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Hinvi L. A.,Koukpémèdji A. A.,Monwanou V. A.,Miwadinou C. H.,Kamdoum Tamba V.,Chabi Orou J. B. 한국물리학회 2021 THE JOURNAL OF THE KOREAN PHYSICAL SOCIETY Vol.79 No.8
This paper addresses the dynamics of a position-dependent mass-driven Duffing-type oscillator (PDM oscillator) subjected to periodic excitation. The approximate equation of the PDM oscillator is considered to analyze the harmonic oscillations and the possible resonance states. The Amplitudes and frequencies of possible resonances are found by using the harmonic balance method and the multiple scales method. The harmonic resonance, primary resonance, order 3, 5 superharmonic resonances and order 3, 5 subharmonic resonances are obtained. The stability conditions for each of these resonances have also been obtained. Chaotic oscillations, multistability, hysteresis, and coexisting attractors have been found using the bifurcation diagram, the Lyapunov exponents, the phase portraits, and the basin of attraction. The effects of the PDM parameter ξ and of the external excitation have been analyzed. Results obtained by using the approximate equation of the system have been compared to the dynamics obtained with the exact equation of the PDM oscillator. The analytical investigations have been complemented and validated using the numerical simulations.