Hidden attractors: A new chaotic system without equilibria
Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata 700108, India
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Received in final form: 10 November 2019
Published online: 26 March 2020
Localization of hidden attractors is one of the most challenging tasks in the nonlinear dynamics due to deficiency of properly justified analytical and numerical procedures. But understanding about the emergence of such unexpected occurrence of hidden attractors is desirable, because that can help to diminish the unexpected switch from one attractor to another undesired behavior. We propose a novel autonomous three-dimensional system exhibiting hidden attractor. These attractors can not be tracked using perpetual points. The reason behind this inefficiency is explained using theory of differential equations. Our system consists a slow manifold depicted through the time-series, although the system has no equilibrium points or such multiplicative parameters. We also discuss the behavior of the attractor using time-series analysis, bifurcation theory, Lyapunov spectrum and Kaplan-Yorke dimension. Moreover, the attractor no longer exists for a range of parameter values due to sudden change of strange attractors indicating a possible inverse crisis route to chaos.
© EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature, 2020