Revisiting asymptotic periodicity in networks of degrade-and-fire oscillators

Asymptotic periodicity in networks of degrade-and-fire oscillators

Networks of coupled degrade-and-fire (DF) oscillators are simple dynamical models of assemblies of interacting self-repressing genes. For mean-field interactions, which most mathematical studies have assumed so far, every trajectory must approach a periodic orbit. Moreover, asymptotic cluster distributions can be computed explicitly in terms of coupling intensity, and a massive collection of di...

Corepressive interaction and clustering of degrade-and-fire oscillators.

Strongly nonlinear degrade-and-fire (DF) oscillations may emerge in genetic circuits having a delayed negative feedback loop as their core element. Here we study the synchronization of DF oscillators coupled through a common repressor field. For weak coupling, initially distinct oscillators remain desynchronized. For stronger coupling, oscillators can be forced to wait in the repressed state un...

Population Dynamics of Globally Coupled Degrade-and-Fire Oscillators

Typical trajectories of coupled degrade-and-fire oscillators: from dispersed populations to massive clustering.

We consider the dynamics of a piecewise affine system of degrade-and-fire oscillators with global repressive interaction, inspired by experiments on synchronization in colonies of bacteria-embedded genetic circuits. Due to global coupling, if any two oscillators happen to be in the same state at some time, they remain in sync at all subsequent times; thus clusters of synchronized oscillators ca...

Clustering behaviors in networks of integrate-and-fire oscillators.

Clustering behavior is studied in a model of integrate-and-fire oscillators with excitatory pulse coupling. When considering a population of identical oscillators, the main result is a proof of global convergence to a phase-locked clustered behavior. The robustness of this clustering behavior is then investigated in a population of nonidentical oscillators by studying the transition from total ...