General references on nonlinear dynamics and chaos are, e.g. Guckenheimer and Holmes (1983) and Arrowsmith and Place (1990); economic applications of 2- and 3-...
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