Abstract
Duffing equation with fifth nonlinear-restoring force, one external forcing and a phase shift is investigated. The conditions of existences for primary resonance, second-order, third-order subharmonics, morder subharmonics and chaos are given by using second-averaging method, Melnikov methods and bifurcation theory. Numerical simulations including bifurcation diagrams, bifurcation surfaces, phase portraits, not only show the consistence with the theoretical analysis, but also exhibit the new dynamical behaviors. We show the onset of chaos, chaos suddenly disappearing to period orbit, one-band and double-band chaos, period-doubling bifurcations from period 1, 2, and 3 orbits, period-windows (period-2, 3 and 5) in chaotic regions.
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Supported by the National Natural Science Foundation of China (No.10371037), and by Chinese Academy Sciences (KZCX2-SW-118)
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Cai, Mx., Yang, Jp. Bifurcation of Periodic Orbits and Chaos in Duffing Equation. Acta Math. Appl. Sin, Engl. Ser. 22, 495–508 (2006). https://doi.org/10.1007/s10255-006-0325-4
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DOI: https://doi.org/10.1007/s10255-006-0325-4