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arXiv · 1304.7679

Towards a general theory for coupling functions allowing persistent synchronization

Tiago Pereira·Jaap Eldering·Martin Rasmussen·Alexei Veneziani
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Abstract

We study synchronisation properties of networks of coupled dynamical systems with interaction akin to diffusion. We assume that the isolated node dynamics possesses a forward invariant set on which it has a bounded Jacobian, then we characterise a class of coupling functions that allows for uniformly stable synchronisation in connected complex networks --- in the sense that there is an open neighbourhood of the initial conditions that is uniformly attracted towards synchronisation. Moreover, this stable synchronisation persists under perturbations to non-identical node dynamics. We illustrate the theory with numerical examples and conclude with a discussion on embedding these results in a more general framework of spectral dichotomies.

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Tiago Pereira, Jaap Eldering, Martin Rasmussen, Alexei Veneziani. 2013-08-29. Towards a general theory for coupling functions allowing persistent synchronization. https://doi.org/10.1088/0951-7715%2F27%2F3%2F501

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