Chaos and complexity in a four-dimensional system with hyperbolic tangent nonlinearity and no equilibrium

Abstract

This paper introduces a new four-dimensional (4-D) dynamical system composed of only seven terms: four linear terms, one nonlinear term involving the hyperbolic tangent function, one absolute value function term, and a constant. The new 4-D system does not have any equilibrium points and is capable of producing hidden attractors. The paper includes a detailed dynamical analysis, which encompasses bifurcation diagrams, Lyapunov exponents, Kaplan-Yorke dimensions, and bias amplification. Additionally, the theoretical model is verified through an electronic simulation of the system using Multisim© 14.2. The paper also demonstrates the synchronization of two identical 4-D hyperchaotic systems using the active control method. The proposed simple dynamic system exhibits a rather complex chaotic behavior and may find applications in various practical domains.