Quasienergy of chaotic states in problems of nonlinear dynamics. Degeneration of states due to the symmetry of the system

Abstract

In this paper we analyse chaotic states in a system of coupled Duffing oscillators. The concept of quasienergy of a system is introduced in a way similar to the concept of quasienergy of a quantum mechanical system driven by an external periodic field. We show that in the absence of a connection between the oscillators in the system under consideration, chaotic states with the same value of quasienergy, but different values of the angular momentum are realized when the external influence changes. This fact can be interpreted as the existence of degenerate chaotic states of the system. A numerical experiment shows that taking into account the interaction between oscillators leads to the splitting of quasienergy, similar to the splitting of the quasienergy level in a quantum mechanical system.

Keywords

• nonlinear dynamics
• chaotic states
• chaotic attractor
• probability density
• quasienergy
• degenerate states