The influence of equilibrium points and initial values on multistability of a multi-scroll chaotic system and predefined-time synchronization

Abstract

In order to explore the effect of the initial value on the symmetry of the coexisting attractor, a novel multi-scroll chaotic system is designed in this paper. The system is proved to be chaotic by analysing the phase diagram, Lyapunov exponential spectrum and dissipativity of the system. Then the equilibrium point of the system is investigated and it is found that the system has four symmetric saddle focus of index 2. By analysing the dynamical behaviour of the system, it is found that the system has a special kind of multistability. Combining the properties of the orbits near the saddle focus of indicator 2, the reason for this special multistability is explained, and the effect of the positional relationship between the initial value and the saddle focus on the symmetry of the coexisting attractors is illustrated, which provides a new way of thinking to analyse the symmetric coexistence of chaotic systems. In order to verify the feasibility and application value of the system, simulation circuits are designed and predefined-time synchronization between systems of different dimensions is achieved.