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Dynamical Chaos

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Nonlinear Dynamics of Chaotic and Stochastic Systems

Part of the book series: Springer Series in Synergetics ((SSSYN))

Abstract

A dynamical system (DS) displays its nonlinear properties in different ways with variation of system control parameters. An increase in the influence of nonlinearity causes the dynamical regime to become complicated. Simple attractors in the phase space of a dissipative system are replaced by more complicated ones. Under certain conditions, nonlinearity can lead to the onset of dynamical chaos. Moving along a relevant direction in parameter space, one can observe a set of bifurcations resulting in the appearance of a chaotic attractor. Such typical bifurcation sequences are called the bifurcation mechanisms, or the scenarios of the transition to chaos.

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Authors and Affiliations

  1. Faculty of Physics, Saratov State University, Astrakhanskaya ul. 83, 410026, Saratov, Russia

    Professor Vadim S. Anishchenko Dr., Professor Vladimir Astakhov Dr. & Professor Tatjana Vadivasova Dr.

  2. Center for Neurodynamics, University of Missouri at St. Louis, 8001 Natural Bridge Road, 63121, St. Louis, MO, USA

    Professor Alexander Neiman Dr.

  3. Institut Physik LS Stochastische Prozesse, Humboldt-Universität Berlin, Newtonstr. 15, 12489, Berlin, Germany

    Professor Lutz Schimansky-Geier Dr.

Authors
  1. Professor Vadim S. Anishchenko Dr.
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  2. Professor Vladimir Astakhov Dr.
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  3. Professor Tatjana Vadivasova Dr.
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  4. Professor Alexander Neiman Dr.
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  5. Professor Lutz Schimansky-Geier Dr.
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Anishchenko, V.S., Astakhov, V., Vadivasova, T., Neiman, A., Schimansky-Geier, L. (2007). Dynamical Chaos. In: Nonlinear Dynamics of Chaotic and Stochastic Systems. Springer Series in Synergetics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-38168-6_2

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