Robustness of a relaxation oscillator

Robust design of polyrhythmic neural circuits.

Neural circuit motifs producing coexistent rhythmic patterns are treated as building blocks of multifunctional neuronal networks. We study the robustness of such a motif of inhibitory model neurons to reliably sustain bursting polyrhythms under random perturbations. Without noise, the exponential stability of each of the coexisting rhythms increases with strengthened synaptic coupling, thus ind...

Qualitative and quantitative stability analysis of penta-rhythmic circuits

Inhibitory circuits of relaxation oscillators are often-used models for dynamics of biological networks. We present a qualitative and quantitative stability analysis of such a circuit constituted by three generic oscillators (of a Fitzhugh–Nagumo type) as its nodes coupled reciprocally. Depending on inhibitory strengths, and parameters of individual oscillators, the circuit exhibits polyrhythmi...

Tracking Rhythms with a Relaxation Oscillator

Enhanced entrainability of genetic oscillators by period mismatch.

Biological oscillators coordinate individual cellular components so that they function coherently and collectively. They are typically composed of multiple feedback loops, and period mismatch is unavoidable in biological implementations. We investigated the advantageous effect of this period mismatch in terms of a synchronization response to external stimuli. Specifically, we considered two fun...

Finding downbeats with a relaxation oscillator.

A relaxation oscillator model of neural spiking dynamics is applied to the task of finding downbeats in rhythmical patterns. The importance of downbeat discovery or 'beat induction' is discussed, and the relaxation oscillator model is compared to other oscillator models. In a set of computer simulations the model is tested on 35 rhythmical patterns. The model performs well, making good predicti...