Limit Cycle-Strange Attractor Competition

Studies in Applied Mathematics

Volumn 112, Issue 2, 2004, Pages 133-160

  Criminale, W O ^a   Jackson, T L ^b   Nelson, P W ^b  

^a UNIVERSITY OF WASHINGTON   (United States)

^b NONE

Author keywords

[No Author keywords available]

Indexed keywords

CHAOS THEORY; CIRCUIT OSCILLATIONS; CONTROL NONLINEARITIES; OSCILLATORS (MECHANICAL);

ATTRACTOR DYNAMICS; CLASSICAL OSCILLATORS; COUPLING STRENGTHS; DUFFING EQUATIONS; EXTERNAL FORCING; LIMIT CYCLE ATTRACTORS; LIMIT-CYCLE; LINEAR FORCING; STRANGE ATTRACTORS; VAN DER POL'S OSCILLATORS;

LYAPUNOV METHODS;

EID: 1342306021     PISSN: 00222526     EISSN: None     Source Type: Journal    
DOI: 10.1111/j.0022-2526.2004.01507.x     Document Type: Article

References (15)

1. P. G. DRAZIN, Nonlinear Systems, Cambridge University Press, Cambridge, 1992.
2. Y. VEDD, Steady motions exhibited by Duffing's equation: A picture book of regular and chaotic motions, in New Approaches to Nonlinear problems in dynamics (P. J. Holmes, Ed.), pp. 311-322, SIAM, Philadelphia (1980).
3. D. W. JORDAN and P. SMITH, Nonlinear Ordinary Differential Equations, Oxford University Press, Oxford, 1999.
4. D. W. STORTI, Bifurcations which destroy the out-of-phase mode in a pair of linearly coupled relaxation oscillators, Int. J. Nonlinear Mech. 22:387-390 (1987).
5. D. W. STORTI and P. G. REINHALL, Phase-locked mode instability for coupled van der Pol oscillators, J. Vib. Acoust. 3:318-323 (2000).
6. E. M. EL-ABBASY and E. M. JAMES, Stable subharmonics of the van der Pol equation, SIAM J. Appl. Math. 31:269-279 (1983).
7. S. E. D. PINTO, S. R. LOPES, and R. L. VIANA, Collective behavior in a chain of coupled van der Pol oscillators with power-law coupling, Physica A 303(3-4):339-356 (2002).
8. H. K. LEUNG, Bifurcation of synchronization as a nonequilibrium phase transition, Physica A 281(1-4):311-317 (2000).
9. G. HU, F. G. XIE, Z. L. QU, and P. L. SHI, Antiphase states in coupled oscillator systems, Commun. Theor. Phys. 31(1):99-106 (1999).
10. I. PASTORDIAZ and A. LOPEZFRAGUAS, Dynamics of 2 coupled van der Pol oscillators, Phys. Rev. E 52(2): 1480-1489 (1995).
11. I. PASTOR, V. M. PEREZ-GARCIA, F. ENCINASSANZ, and J. M. GUERRA, Ordered and chaotic behavior of 2 coupled oscillators, Phys. Rev. E 48(1): 171-182 (1993).
12. J. M. GONZALEZ-MIRANDA, Amplitude envelope synchronization in coupled chaotic oscillators, Phys. Rev. E 65(3):036232-1-036232-10 (2002).
13. A. K. KOZLOV, M. M. SUSHCHIK, Y. I. MOLKOV, and A. S. KUZNETSOV, Bistable phase synchronization and chaos in a system of coupled van der Pol-Duffing oscillators, Int. J. Bifurcation Choas 9(12):2271-2277 (1999).
14. Y. J. HAN, Dynamics of coupled nonlinear oscillators of different attractors van der Pol and damped Duffing oscillator, J. Korean Phys. Soc. 37(1):3-9 (2000).
15. J. C. CHEDJOU, H. B. FOTSIN, and S. DOMNGANG, Analong simulation of the dynamics of a van der Pol oscillator coupled to a Duffing oscillator, IEEE Trans. Circuits Syst. I-Fundam. Theor. Appl. 48(6):748-757 (2001).