Related papers: Dynamics of delay-coupled excitable neural systems
This paper considers $L_2$ and BIBO stability and stabilization issues for systems with time-varying delays which can be of retarded or neutral type. An important role is played by a nominal system with fixed delays which are close to the…
We investigate the stability of synchronization in networks of delay-coupled excitable neural oscillators. On the basis of the master stability function formalism, we demonstrate that synchronization is always stable for excitatory coupling…
The elapsed-time model describes the behavior of interconnected neurons through the time since their last spike. It is an age-structured non-linear equation in which age corresponds to the elapsed time since the last discharge, and models…
In this paper, we complete the global qualitative analysis of the well-known FitzHugh-Nagumo neuronal model. In particular, studying global limit cycle bifurcations and applying the Wintner-Perko termination principle for multiple limit…
We consider a stochastic perturbation of a FitzHugh-Nagumo system. We show that it is possible to generate oscillations for values of parameters which do not allow oscillations for the deterministic system. We also study the appearance of a…
The paper studies the excitability properties of a generalized FitzHugh-Nagumo model. The model differs from the purely competitive FitzHugh-Nagumo model in that it accounts for the effect of cooperative gating variables such as activation…
We study delay-induced transitions in consensus dynamics on signed networks with a ring topology. The proposed model is formulated as a system of delay differential equations incorporating both cooperative and antagonistic interactions, as…
The behavior of neurons can be modeled by the FitzHugh-Nagumo oscillator model, consisting of two nonlinear differential equations, which simulates the behavior of nerve impulse conduction through the neuronal membrane. In this work, we…
We study synchronization and rhythmic patterns generated in the heterogeneous cluster of FitzHugh$-$Nagumo oscillators with transition between self-oscillating and excitable elements. Such cluster models the sinoatrial node of the heart,…
We study a noisy oscillator with pulse delayed feedback, theoretically and in an electronic experimental implementation. Without noise, this system has multiple stable periodic regimes. We consider two types of noise: i) phase noise acting…
We consider the long-time behavior of a population of mean-field oscillators modeling the activity of interacting excitable neurons in large population. Each neuron is represented by its voltage and recovery variables, which are solution to…
The analysis on stability and bifurcations in the macroscopic dynamics exhibited by the system of two coupled large populations comprised of $N$ stochastic excitable units each is performed by studying an approximate system, obtained by…
Delay differential equations (DDEs) are widely used in mathematical modeling to describe physical and biological systems. Delays can impact model dynamics, resulting in oscillatory behavior. In physiological systems, this instability may…
In this paper we develop novel results on self triggering control of nonlinear systems, subject to perturbations and actuation delays. First, considering an unperturbed nonlinear system with bounded actuation delays, we provide conditions…
We investigate a ring of $N$ FitzHugh--Nagumo elements coupled in \emph{phase-repulsive} fashion and submitted to a (subthreshold) common oscillatory signal and independent Gaussian white noises. This system can be regarded as a reduced…
Dynamical systems with complex delayed interactions arise commonly when propagation times are significant, yielding complicated oscillatory instabilities. In this Letter, we introduce a class of systems with multiple, hierarchically long…
A new delay equation is introduced to describe the punctuated evolution of complex nonlinear systems. A detailed analytical and numerical investigation provides the classification of all possible types of solutions for the dynamics of a…
This paper studies the problem of event-triggered impulsive control for discrete-time systems. A novel periodic event-triggering scheme with two tunable parameters is presented to determine the moments of updating impulsive control signals…
We generalize the Kuramoto model of coupled oscillators to allow time-delayed interactions. New phenomena include bistability between synchronized and incoherent states, and unsteady solutions with time-dependent order parameters. We derive…
We investigate the dynamics of large, globally-coupled systems of Kuramoto oscillators with heterogeneous interaction delays. For the case of exponentially distributed time delays we derive the full stability diagram that describes the…