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Many biological oscillators are arranged in networks composed of many inter-coupled cellular oscillators. However, results are still lacking on the collective oscillation period of inter-coupled gene regulatory oscillators, which, as has been reported, may be different from the oscillation period of an autonomous cellular oscillator. Based on the Goodwin oscillator, we analyze the collective oscillation...
Pulse-coupled oscillators (PCOs) are limit cycle oscillators coupled in an impulsive rather than smooth manner. Its importance in biology and engineering has motivated the community to understand basic properties and design principles of PCO networks. In this work we address synchronization of PCO networks subject to both a global cue and local interactions using a hybrid systems approach. We characterize...
This work addresses the influences of global and local cues on the synchronization of Kuramoto oscillators coupled by nonlinear interactions. We first give a condition under which the network can be globally synchronized. This condition is more general than existing results and it is one of the first analytical results that ensure global synchronization of a general coupling structure when phase differences...
Understanding the mechanisms behind synchronisation of coupled systems is important in biology, chemistry, physics and engineering. For example, research on the synchronisation of coupled circadian clocks is of much importance to better understand many different disease states. Or, different applications in engineering require certificates for synchronised behaviour between the different coupled subsystems...
This paper analyzes influences of global and local cues on the synchronization rate of inter-connected oscillator networks subject to time delays. The coupling between oscillators is assumed to be directed, which includes the symmetric bi-directional coupling as a special case. In order to study the rate of synchronization, we first give a synchronization condition, which guarantees synchronization...
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