Nonlinear dynamics of classical counterpart of the generalized quantum nonlinear oscillator driven by position dependent mass

• Mass parameter ηη plays a crucial role in the chaotic dynamics of the system.
• For η>0η>0, period doubling route to chaos occurs.
• For η<0η<0, quasiperiodic route to chaos occurs via strange nonchaotic attractor.
• Period five orbit occurs after period four for fixed η>0η>0 when other parameters vary.
• Fractal boundaries are observed in the f−αf−α bifurcation diagram.

This paper examines the chaotic dynamics of certain damped and forced versions of classical counterpart of generalized quantum nonlinear oscillator endowed with position dependent mass (PDM). Various bifurcations such as symmetry breaking, period doubling, inverse period doubling, interior and boundary crises are reported. Sensitivity of the mass parameter ηη to the chaotic dynamics of the system is demonstrated by the appearance of completely different route to chaos for η>0η>0 and η<0η<0. In the former case the chaotic motion is found to set in through period doubling route while in the latter case there is quasiperiodic route to chaos via strange non-chaotic attractor. Fractal boundaries are observed in chaos plots for η>0η>0.