Behaviors of the modified nonlinear Schrödinger system in an inhomogeneous alpha helical protein

In this paper, under investigation is the modified nonlinear Schrödinger system, which could be used to describe the behaviors of solitons in an inhomogeneous alpha helical protein. We derive the travelling wave solutions of the system by transforming it to an ordinary differential equation. With those solutions, we analyze the stability of each equilibrium point through the phase-plane analysis. Upon the introduction of a periodic external forcing term, we observe two kinds of the chaotic motions, i.e., weak and developed chaos. We also find that the two chaotic motions can be transformed to each other when we change the strength of the external forcing term. Furthermore, we obtain the periodic motion of the system by balancing the external forcing term and nonlinear term.