Synchronization in Oscillator Networks: Switching Topologies and Non-homogeneous Delays

We investigate the problem of synchronization in oscillator networks when the delay inherent in such systems is taken into account. We first investigate a general Kuramoto- type model with heterogeneous time delays, both with a complete network as well as a nearest neighbor interaction, for which we propose conditions for synchronization around a rotating frequency. Then, we turn our attention to the problem of synchronization when the topologies are allowed to change. We show that synchronization is possible in the presence of delay, using a common Lyapunov functional argument.

[1]  Yoshiki Kuramoto,et al.  Chemical Oscillations, Waves, and Turbulence , 1984, Springer Series in Synergetics.

[2]  Smith,et al.  Phase locking of relativistic magnetrons. , 1989, Physical review letters.

[3]  Vicsek,et al.  Novel type of phase transition in a system of self-driven particles. , 1995, Physical review letters.

[4]  Anders Rantzer,et al.  Computation of piecewise quadratic Lyapunov functions for hybrid systems , 1997, 1997 European Control Conference (ECC).

[5]  E. Izhikevich.  Phase models with explicit time delays , 1998 .

[6]  Kolmanovskii,et al.  Introduction to the Theory and Applications of Functional Differential Equations , 1999 .

[7]  S. Strogatz,et al.  Time Delay in the Kuramoto Model of Coupled Oscillators , 1998, chao-dyn/9807030.

[8]  Sen,et al.  Experimental evidence of time-delay-induced death in coupled limit-cycle oscillators , 1998, Physical review letters.

[9]  S. Strogatz.  From Kuramoto to Crawford: exploring the onset of synchronization in populations of coupled oscillators , 2000 .

[10]  D. V. Reddy,et al.  Experimental Evidence of Time Delay Induced Death in Coupled Limit Cycle Oscillators , 2000 .

[11]  Mandel,et al.  Global coupling with time delay in an array of semiconductor lasers , 2000, Physical review letters.

[12]  Tamas Vicsek,et al.  A question of scale , 2001, Nature.

[13]  Glenn Vinnicombe,et al.  On the stability of end-to-end congestion control for the internet , 2001 .

[14]  M. G. Earl,et al.  Synchronization in oscillator networks with delayed coupling: a stability criterion. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[15]  Rayadurgam Srikant,et al.  The Mathematics of Internet Congestion Control , 2003 .

[16]  R. Murray,et al.  Consensus protocols for networks of dynamic agents , 2003, Proceedings of the 2003 American Control Conference, 2003..

[17]  Steven H. Strogatz,et al.  Sync: The Emerging Science of Spontaneous Order , 2003 .

[18]  Luc Moreau,et al.  Leaderless coordination via bidirectional and unidirectional time-dependent communication , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[19]  Jie Lin,et al.  Coordination of groups of mobile autonomous agents using nearest neighbor rules , 2003, IEEE Trans. Autom. Control..

[20]  G. Bard Ermentrout.  Review of Sync : The Emerging Science of Spontaneous Order , 2003 .

[21]  João Pedro Hespanha,et al.  Uniform stability of switched linear systems: extensions of LaSalle's Invariance Principle , 2004, IEEE Transactions on Automatic Control.

[22]  R. Srikant,et al.  Global stability of Internet congestion controllers with heterogeneous delays , 2004, IEEE/ACM Transactions on Networking.

[23]  Juebang Yu,et al.  Synchronization in small-world oscillator networks with coupling delays , 2004 .

[24]  Richard M. Murray,et al.  Consensus problems in networks of agents with switching topology and time-delays , 2004, IEEE Transactions on Automatic Control.

[25]  L. Moreau,et al.  Stability of continuous-time distributed consensus algorithms , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[26]  D. Angeli,et al.  Stability of leaderless multi-agent systems. Extension of a result by Moreau , 2004, math/0411338.

[27]  Chunguang Li,et al.  Synchronization in general complex dynamical networks with coupling delays , 2004 .

[28]  A. Jadbabaie,et al.  On the stability of the Kuramoto model of coupled nonlinear oscillators , 2005, Proceedings of the 2004 American Control Conference.

[29]  Antonis Papachristodoulou,et al.  Global stability analysis of a TCP/AQM protocol for arbitrary networks with delay , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).