Modeling, dynamical analysis and numerical simulation of a new 3D cubic Lorenz-like system

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 x(2)y to the second equation of the system, this paper introduces the new 3D cubic Lorenz-like system: x = a(y - x), y = b(1)y + b(2)yz + b(3)xz + b(4)x(2)y, z = -cz + y(2), 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 S-x = {(x, x, x(2)/c)|x is an element of R, c not equal 0}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.