Dynamical Analysis and Periodic Solution of a Chaotic System with Coexisting Attractors

Chaotic attractors with no equilibria, with an unstable node, and with stable node-focus are presented in this paper. The conservative solutions are investigated by the semianalytical and seminumerical method. Furthermore, multiple coexisting attractors are investigated, and circuit is carried out. To study the system's global structure, dynamics at infinity for this new chaotic system are studied using Poincare compactification of polynomial vector fields in R3. Meanwhile, the dynamics near the infinity of the singularities are obtained by reducing the system's dimensions on a Poincare ball. The averaging theory analyzes the periodic solution's stability or instability that bifurcates from Hopf-zero bifurcation.

Automated summary

This paper introduces chaotic attractors without equilibria, with an unstable node, and with stable node-focus. The dynamics of conservative solutions are investigated using semi-analytical and semi-numerical methods. Multiple coexisting attractors are studied along with the system's global structure and dynamics at infinity, while the stability of periodic solutions bifurcating from Hopf-zero bifurcation is analyzed using the averaging theory.