Abstract
Chaotic systems with hidden attractors, infinite number of equilibrium points and different closed curve equilibrium have received much attention in the past six years. In this work, we introduce a new family of chaotic systems with different closed curve equilibrium. Using the methods of equilibrium points, phase portraits, maximal Lyapunov exponents, Kaplan–Yorke dimension, and eigenvalues, we analyze the dynamical properties of the proposed systems and extend the general knowledge of such systems.
Highlights
Over the past fifty years, investigating chaotic systems has attracted many researchers’ attention.Generating chaotic attractors may help one to understand the dynamics of the real system
The authors present a family of chaotic systems with different closed curve equilibriums, being the promotion of published papers, which may extend the general knowledge of such systems
The main goal of the current study is to propose a novel and more general family of chaotic systems with different curve equilibriums located on a quadrangle, a circle or other general cases
Summary
Over the past fifty years, investigating chaotic systems has attracted many researchers’ attention. The authors present a family of chaotic systems with different closed curve equilibriums, being the promotion of published papers, which may extend the general knowledge of such systems. Motivated by the works mentioned above, in this paper, we introduce and investigate a new family of chaotic systems with different closed curve equilibriums. Model (4) was studied by Gotthans and Petržela in [15] and has shown that there exists some chaotic system with a circle of equilibrium points as ( x, y, 0) : x2 + y2 = 1. The aim of this study is to introduce a new family of chaotic systems generating hidden attractors with differently shaped equilibrium points, containing systems (4) and (5) as two particular cases, being the generalization of the existing results, and to broaden the views on the hidden attractors.
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