Modeling, dynamical analysis and numerical simulation of a new 3D cubic Lorenz-like system
Haijun Wang, Guiyao Ke, Jun Pan, Qifang Su
Abstract
Little seems to be considered about the globally exponentially asymptotical stability of parabolic type equilibria and the existence of heteroclinic orbits in the Lorenz-like system with high-order nonlinear terms. To achieve this target, by adding the nonlinear terms yz and [Formula: see text] to the second equation of the system, this paper introduces the new 3D cubic Lorenz-like system: [Formula: see text], [Formula: see text], [Formula: see text], which does not belong to the generalized Lorenz systems family. In addition to giving rise to generic and degenerate pitchfork bifurcation, Hopf bifurcation, hidden Lorenz-like attractors, singularly degenerate heteroclinic cycles with nearby chaotic attractors, etc., one still rigorously proves that not only the parabolic type equilibria [Formula: see text] are globally exponentially asymptotically stable, but also there exists a pair of symmetrical heteroclinic orbits with respect to the z-axis, as most other Lorenz-like systems. This study may offer new insights into revealing some other novel dynamic characteristics of the Lorenz-like system family.