Table 2 The local dynamical behaviors of points of \(S_{z}\).
From: Modeling, dynamical analysis and numerical simulation of a new 3D cubic Lorenz-like system
\(\rho _{1}\) | \(\tau _{1}\) | \(\sigma _{1}\) | Property of \(S_{z}\) |
|---|---|---|---|
\(<0\) | \( < 0\) | \( < 0\) | Stable foci normally hyperbolic to \(S_{z}\) |
\( < 0\) | \( \ge 0\) | Stable nodes normally hyperbolic to \(S_{z}\) | |
\( = 0\) | \( < 0\) | Fold-Hopf bifurcation may occur | |
\( > 0\) | \( < 0\) | Unstable foci normally hyperbolic to \(S_{z}\) | |
\( > 0\) | \( \ge 0\) | Unstable nodes normally hyperbolic to \(S_{z}\) | |
\( < 0\) | A 1D \(W_{loc}^{s}\) and a 2D \(W_{loc}^{c}\) | ||
\(=0\) | \( = 0\) | A 3D \(W_{loc}^{c}\) | |
\( > 0\) | A 2D \(W_{loc}^{c}\) and a 1D \(W_{loc}^{u}\) | ||
\(>0\) | Saddles normally hyperbolic to \(S_{z}\) |
