Dynamics of a Four-Dimensional System with Cubic Nonlinearities

In this paper, we investigate a three-parameter four-dimensional dynamical system, which is modeled by a set of four first-order nonlinear ordinary differential equations, each of which contains a crossed cubic term. Dynamical behaviors are characterized in the parameter space of the model. In fact, we use some cross-sections of a three-dimensional parameter-space, namely three related parameter planes, to locate regular and chaotic regions, as well as multistability regions. Lyapunov exponents spectra, bifurcation diagrams, and phase-space portraits are used to complete the analysis.