Complex dynamics of a particle in an oscillating potential field

Abstract

In this paper, the classical problem of the motion of a particle in one dimension with an external time-dependent field is studied from the point of view of the dynamical system. The dynamical equations of motion of the particle are formulated. Equilibrium points of the non-oscillating systems are found and their local stability natures are analysed. Effect of oscillating potential barrier is analysed through numerical simulations. Phase diagrams, bifurcation diagrams and variations of largest Lyapunov exponents are presented to show the existence of a wide range of nonlinear phenomena such as limit cycle, quasiperiodic and chaotic oscillations in the system. Effects of nonlinear damping in the model are also reported. Analysis of the physically interesting cases where damping is proportional to higher powers of velocity are presented for the sake of generalizing our findings and establishing firm conclusion.

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