Abstract
Discovering systems with hidden attractors is a challenging topic which has received considerable interest of the scientific community recently. This work introduces a new chaotic system having hidden chaotic attractors with an infinite number of equilibrium points. We have studied dynamical properties of such special system via equilibrium analysis, bifurcation diagram, and maximal Lyapunov exponents. In order to confirm the system’s chaotic behavior, the findings of topological horseshoes for the system are presented. In addition, the possibility of synchronization of two new chaotic systems with infinite equilibria is investigated by using adaptive control.
Highlights
Nonlinear systems with chaotic behavior have been exploited since the 1960s [1,2,3,4]
A new chaotic system with a curve of equilibria has been introduced in this work
Because of having an infinite number of equilibrium points, the system is a special system with hidden attractors, which is rarely reported in the literature
Summary
Nonlinear systems with chaotic behavior have been exploited since the 1960s [1,2,3,4]. The community has raised some concerns about discovering hidden attractors in known systems [27, 28], finding new systems with hidden attractors [29, 30], studying synchronization schemes for systems with hidden attractors [31], or verifying chaotic dynamics in systems with hidden attractors with topological horseshoes [32, 33]. Motivated by special features of systems with hidden attractors, we introduce a new system with an open curve of equilibrium points in this work. The model of the new system is described and its dynamics are discovered through different nonlinear tools.
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