New conditions on synchronization of networks of linearly coupled dynamical systems with non-Lipschitz right-hand sides

Neural Networks

Volumn 25, Issue , 2012, Pages 5-13

  Liu, Bo ^a   Lu, Wenlian ^a   Chen, Tianping ^a  

^a FUDAN UNIVERSITY   (China)

Author keywords

Discontinuous right hand side; Linearly coupled systems; Non Lipschitz; Synchronization

Indexed keywords

COUPLED DYNAMICAL SYSTEMS; COUPLED SYSTEMS; LINEARLY COUPLED SYSTEMS; NON-LIPSCHITZ; RIGHT-HAND SIDES; SUFFICIENT CONDITIONS; THEORETICAL RESULT;

DYNAMICS; SYNCHRONIZATION;

DYNAMICAL SYSTEMS;

ARTICLE; ARTIFICIAL NEURAL NETWORK; COMPUTER SIMULATION; CORTICAL SYNCHRONIZATION; DYNAMICS; LINEAR SYSTEM; MATHEMATICAL COMPUTING; PRIORITY JOURNAL; SIGNAL PROCESSING; THEORETICAL MODEL;

LINEAR MODELS; NEURAL NETWORKS (COMPUTER); TIME FACTORS;

EID: 82355169673     PISSN: 08936080     EISSN: 18792782     Source Type: Journal    
DOI: 10.1016/j.neunet.2011.07.007     Document Type: Article

References (39)

1. Aubin J.P. Viability theory 1991, Birkhauser.
2. Aubin J.P., Frankowska H. Set-valued analysis 1990, Birkhauser, Boston.
3. Belykh I., Belykh V., Hasler M. Connection graph stability method for synchronized coupled chaotic systems. Physica D 2004, 195:159-187.
4. Belykh I., Belykh V., Hasler M. Blinking model and synchronization in small-world networks with a time-varying coupling. Physica D 2004, 195:188-206.
5. Belykh I., Belykh V., Hasler M. Synchronization in asymmetrically coupled networks with node balance. Chaos 2006, 16:015102.
6. Chatterjee, D., & Liberzon, D. 2006 Stability analysis and stabilization of randomly switched systems, Proceedings of the 45th IEEE conference on decision and control, 1-14, pp. 1217-1222.
7. Chen M.Y. Chaos synchronization in complex networks. IEEE Transactions on Circuits and Systems I 2008, 55:1335-1346.
8. Clarke F.H. Optimization and nonsmooth analysis 1983, Wiley and Sons, New York.
9. Collins J.J., Stewart I. Coupled nonlinear oscillators and the symetries of animal gaits. Science 1993, 3:349-392.
10. Duan Z.S., Chen G.R. Global robust stability and synchronization of networks with Lorenz-Type nodes. IEEE Transactions on Circuits and Systems II 2009, 56:679-683.
11. Duane G.S., Webster P.J., Weiss J.B. Go-occurrence of Northern and Southern Hemisphere blocks as partially synchronized chaos. Journal of the Atmospheric Sciences 1999, 56:4183-4205.
12. Filippov A.F. Differential equations with discontinuous right-hand sides. Mathematics and its applications Soviet Series 1988, Kluwer Academic Publishers, Boston.
13. Honerkamp J. The heat as a system of coupled nonlinear oscillators. Journal of Mathematical Biology 1983, 19:69-88.
14. Hoppensteadt F.C., Izhikevich E.M. Pattern recognition via synchronization in phase-locked loop neural networks. IEEE Transactions on Neural Networks 2000, 11:734-738.
15. Horn R.A., Johnson C.R. Topics in matrix analysis 1991, Cambridge University Press.
16. Kuramoto Y. Chemical oscillations, waves and turbulence 1984, Berlin:Springer.
17. Liberzon D. Switched systems (Control engineering series) (559-574) 2005, Birkhauser, Boston.
18. Liberzon D., Morse A.S. Basic problems in stability and design of switched systems. IEEE Control Systems Magazine 1999, 19:59-70.
19. Liu X.W., Chen T.P. Boundedness and synchronization of y-coupled Lorenz systems with or without controllers. Physica D 2008, 237:630-639.
20. Lu W.L., Chen T.P. Synchronization of coupled connected neural networks with delays. IEEE Transactions on Circuits and Systems I 2004, 51(12):2491-2503.
21. Lu W.L., Chen T.P. New approach to synchronization analysis of linearly coupled ordinary differential systems. Physica D 2006, 213:214-230.
22. Mirollo R., Strogatz S. Synchronization of pulsed-coupled biological oscillators. SIAM Journal on Applied Mathematics 1990, 50:1645-1662.
23. Netoff T.I., Schiff S.J. Decreased neuronal synchronization during experimental seizures. Journal of Neuroscience 2002, 22:7297-7307.
24. Ohtsubop J. Feedback induced instability and chaos in semiconductor lasers and their applications. Optical Review 1999, 6:1-15.
25. Pavlov A.V., van de Wouw N., Nijmeijer H. On convergence properties of piecewise affine systems. International Journal of Control 2007, 80:1233-1247.
26. Pecora L.M., Carroll T.L. Synchronization in chaotic systems. Physical Review Letters 1990, 64:821-824.
27. Petreczky M. Realization theory for linear switched systems:formal power series approach. Systems and Control Letters 2007, 56:588-595.
28. Porfiri M., Stilwell D.J., Bollt E.M. Synchronization in random weighted directed networks. IEEE Transactions on Circuits and Systems I 2008, 55:3170-3177.
29. Russo G., di Bernardo M. Contraction theory and master stability function: linking two approaches to study synchronization of complex networks. IEEE Transactions on Circuits and Systems II 2009, 56:177-181.
30. Strogatz S. Exploring complex networks. Nature 2001, 410:268-276.
31. Torre V. A theory of synchronization of two heart pacemaker cells. Journal of Theoretical Biology 1976, 61:55-71.
32. Van de Wouw N., Pavlov A. Tracking and synchronisation for a class of PWA systems. Automatica 2008, 44:2909-2915.
33. VanWiggeren G.D., Roy P. Communication with laser. Science 1998, 279:1198-1200.
34. Vieria M.de S. Chaos and synchronized chaos in an earthquake model. Physical Review Letters 1999, 82:201-204.
35. Wu C.W. Synchronization in coupled arrays of chaotic oscillators with nonreciprocal coupling. IEEE Transactions on Circuits and Systems I 2003, 50:294-297.
36. Wu C.W. Synchronization in arrays of coupled nonlinear systems with delay and nonreciprocal time-varying coupling. IEEE Transactions on Circuits and Systems II 2005, 52:282-286.
37. Wu C.W., Chua L.O. Synchronization in an array of linearly coupled dynamical systems. IEEE Transactions on Circuits and Systems I 1995, 42:430-447.
38. Yang T., Chua L. Impulsive control and synchronization of nonlinear dynamical systems and application to secure communication. International Journal of Bifurcation and Chaos 1997, 7:645-664.
39. Zhao J., Hill D.J. Passivity and stability of switched systems: a multiple storage function method. Systems and Control Letters 2008, 57:158-164.