Dr. Erik Steur, Synchronization in networks of linearly time-delayed coupled oscillators
Date: Fri 29 Nov 2013, 14:30 - 15:30
Location: Nanoforce Seminar Room (Joseph Priestley Building)
Dr. Erik Steur, from the Laboratory for Perpetual Dynamics, KU Leuven, Belgium
Synchronization in networks of linearly coupled oscillators has been observed in fields varying from neuroscience and biology to engineering. It is an intriguing question how and when such networks synchronize, especially when time-delays appear in the coupling. In this talk I consider networks of oscillators, modeled by ordinary differential equations, that interact via linear coupling functions with time-delays. I present the notion of semi-passivity, which states that each oscillator has a finite amount of ``free energy’’, and I show that solutions of linearly time-delayed coupled semi-passive oscillators are bounded. Next I identify a class of oscillators that are guaranteed to synchronize for sufficiently strong coupling provided that the product of the time-delays and coupling strength is sufficiently small. In addition I show that networks with certain symmetries can exhibit a form of incomplete synchronization called partial synchronization. All these theoretical results are supported by numerical simulations and data obtained from an experimental setup with electronic circuit realizations of the Hindmarsh-Rose neuron model.