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

In this section, the stability and bifurcation of equilibria of system (2) are studied by aid of the center manifold theorem, Routh-Hurwitz criterion, the theory of pitchfork bifurcation and Hopf bifurcation, Lyapunov function and so on.

Firstly, from the algebraic structure of system (2), one easily presents the distribution of equilibrium points in the following proposition.

Proposition 4.1

(i) When \(c = 0\), \(S_{z} = \{(0, 0, z)|z\in \mathbb {R}\}\) is a line of semi-hyperbolic equilibria of system (2).

(ii) When \(b_{1} = 0\), \(c \ne…