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- W830528519 abstract "This thesis is devoted to the analysis of synchronization in large networks of heterogeneous nonlinear oscillators using tools and methods issued from control theory. We consider two models of networks; namely, the Kuramoto model which takes into account only phase coordinates of the oscillators and networks composed of nonlinear Stuart-Landau oscillators interconnected by linear coupling. For the Kuramoto model we construct an auxiliary linear system that preserves information on the natural frequencies and interconnection gains of the original Kuramoto model. We show next that existence of phase locked solutions of the Kuramoto model is equivalent to the existence of such a linear system with certain properties. This system is used to formulate conditions that ensure existence of phase-locked solutions and their stability for particular structures of network interconnections. Next, this analysis is extended to the case where both attractive and repulsive interactions are present in the network that is we consider the situation where some of the interconnection gains are allowed to be negative. In the context of networks of Stuart-Landau oscillators, we present a new coordinate transformation of the network which allows to split the network model into two parts, one describing behaviour of an averaged network oscillator and the second one, describing dynamics of the synchronization errors relative to this averaged oscillator. This transformation allows us to characterize properties of the network in terms of stability of synchronization errors and limit cycle of the averaged oscillator. To do so, we recast this problem as a problem of stability of compact sets and use Lyapunov stability tools to ensure practical stability of both sets for sufficiently large values of the coupling strength." @default.
- W830528519 created "2016-06-24" @default.
- W830528519 creator A5030553353 @default.
- W830528519 date "2014-12-04" @default.
- W830528519 modified "2023-09-27" @default.
- W830528519 title "Synchronization analysis of complex networks of nonlinear oscillators" @default.
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