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Nonlinear dynamics of classical counterpart of the generalized quantum nonlinear oscillator driven by position dependent mass. (English) Zbl 1343.34088
Summary: 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 \(\eta\) to the chaotic dynamics of the system is demonstrated by the appearance of completely different route to chaos for \(\eta>0\) and \(\eta<0\). 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 \(\eta>0\).

MSC:
34C15 Nonlinear oscillations and coupled oscillators for ordinary differential equations
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
34C28 Complex behavior and chaotic systems of ordinary differential equations
34C23 Bifurcation theory for ordinary differential equations
37N20 Dynamical systems in other branches of physics (quantum mechanics, general relativity, laser physics)
Software:
Dynamics
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