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One of the main motivations for analysis of networks of nonlinear oscillators lies in the role these play in undertanding synchronization and collective behavior in chemical and biological systems. In medical systems such networks are used for synchronization analysis of neuronal populations and control design for synchrony suppression. In this paper we use tools issued from nonlinear stability theory...
We consider a synchronization problem for the Kuramoto oscillators using a linear modeling framework. For the general case of Kuramoto model with directed and weighted graph of interconnections we show that the problem of existence of phase locked solutions is equivalent to an algebraic problem of existence of a corresponding matrix with a single purely imaginary eigenvalue. In the case of complete...
We employ stability theory to analyse the synchronization behavior of a network of symmetrically couples Stuart-Landau oscillators and we show that if the coupling strength is sufficiently large, the networked system practically synchronizes to a common limit cycle. We give an analytical expression for the approximate synchronization frequency and we establish stability properties of the limit cycle.
We consider Kuramoto model of phase oscillators with attractive-repulsive interconnections. We generalize results on existence of phase locked solutions for a family of input-output weighted sign-symmetric interconnection digraphs. Necessary and sufficient conditions for existence of phase locked solutions are formulated and their local asymptotically stability is analysed. In particular, we show...
We consider Kuramoto model of phase oscillators with attractive-repulsive interconnections, that is, part of interconnection gains can be negative. We generalize results on existence of phase locked solutions of input-output weighted sign-symmetric interconnections and present corresponding necessary and sufficient conditions for phase locking. We give an expression for synchronization frequency,...
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