Related papers: Phase response function for oscillators with stron…
In many real-world oscillator systems, the phase response curves are highly heterogeneous. However, dynamics of heterogeneous oscillator networks has not been seriously addressed. We propose a theoretical framework to analyze such a system…
Building oscillator based computing systems with emerging nano-device technologies has become a promising solution for unconventional computing tasks like computer vision and pattern recognition. However, simulation and analysis of these…
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…
The phase reduction method for limit cycle oscillators subjected to weak perturbations has significantly contributed to theoretical investigations of rhythmic phenomena. We here propose a generalized phase reduction method that is also…
We study the synchronization behavior of a noisy network in which each system is driven by two sources of state-dependent noise: (1) an intrinsic noise which is common among all systems and can be generated by the environment or any…
Rhythmic behaviors in neural systems often combine features of limit cycle dynamics (stability and periodicity) with features of near heteroclinic or near homoclinic cycle dynamics (extended dwell times in localized regions of phase space).…
In a recent paper, Suppes et al. (2012) [arXiv:arXiv:1010.3063] used neural oscillators to create a model, based on reasonable neurophysiological assumptions, of the behavioral stimulus-response (SR) theory. In this paper, we describe the…
Pulse-coupled threshold units serve as paradigmatic models for a wide range of complex systems. When the state variable of a unit crosses a threshold, the unit sends a pulse that is received by other units, thereby mediating the…
In a recent paper [Chaos 30, 073139 (2020)] we analyzed an extension of the Winfree model with nonlinear interactions. The nonlinear coupling function Q was mistakenly identified with the non-infinitesimal phase-response curve (PRC). Here,…
Small continuous sensory and mechanical perturbations have often been used to identify properties of the closed-loop neural control of posture and other systems that are approximately linear time invariant. Here we extend this approach to…
We study an extension of the Winfree model of coupled phase oscillators in which both natural frequencies and phase-response curves (PRCs) are heterogeneous. In the first part of the paper we resort to averaging and derive an approximate…
We consider a simple dynamic model of the vibrating screen operating in the parametric resonance (PR) mode. This model was used in the course of designing and setting of such a screen in LPMC. The PR-based screen compares favorably with…
When dynamical systems that produce rhythmic behaviors operate within hard limits, they may exhibit limit cycles with sliding components, that is, closed isolated periodic orbits that make and break contact with a constraint surface.…
Models of coupled oscillators are useful in describing a wide variety of phenomena in physics, biology and economics. These models typically rest on the premise that the oscillators are weakly coupled, meaning that amplitudes can be assumed…
We present an approach for reconstructing networks of pulse-coupled neuron-like oscillators from passive observation of pulse trains of all nodes. It is assumed that units are described by their phase response curves and that their phases…
Populations of flashing fireflies, claps of applauding audience, cells of cardiac and circadian pacemakers reach synchrony via event-triggered interactions, referred to as pulse couplings. Synchronization via pulse coupling is widely used…
The phase reduction technique is essential for studying rhythmic phenomena across various scientific fields. It allows the complex dynamics of high-dimensional oscillatory systems to be expressed by a single phase variable. This paper…
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…
The resonances of forced dynamical systems occur when either the amplitude of the frequency response undergoes a local maximum (amplitude resonance) or phase lag quadrature takes places (phase resonance). This study focuses on the phase…
We formulate a reduction theory that describes the response of an oscillator network as a whole to external forcing applied nonuniformly to its constituent oscillators. The phase description of multiple oscillator networks coupled weakly is…