Abstract
The study of the parameter space of chaotic systems is complicated by its high dimensionality (multi-parametricability). Two approaches to the study of chaotic systems are presented: multi-parameter analysis and optimal suppression of chaotic dynamics. For non-autonomous chaotic systems, this is the way to compare the effectiveness of various correction parameters that provide optimal removal of irregular dynamics. For the class of autonomous chaotic systems, this is the way to investigate the optimal conditions of super-stable behavior for the chaotic system.
Highlights
A rather wide class of dynamic systems that demonstrate chaotic behavior is mathematically described by the systems of non-linear autonomous and non-autonomous differential equations [1,2,3]
We present the results of a two-parametrical analysis of optimal chaotic dynamics suppression in dissipative nonlinear oscillators
Two results presented in the paper illustrate the effectiveness of implementation of multi-parametrical analysis for the peculiarities of chaos dynamics suppression
Summary
A rather wide class of dynamic systems that demonstrate chaotic behavior is mathematically described by the systems of non-linear autonomous and non-autonomous differential equations [1,2,3]. A clear insight into the mechanisms of chaotic dynamics appearance (disappearance) is possible only through multi-parameter analysis of the system. It is shown in [4] that multi-parameter generalization of classical stability methods of non-linear systems is efficient. This approach is based on the studies of the peculiarities of boundaries of stability and instability areas of the system’s linearized equations. We show two approaches to multi-parameter analysis of non-autonomous (dissipative nonlinear oscillators) and autonomous (Lorenz-like) chaotic systems. Among other non-autonomous chaos models this oscillator is knows as a paradigmatic one, as it clearly demonstrates principal characteristics of a wide class of nonlinear dissipative oscillators
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