Related papers: Analysis of biological integrate-and-fire oscillat…
Oscillator models are central to the study of system properties such as entrainment or synchronization. Due to their nonlinear nature, few system-theoretic tools exist to analyze those models. The paper develops a sensitivity analysis for…
We develop a framework in which the activity of nonlinear pulse-coupled oscillators is posed within the renewal theory. In this approach, the evolution of inter-event density allows for a self-consistent calculation that determines the…
We study the global dynamics of integrate and fire neural networks composed of an arbitrary number of identical neurons interacting by inhibition and excitation. We prove that if the interactions are strong enough, then the support of the…
Living systems have time-evolving interactions that, until recently, could not be identified accurately from recorded time series in the presence of noise. Stankovski et al. (Phys. Rev. Lett. 109 024101, 2012) introduced a method based on…
Collective behavior of pulse-coupled oscillators has been investigated widely. As an example of pulse-coupled networks, fireflies display many kinds of flashing patterns. Mirollo and Strogatz (1990) proposed a pulse-coupled oscillator model…
Feasible setup for pulsed quantum non-demolition interaction between two distant mechanical oscillators through optical or microwave mediator is proposed. The proposal uses homodyne measurement of the mediator and feedforward control of the…
The model of coupled oscillators plays an important role in modern physics. It is used for description of various processes: from vibrations atoms in solid states to electromagnetic oscillations in slow-wave structures. The model with…
Intermittent synchronization is observed in a variety of different experimental settings in physics and beyond and is an established research topic in nonlinear dynamics. When coupled oscillators exhibit relatively weak, intermittent…
In this work we consider a general non-autonomous hybrid system based on the integrate-and-fire model, widely used as simplified version of neuronal models and other types of excitable systems. Our unique assumption is that the system is…
Excitable systems with delayed feedback are important in areas from biology to neuroscience and optics. They sustain multistable pulsing regimes with different number of equidistant pulses in the feedback loop. Experimentally and…
We analyze two pulse-coupled resonate-and-fire neurons. Numerical simulation reveals that an anti-phase state is an attractor of this model. We can analytically explain the stability of anti-phase states by means of a return map of firing…
Synchronization of two or more self-sustained oscillators is a well-known and studied phenomenon, appearing both in natural and designed systems. In some cases, the synchronized state is undesired, and the aim is to destroy synchrony by…
Intractable phase dynamics often challenge our understanding of complex oscillatory systems, hindering the exploration of synchronisation, chaos, and emergent phenomena across diverse fields. We introduce a novel conceptual framework for…
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…
A simple system composed of electronic oscillators capable of emitting and detecting light-pulses is studied. The oscillators are biologically inspired, their behavior is designed for keeping a desired light intensity, W, in the system.…
The possibility of production of pulses with scale-invariant properties at presence of fluctuations of parameters of self-oscillatory system with three-dimensional phase space is shown. The system of equations of inertial nonlinearity…
Synchronization is studied in an array of identical linear oscillators of arbitrary order, coupled through a dynamic network comprising dissipative connectors (e.g., dampers) and restorative connectors (e.g., springs). The coupling network…
Driven by increased applications in biological networks and wireless sensor networks, synchronization of pulse-coupled oscillators (PCOs) has gained increased popularity. However, most existing results address the local synchronization of…
Nonlinear isolated and coupled oscillators are extensively studied as prototypical nonlinear dynamics models. Much attention has been devoted to oscillator synchronization or the lack thereof. Here, we study the synchronization and…
Coupled parametric oscillators were recently employed as simulators of artificial Ising networks, with the potential to solve computationally hard minimization problems. We demonstrate a new dynamical regime within the simplest network -…