Related papers: Dynamics of delay-coupled excitable neural systems
We discuss synchronization in networks of neuronal oscillators which are interconnected via diffusive coupling, i.e. linearly coupled via gap junctions. In particular, we present sufficient conditions for synchronization in these networks…
We show that peculiar collective dynamics called slow switching arises in a population of leaky integrate-and-fire oscillators with delayed, all-to-all pulse-couplings. By considering the stability of cluster states and symmetry possessed…
We study a system of globally coupled FitzHugh-Nagumo oscillators, showing that the presence of higher-order interactions affects the character of the transition between synchronous and asynchronous states. In particular, we demonstrate…
We study the dynamics of a reaction-diffusion system composed of two mutually coupled excitable fibers. We focus on the situation in which dynamical properties of the two fibers are not identical because of the parameter difference between…
For networks of pulse-coupled oscillators with delayed excitatory coupling, we analyze the firing behaviors depending on coupling strength and transmission delay. The parameter space consisting of strength and delay is partitioned into two…
In this manuscript, we study the problem of robust synchronization in networks of diffusively time-delayed coupled nonlinear systems. In particular, we prove that, under some mild conditions on the input-output dynamics of the systems and…
Propagation of pulses in myelinated fibers may be described by appropriate solutions of spatially discrete FitzHugh-Nagumo systems. In these systems, propagation failure may occur if either the coupling between nodes is not strong enough or…
The dynamics of three mutually coupled cortical neurons with time delays in the coupling are explored numerically and analytically. The neurons are coupled in a line, with the middle neuron sending a somewhat stronger projection to the…
We consider a Kuramoto model for the dynamics of an excitable system consisting of two coupled active rotators. Depending on both the coupling strength and the noise, the two rotators can be in a synchronized or desynchronized state. The…
Cells and tissues exhibit oscillatory deformations during remodelling, migration or embryogenesis. Although it has been shown that these oscillations correlate with cell biochemical signalling, it is yet unclear the role of these…
This paper investigates the stability and stabilization of diffusively coupled network dynamical systems. We leverage Lyapunov methods to analyze the role of coupling in stabilizing or destabilizing network systems. We derive critical…
We explore a biomimetic model that simulates a cell, with the internal cytoplasm represented by a two-dimensional circular domain and the external cortex by a surrounding ring, both modeled using FitzHugh-Nagumo systems. The external ring…
Existence of a new type of oscillating synchronization that oscillates between three different types of synchronizations (anticipatory, complete and lag synchronizations) is identified in unidirectionally coupled nonlinear time-delay…
This paper investigates the global stability and the global asymptotic stability independent of the sizes of the delays of linear time-varying Caputo fractional dynamic systems of real fractional order possessing internal point delays. The…
We study delay-independent stability in nonlinear models with a distributed delay which have a positive equilibrium. Such models frequently occur in population dynamics and other applications. In particular, we construct a relevant…
Noise-induced dynamics of a prototypical bistable system with delayed feedback is studied theoretically and numerically. For small noise and magnitude of the feedback, the problem is reduced to the analysis of the two-state model with…
Many natural systems including the brain comprise coupled non-uniformly stimulated elements. In this paper we show that heterogeneously driven networks of excitatory-inhibitory units exhibit striking collective phenomena, including…
Learning how complex dynamical systems evolve over time is a key challenge in system identification. For safety critical systems, it is often crucial that the learned model is guaranteed to converge to some equilibrium point. To this end,…
Many neurons display bistability - coexistence of two firing modes such as bursting and tonic spiking or tonic spiking and silence. Bistability has been proposed to endow neurons with richer forms of information processing in general and to…
Additive noise is known to produce counter-intuitive behaviors in nonlinear dynamical systems. Previously, it was shown that systems with a deterministic limit cycle can display bistable switching between metastable states in the presence…