Analysis of basins of attraction of new coupled hidden attractor system

Abstract This paper mainly discusses the characteristic of the basin of attraction of two coupled chaotic systems, which provides a theoretical basis for the application of nonlinear systems in the fields of communication, control and artificial intelligence. Thus, in order to increase the complexity of the chaotic systems, two identical linear couplings are used to hide a system composed of attractors, and therefore the system has chaotic characteristic within a specific coupling strength range. We use an ode45 algorithm to solve the coupled chaotic systems to obtain a chaotic phase diagram, Lyaponov exponential spectrum and a bifurcation diagram of the system and prove that the attractors of the coupled systems are attractors in the sense of Milnor, and the basin of attraction of the coupled chaotic systems has a sieve-type property. A Lyaponov exponential function of the nonlinear system can be used to analyze the stability of the system, when the system operates in an initial state, the system will move in the direction that the Lyaponov exponential function decreases until it reaches a local minimum, a local minimum point of the Lyaponov exponential function represents a stable point of a phase space, and each attractor surrounds one substantial basin of attraction. Therefore, we use a Lyaponov exponent to describe and analyze the basin of attraction of the coupled chaotic systems. And meanwhile, when analyzing the system, we found that the system has rich dynamic behavior and multi-stability for hiding of the attractors.