Dynamics of a Lorenz-type multistable hyperchaotic system

Little seems to be known about the multistable hyperchaotic systems. In this paper, based on the classical Lorenz system, a new Lorenz-type hyperchaotic system with a curve of equilibria is proposed. Firstly, the local stability of the curve of equilibria is studied, based on this, infinity many singular degenerate heteroclinic cycles are proved numerically coexisting in the phase space of this hyperchaotic system. Secondly, the discovery of lots of coexisting behaviors mean that this hyperchaotic system possess multistability, such as (i) chaotic attractor and periodic attractor, (ii) different periodic attractors, (iii) chaotic attractor and singular degenerate heteroclinic cycle, and (iv) periodic attractor and singular degenerate heteroclinic cycle. Thirdly, in order to study the global dynamical behavior, the technique of Poincare compactification is used to investigate the dynamics at infinity of this hyperchaotic system.