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Time-dependent potential; Lyapunov exponents; bifurcation; equilibrium points; integrable systems

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 ofnonlinear 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 establishingfirm conclusion.

BARNALI PAL¹ DEBJIT DUTTA² SWARUP PORIA¹

1. Department of Applied Mathematics, University of Calcutta, 92 Acharya Prafulla Chandra Road, Kolkata 700 009, India
2. Department of Basic and Applied Science, National Institute of Technology, Arunachal Pradesh 791 112, India

Published

15 August 2017

Manuscript received

15 August 2015

Manuscript revised

9 March 2017

Accepted

6 April 2017

Early published

Unedited version published online

Final version published online

25 July 2017