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Synchronization in Networks of Diffusively Time-Delay Coupled (Semi-)Passive Systems

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2 Author(s)
Steur, E. ; Dept. of Mech. Eng., Eindhoven Univ. of Technol., Eindhoven, Netherlands ; Nijmeijer, H.

We consider networks with a general topology which consist of nonlinear systems that interact via diffusive coupling with constant time-delays. Using the notion of (semi-)passivity we prove under some mild assumptions that passive systems will synchronize and that the solutions of interconnected semi-passive systems will be bounded. Furthermore we prove that identical strictly semi-passive systems, whose internal dynamics are stable, always will synchronize given that the coupling between the systems is sufficiently strong and a possible constant time delay is sufficiently small. We demonstrate our results using numerical simulations of a network consisting of linear systems and a network consisting Hindmarsh-Rose neurons.

Published in:

Circuits and Systems I: Regular Papers, IEEE Transactions on  (Volume:58 ,  Issue: 6 )