Melnikov chaos in a periodically driven Rayleigh–Duffing oscillator

[1]  N. Levinson,et al.  A Second Order Differential Equation with Singular Solutions , 1949 .

[2]  A. Winfree.  The geometry of biological time , 1991 .

[3]  P. Holmes,et al.  Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields , 1983, Applied Mathematical Sciences.

[4]  Grebogi,et al.  Metamorphoses of basin boundaries in nonlinear dynamical systems. , 1986, Physical review letters.

[5]  Collective-coordinate description of chaotic sine-Gordon breathers and zero-frequency breathers: The nondissipative case. , 1988, Physical review. A, General physics.

[6]  S. Wiggins.  Introduction to Applied Nonlinear Dynamical Systems and Chaos , 1989 .

[7]  G. Kovačič,et al.  Orbits homoclinic to resonances, with an application to chaos in a model of the forced and damped sine-Gordon equation , 1992 .

[8]  Analog study of bifurcation structures in a Van der Pol oscillator with a nonlinear restoring force. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[9]  Chaos in rf-driven long Josephson junctions in the presence of an external field. , 1995, Physical review. B, Condensed matter.

[10]  H. Kawakami,et al.  Unstable saddle-node connecting orbits in the averaged Duffing-Rayleigh equation , 1996, 1996 IEEE International Symposium on Circuits and Systems. Circuits and Systems Connecting the World. ISCAS 96.

[11]  M. Lakshmanan,et al.  Bifurcation and chaos in the double-well Duffing–van der Pol oscillator: Numerical and analytical studies , 1997, chao-dyn/9709013.

[12]  Melnikov's Method for Spatial Periodic Field and Bifurcation in a Modified Sine-Gordon Model , 1998 .

[13]  G. Litak,et al.  VIBRATION OF EXTERNALLY-FORCED FROUDE PENDULUM , 1999 .

[14]  Tetsuya Yoshinaga,et al.  The bifurcation structure of fractional-harmonic entrainments in the forced Rayleigh oscillator , 2001, ICECS 2001. 8th IEEE International Conference on Electronics, Circuits and Systems (Cat. No.01EX483).

[15]  Miguel A. F. Sanjuán,et al.  A generalized perturbed pendulum , 2003 .

[16]  Shaopu Yang,et al.  Investigation on chaotic motion in hysteretic non-linear suspension system with multi-frequency excitations , 2004 .

[17]  Paul Woafo,et al.  Dynamics and synchronization of coupled self-sustained electromechanical devices , 2005 .

[18]  Guanrong Chen,et al.  Global and Local Control of homoclinic and heteroclinic bifurcations , 2005, Int. J. Bifurc. Chaos.

[19]  Grzegorz Litak,et al.  Chaotic Vibration of a Quarter-Car Model Excited by the Road Surface Profile , 2006, nlin/0601030.