Abstract
A new five-dimensional chaotic system with extreme multi-stability is introduced in this article. The mathematical model is established, and numerical simulations are done. This dynamical system complicates incident of extreme multi-stability. Most significantly, relied on the mathematical model, the recently proposed system has a curve of equilibria that ends in the occurrence of hidden attractors. We examine the initial-condition-dependent dynamics of this system. We inspect that there is an unrestricted number of coexistent attractors, which signifies the occurrence of extreme multi-stability strictly. In addition, the extreme multi-stability according to initial condition is investigated consuming the Lyapunov exponent spectra and bifurcation diagrams. The existence of coexisting infinitely many attractors is displayed with phase portraits. In the end, we calculate and debate Kolmogorov–Sinai entropy in the chaotic system. We direct trying the Kolmogorov–Sinai technique of entropic inspection for the dynamics of the system.
Highlights
Investigation of chaotic systems has been a hot topic.[1]
The results prove that the long-term dynamical behaviors related to different initial conditions result in the existence of extreme multi-stability of the system (1)
The impression of the Kolmogorov–Sinai entropy (KSE) was deliberated by Kolmogorov in 1958 for the first time on the troubles emerging from the dimension of functional spaces and information theory, that evaluates the hesitancy of the dynamical systems.[29,30]
Summary
Investigation of chaotic systems has been a hot topic.[1]. Many studies have been conducted on designing new chaotic attractors.[2]. Keywords Infinitely many attractor, extreme multi-stability, hidden attractors, curve equilibrium, Kolmogorov–Sinai entropy
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