A Parametric Resonance for the Nonlocal Hirota–Maccari Equation

Abstract

The nonlocal Hirota–Maccari equation is considered when a parametric excitation is acting over the frequency of a generic mode. Using the well-known asymptotic perturbation (AP) method, two coupled equations for the amplitude and phase can be obtained. We discovered the existence of an infinite-period bifurcation when the parametric force increases its value. Moreover, symmetry considerations suggest performing a global analysis of the two couples, in such a way that we find an energy-like function and corroborate and verify the existence of this infinite period bifurcation.

Keywords

• Hirota–Maccari equation
• infinite-period bifurcation
• global analysis
• parametric excitation