Connected oscillations in a nonlinearly coupled system

Nonlinearly coupled harmonic oscillators: high frequency oscillations yield synchronization

Synchronization of coupled harmonic oscillators is investigated. Coupling considered here is pairwise, unidirectional, and described by a nonlinear function (whose graph resides in the first and third quadrants) of some projection of the relative distance (between the states of the pair being coupled) vector. Under the assumption that the interconnection topology defines a connected graph, it i...

Consensus in discrete-time nonlinearly coupled networks

We consider consensus algorithms for multi-agent networks with discrete-time linear identical MIMO agents. The agents may be of arbitrary order, the interaction topology may be time-varying and the couplings may be nonlinear and uncertain, however assumed to satisfy a slope restriction or, more generally, quadratic constraint. Using the discrete-time version of the KYP Lemma (referred to as the...

Desynchronization transitions in nonlinearly coupled phase oscillators

We consider the nonlinear extension of the Kuramoto model of globally coupled phase oscillators where the phase shift in the coupling function depends on the order parameter. A bifurcation analysis of the transition from fully synchronous state to partial synchrony is performed. We demonstrate that for small ensembles it is typically mediated by stable cluster states, that disappear with creati...

Self-Sustained Oscillations of Nonlinearly Viscoelastic Layers

Impulsive Synchronization of Nonlinearly Coupled Complex Networks

This paper investigates synchronization problem of nonlinearly coupled dynamical networks, and an effectively impulsive control scheme is proposed to synchronize the network onto the objective state. Based on the stability analysis of impulsive differential equations, a low-dimensional sufficient condition is derived to guarantee the exponential synchronization in virtual of average impulsive i...