Pseudo and true singularly degenerate heteroclinic cycles of a new 3D cubic Lorenz-like system

Abstract

In contrast to the coexistence of infinitely many pseudo and true singularly degenerate heteroclinic cycles with nearby two-scroll hyperchaotic Lorenz-like attractors coined in four-dimensional systems, this note reports the ones with nearby bifurcated chaotic attractors in a new 3D cubic Lorenz-like system. Except for the rabbit head/boat shape two-scroll attractors, there exist globally exponentially asymptotically stable parabolic type equilibria and a pair of heteroclinic orbits. In addition, numerical simulations also validate the correctness of the theoretical analysis.

Keywords

• New cubic Lorenz-like system
• Coexistence of infinitely many pseudo and true singularly degenerate heteroclinic cycles
• Globally exponentially asymptotical stability
• Heteroclinic orbit
• Lyapunov function