We examine some nontrivial consequences that emerge from interpreting a position-dependent mass (PDM) driven Duffing oscillator in the presence of a quartic potential. The propagation dynamics is studied numerically and sensitivity to the PDM-index is noted. Remarkable transitions from a limit cycle to chaos through period doubling and from a chaotic to a regular motion through intermediate periodic and chaotic routes are demonstrated. PACS number(s): 05.45.-a, 03.50.Kk, 03.65.-w
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