Analysis of the Dynamics of a $\phi^{6}$ Duffing Type Jerk System

Abstract

A theoretically and numerically analysis on Duffing Jerk systems with a sixth-order type potential and a sixth-order potential smoothed by a gaussian function are carried out in this work. The Jerk is transformed into a dynamical system of dimension three. The dynamics and stability of the resulting system are analyzed, through phase space, bifurcation diagrams and Lyapunov exponents by varying the relevant parameters, finding the existence of a strange attractor. The dynamics of system with potential smoothed was studied by varying the smoothing parameter $\alpha$, finding that this parameter can be used to controlling chaos, since the exponential factor keeps the same fixed points and it regulates smoothly the amplitude of the potential.