Bifurcation, sensitivity analysis and exact traveling wave solutions for the stochastic fractional Hirota–Maccari system

Abstract

The stochastic fraction Hirota–Maccari system is used as a governing model to check the wave propagation in nonlinear optics, plasma physics and hydrodynamics. Firstly, the random fractional order Hirota–Maccari system is transformed into a two-dimensional plane dynamic system by using traveling wave transformation. Secondly, the bifurcation is discussed by using the theory of plane dynamic system, and the sensitivity to the strength and frequency of perturbation is analyzed. In addition, the exact traveling wave solution of the stochastic fractional Hirota–Maccari system is constructed by using the analytical method of the plane dynamic system. Finally, the results of comparison analysis indicated that the fractional derivatives and noises will greatly influence the solution behavior.

Keywords

• Bifurcation
• Sensitivity analysis
• Exact traveling wave solution
• Stochastic fractional Hirota–Maccari system
• Planar dynamic system method