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A new megastable nonlinear oscillator with infinite attractors. (English) Zbl 1483.37047

Summary: Dynamical systems with megastable properties are very rare in the literature. In this paper, we introduce a new two-dimensional megastable dynamical system with a line of equilibria, having an infinite number of stable states. By modifying this new system with temporally-periodic forcing term, a new two-dimensional non-autonomous nonlinear oscillator capable to generate an infinite number of coexisting limit cycle attractors, torus attractors and, strange attractors is constructed. The analog implementation of the new megastable oscillator is investigated to further support numerical analyses and henceforth validate the mathematical model.

MSC:

37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
34C28 Complex behavior and chaotic systems of ordinary differential equations
34D45 Attractors of solutions to ordinary differential equations
34C60 Qualitative investigation and simulation of ordinary differential equation models
34C23 Bifurcation theory for ordinary differential equations
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