Homoclinic transition to chaos in the Ueda oscillator with external forcing

作者: Arkadiusz Syta , Grzegorz Litak , Marek Borowiec

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摘要: We examine the Melnikov criterion for transition to chaos in case of a single degree freedom nonlinear oscillator with Ueda well potential and an external periodic excitation term. Using effective Hamiltonian we have examined homoclinic orbits cross-sections stable unstable manifolds which gave condition through bifurcation.

参考文章(13)
Yoshisuke Ueda, Randomly transitional phenomena in the system governed by Duffing's equation Journal of Statistical Physics. ,vol. 20, pp. 181- 196 ,(1979) , 10.1007/BF01011512
G. Chakraborty, A conjecture on route to chaos in a hard Duffing oscillator by homoclinic entanglement Journal of Sound and Vibration. ,vol. 294, pp. 435- 440 ,(2006) , 10.1016/J.JSV.2005.10.026
Grzegorz Litak, Arkadiusz Syta, Marek Borowiec, None, Suppression of chaos by weak resonant excitations in a non-linear oscillator with a non-symmetric potential Chaos, Solitons & Fractals. ,vol. 32, pp. 694- 701 ,(2007) , 10.1016/J.CHAOS.2005.11.026
Wanda Szemplińska-Stupnicka, Jerzy Rudowski, Bifurcations phenomena in a nonlinear oscillator: approximate analytical studies versus computer simulation results Physica D: Nonlinear Phenomena. ,vol. 66, pp. 368- 380 ,(1993) , 10.1016/0167-2789(93)90073-A
ELŻBIETA TYRKIEL, ON THE ROLE OF CHAOTIC SADDLES IN GENERATING CHAOTIC DYNAMICS IN NONLINEAR DRIVEN OSCILLATORS International Journal of Bifurcation and Chaos. ,vol. 15, pp. 1215- 1238 ,(2005) , 10.1142/S0218127405012727
T. Kapitaniak, Analytical Method of Controlling Chaos in Duffing's Oscillator Journal of Sound and Vibration. ,vol. 163, pp. 182- 187 ,(1993) , 10.1006/JSVI.1993.1158
John Guckenheimer, Philip Holmes, M. Slemrod, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields ,(1983)