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We analyze the physical mechanisms leading either to synchronization or to the formation of spatio-temporal patterns in a lattice model of pulse-coupled oscillators. In order to make the system tractable from a mathematical point of view we…
Oscillations are omnipresent in neural population signals, like multi-unit recordings, EEG/MEG, and the local field potential. They have been linked to the population firing rate of neurons, with individual neurons firing in a…
We show that the simplest stochastic epidemiological models with spatial correlations exhibit two types of oscillatory behaviour in the endemic phase. In a large parameter range, the oscillations are due to resonant amplification of…
We study the effects of delayed coupling on timing and pattern formation in spatially extended systems of dynamic oscillators. Starting from a discrete lattice of coupled oscillators, we derive a generic continuum theory for collective…
The study of motion in animals and robots has been aided by insights from geometric mechanics. In friction dominated systems, a mechanical "connection" can provide a high fidelity mechanical model. The connection is a co-vector (Lie…
The global stability of oscillator networks has attracted much recent attention. Ordinarily, the oscillators in such studies are motionless; their spatial degrees of freedom are either ignored (e.g. mean field models) or inactive (e.g…
We present a model of systems of cells with intracellular oscillators (`clocks'). This is motivated by examples from developmental biology and from the behavior of organisms on the threshold to multicellularity. Cells undergo random motion…
Understanding cell fate selection remains a central challenge in developmental biology. We present a class of simple yet biologically-motivated mathematical models for cell differentiation that generically generate oscillations and hence…
Mathematical models of spatial population dynamics typically focus on the interplay between dispersal events and birth/death processes. However, for many animal communities, significant arrangement in space can occur on shorter timescales,…
A minimalistic model of the half-center oscillator is proposed. Within it, we consider dynamics of two excitable neurons interacting by means of the excitatory coupling. In the parameter space of the model, we identify the regions of…
Mounting evidence shows that oscillatory activity is widespread in cell signaling. Here we review some of this recent evidence, focusing on both the molecular mechanisms that potentially underlie such dynamical behavior, and the potential…
The spontaneous generation of electrical activity underpins a number of essential physiological processes, and is observed even in tissues where specialized pacemaker cells have not been identified. The emergence of periodic oscillations in…
The phase oscillator model with global coupling is extended to the case of finite-range nonlocal coupling. Under suitable conditions, peculiar patterns emerge in which a quasi-continuous array of identical oscillators separates sharply into…
A formalism is developed which describes the extent to which stochastic oscillations in biochemical models are synchronised. It is based on the calculation of the complex coherence function within the linear noise approximation. The method…
In this paper, we investigate the stability of the configurations of harmonic oscillator potential that are directly proportional to the square of the displacement. We derive expressions for fluctuations in partition function due to…
We investigate synchronization effects in quantum self-sustained oscillators theoretically using the micromaser as a model system. We use the probability distribution for the relative phase as a tool for quantifying the emergence of…
Many biological and chemical systems could be modeled by a population of oscillators coupled indirectly via a dynamical environment. Essentially, the environment by which the individual elements communicate is heterogeneous. Nevertheless,…
We analyze the emergence of synchronization in a population of moving integrate-and-fire oscillators. Oscillators, while moving on a plane, interact with their nearest neighbor upon firing time. We discover a non-monotonic dependence of the…
Synchronization of neurons forming a network with a hierarchical structure is essential for the brain to be able to function optimally. In this paper we study synchronization of phase oscillators on the most basic example of such a network,…
Theoretical studies of synchronization are usually based on models of coupled phase oscillators which, when isolated, have constant angular frequency. Stochastic discrete versions of these uniform oscillators have also appeared in the…