The dynamical behavior analysis of the fractional perturbed Gerdjikov–Ivanov equation

Abstract

In this article, the fractional perturbed Gerdjikov–Ivanov equation is investigated. Firstly, the fractional perturbed Gerdjikov–Ivanov equation is transformed into an ordinary differential equation through traveling wave transformation. Secondly, using the trial method of rank homogeneous equation polynomials and the principle of homogeneous equilibrium, a two-dimensional planar dynamic system is presented and its bifurcation behavior is studied. Then, its two-dimensional phase portraits are drawn by using Maple software. Finally, disturbance factors are introduced into the planar dynamical system to study its chaotic behavior, and some two-dimensional phase portraits, three-dimensional phase portraits, Poincaré sections, and sensitivity analysis graphs of the perturbed system are plotted by using Maple software. The novelty lies in studying the dynamic behavior of the objective equation without the need for solving.

Keywords

• Gerdjikov–Ivanov equation
• Bifurcation behavior
• Chaotic behavior
• Phase portrait
• Poincaré section
• Sensitivity analysis