Dissipativity characterization of a class of oscillators and networks of oscillators

Proceedings of the IEEE Conference on Decision and Control

Volumn 4, Issue , 2003, Pages 4169-4173

  Stan, Guy Bart ^a,b   Sepulchre, Rodolphe ^a  

^a UNIVERSITY OF LIÈGE   (Belgium)

^b FUND FOR SCIENTIFIC RESEARCH   (Belgium)

Author keywords

Dissipativity; HOPF bifurcation; Limit cycles; Networks of oscillators

Indexed keywords

APPROXIMATION THEORY; ASYMPTOTIC STABILITY; BIFURCATION (MATHEMATICS); COMPUTER SIMULATION; OSCILLATORS (ELECTRONIC); THEOREM PROVING;

HOPF BIFURCATIONS; LIMIT CYCLES; NETWORKS OF OSCILLATORS;

CONTROL SYSTEMS;

EID: 1542319184     PISSN: 07431546     EISSN: 25762370     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (15)

1. M. FARKAS, Periodic Motions, Applied Mathematical Sciences, Vol. 104, Springer Verlag, 1994.
2. M. GOLUTBITSKY and I. STEWART, Symmetry and pattern formation in coupled cell networks, Pattern Formation in Continuous and Coupled Systems, IMA Volumes in Mathematics and its Applications, Vol. 115, Springer Verlag, New York, 1999, pp. 65-82.
3. M. GOLUTBITSKY and I. STEWART, HOPF bifurcation in the presence of symmetry, Archive for Rational Mechanics and Analysis, Vol. 87, n. 2, 1985, pp. 107-165.
4. M. GOLUTBITSKY and I. STEWART, The Symmetry Perspective, From Equilibrium to Chaos in Phase Space and Physical Space, Birkhuser Verlag, Progress in mathematics, Vol. 200, 2002.
5. B. D. HASSARD and N. D. KAZARINOFF and Y-H. WAN, Theory and applications of HOPF bifurcation, London Mathematical Society, Lecture Notes Series, Vol. 41, Cambridge University Press, 1981.
6. F. C. HOPPENSTEADT and E. M. IZHIKEVICH, Weakly Connected Neural Networks, Applied Mathematical Sciences, Vol. 126, Springer Verlag, 1997.
7. H. K. KHALIL, Nonlinear systems, Prentice Hall, second edition, 1996.
8. N. KOPELL and G. B. ERMENTROUT, Mechanisms of phase-locking and frequency control in pairs of coupled neural oscillators, Handbook on Dynamical Systems, Vol. 2: Towards applications, Ed. B. Fiedler, Elsevier, 2002, pp. 3-5.
9. A. I. MEES, Dynamics of Feedback Systems, Willey-Interscience, 1981.
10. E. MOSEKILDE, Topics in Nonlinear Dynamics. Applications to Physics, Biology and Economic Systems, World Scientific Press, Singapore, 1997.
11. R. SEPULCHRE, M. JANKOVIC and P. KOKOTOVIC, Constructive Nonlinear Control, Springer Verlag, London, 1997.
12. G.-B. STAN and R. SEPULCHRE, manuscript in preparation.
13. S. H. STROGATZ and I. STEWART, Coupled oscillators and biological synchronization, Scientific American, Vol. 269, n. 6, 1993, pp. 102-109.
14. S. H. STROGATZ, From Kuramoto to Crawford: exploring the onset of synchronization in populations of coupled oscillators, Physica D, Vol. 143, 2000, pp. 120.
15. 2-Gain and Passivity Techniques in Nonlinear Control, Springer Verlag, London, 2000.