Generalizations of the concept of marginal synchronization of chaos |
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| Affiliation: | 1. Department of Mathematics, Addis Ababa University, Addis Ababa, Ethiopia;2. Department of Mathematics and Applications, University of Naples Federico II, via Cintia, I-80126 Naples, Italy;3. Department of Mathematics and Geosciences, University of Trieste, via A. Valerio, 12, I-34127 Trieste, Italy;4. Department of Mathematics and Statistics, Strathclyde University, Glasgow, Scotland, UK;1. Laboratory for Rheology and Fluid Dynamics, Universidad de Chile, Beauchef 850, Santiago 8370448, Chile;2. Centre for Biotechnology and Bioengineering, Universidad de Chile, Beauchef 851, Santiago 8370448, Chile;3. Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, CA 91125, USA;4. Department of Chemical Engineering, Biotechnology and Materials, Universidad de Chile, Beauchef 851, Santiago 8370448, Chile |
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| Abstract: | Generalizations of the concept of marginal synchronization between chaotic systems, i.e. synchronization with zero largest conditional Lyapunov exponent, are considered. Generalized marginal synchronization in drive–response systems is defined, for which the function between points of attractors of different systems is given up to a constant. Auxiliary system approach is shown to be able to detect this synchronization. Marginal synchronization in mutually coupled systems which can be viewed as drive–response systems with the response system influencing the drive system dynamics is also considered, and an example from solid-state physics is analyzed. Stability of these kinds of synchronization against changes of system parameters and noise is investigated. In drive–response systems generalized marginal synchronization is shown to be rather sensitive to the changes of parameters and may disappear either due to the loss of stability of the response system, or as a result of the blowout bifurcation. Nonlinear coupling of the drive system to the response system can stabilize marginal synchronization. |
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