Coexisting Attractors, Energy Analysis and Boundary of Lü System

Abstract

In this study, first, the phenomenon of multistability in the Lü system is found, which shows the coexistence of two different point attractors and one chaotic attractor. These coexisting attractors are dependent on initial conditions of the system while the parameters of the system are fixed. Then, the Lü system is transformed to a Kolmogorov-type system, which includes the conservative torque consisting of the inertial torque and the internal torque, the dissipative torque, and the external torque. Moreover, by analyzing the combination of different types of torques and investigating the cycling of energy based on the Casimir function and Hamiltonian function, the interaction between the external torque and other torques is found to be the main reason for the Lü system to generate chaos. Finally, by investigating the Casimir function, it is found that the boundary of the Lü system is only related to system parameters.