Abstract
We show that the chaotic dynamics of the conservative Duffing-Holmes oscillator obeys the universal Feigenbaum-Sharkovskii-Magnitskii theory of passage to chaos in dynamical systems of ordinary differential equations. Moreover, the cascades of bifurcations of the conservative and dissipative oscillators are continuously related to each other. Our study uses the stable control method, which permits rapidly stabilizing nearly any periodic solution and dynamically changing system parameters without moving far away from that periodic solution.
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Original Russian Text © A.D. Dubrovskii, 2010, published in Differentsial’nye Uravneniya, 2010, Vol. 46, No. 11, pp. 1652–1656.
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Dubrovskii, A.D. Nature of chaos in conservative and dissipative systems of the Duffing-Holmes oscillator. Diff Equat 46, 1653–1657 (2010). https://doi.org/10.1134/S0012266110110133
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DOI: https://doi.org/10.1134/S0012266110110133