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Chaotic and non-chaotic strange attractors of a class of non-autonomous systems. (English) Zbl 1390.34164
Summary: In this paper, the dynamics of a class of non-autonomous systems, generated from a unified chaotic autonomous system, is studied. It is found, via parameter modulation, that they have chaotic and non-chaotic strange attractors (NCSA). Several representative systems are constructed to illustrate the complex strange dynamics. The first example exhibits Lorenz-like behavior and Chen-like behavior at different time intervals. The second illustrates the existence of NCSA, which is constructed by “joining” the chaotic Chen system and a system with regular dynamics. The third is constructed based on the topological structure of the original autonomous systems, which has complex transient dynamics at the beginning, with a periodic orbit as the omega-limit set. The last one has quasi-periodic coefficients, yielding strange dynamics. These examples demonstrate that non-autonomous systems can have extremely rich and interesting dynamics under certain conditions.{
©2018 American Institute of Physics}

MSC:
34C60 Qualitative investigation and simulation of ordinary differential equation models
37C60 Nonautonomous smooth dynamical systems
34C28 Complex behavior and chaotic systems of ordinary differential equations
34D45 Attractors of solutions to ordinary differential equations
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
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