Singularity Structure and Chaotic Dynamics of the Parametrically Driven Duffing Oscillator

Abstract

The nonintegrability aspects of the generalised parametrically driven Duffing oscillator is reviewed by investigating analytically the singularity structure exhibited by the solution of the system in the complex time domain. The simultaneous contraction and rotation of this singularity pattern in the z = t4 lnt plane, as the control parameter is varied, results in complicated clustering of singularities in the t-plane is pointed out. The corresponding chaotic dynamics of the system is studied numerically.