相关论文: Nonlocal control of pulse propagation in excitable…
We demonstrate that nonlocal coupling enables control of the collective stochastic dynamics in the regime of coherence resonance. The control scheme based on the nonlocal interaction properties is presented by means of numerical simulation…
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…
A one-component bistable reaction-diffusion system with asymmetric nonlocal coup ling is derived as limiting case of a two-component activator-inhibitor reaction -diffusion model with differential advection. The effects of asymmetric…
We prove the existence of fast traveling pulse solutions in excitable media with non-local coupling. Existence results had been known, until now, in the case of local, diffusive coupling and in the case of a discrete medium, with…
We consider the effects of a Mexican-hat-shaped nonlocal spatial coupling, i.e., symmetric long-range inhibition superimposed with short-range excitation, upon front propagation in a model of a bistable reaction-diffusion system. We show…
The onset of pulse propagation is studied in a reaction-diffusion (RD) model with control by augmented transmission capability that is provided either along nonlocal spatial coupling or by time-delayed feedback. We show that traveling…
A commonly accepted feature of an excitable medium is that a local excitation leads to a propagation of circular or spiral excitation wave-fronts. This is indeed the case in fully excitable medium. However, with a decrease of an…
Models of pulse formation in nerve conduction have provided manifold insight not only into neuronal dynamics but also the non-linear dynamics of pulse formation in general. Recent observation of neuronal electro-chemical pulses also driving…
Transient wave forms in neural networks with diffusive and nonlocal coupling have attracted particular interest because they may mediate recruitment of healthy cortical tissue into a pathological state during migraine. To investigate this…
We study reaction-diffusion waves on curved two-dimensional surfaces, and determine the influence of curvature upon the nucleation and propagation of spatially localized waves in an excitable medium modelled by the generic FitzHugh-Nagumo…
Based on methods of numerical simulation, the constructive role of nonlocal coupling is demonstrated in the context of wavefront propagation observed in an ensemble of overdamped bistable oscillators. Firstly, it is shown that the wavefront…
In this paper, we report on the generation and propagation of traveling pulses in a homogeneous network of diffusively coupled, excitable, slow-fast dynamical neurons. The spatially extended system is modelled using the nearest neighbor…
Understanding how external stimuli propagate in neural systems is an important challenge in the fields of neuroscience and nonlinear dynamics. Despite extensive studies over several decades, this problem remains poorly understood. In this…
In the bistable regime of the FitzHugh-Nagumo model of reaction-diffusion systems, spatially homogeneous patterns may be nonlinearly unstable to the formation of compact ``localized states." The formation of space-filling patterns from…
How individual dispersal patterns and human intervention behaviours affect the spread of infectious diseases constitutes a central problem in epidemiological research. This paper develops an impulsive nonlocal faecal-oral model with free…
We explore the influence of a block of excitable units on the existence and behavior of chimera states in a nonlocally coupled ring-network of FitzHugh-Nagumo elements. The FitzHugh-Nagumo system, a paradigmatic model in many fields from…
In this paper, we study an excitable, biophysical system that supports wave propagation of nerve impulses. We consider a slow-fast, FitzHugh-Rinzel neuron model where only the membrane voltage interacts diffusively, giving rise to the…
In various neurological disorders spatio-temporal excitation patterns constitute examples of excitable behavior emerging from pathological pathways. During migraine, seizure, and stroke an initially localized pathological state can…
We developed a new self-adjoint, consistent, and stable coupling strategy for nonlocal diffusion models, inspired by the quasinonlocal atomistic-to-continuum method for crystalline solids. The proposed coupling model is coercive with…
Nonlinear dynamical stochastic models are ubiquitous in different areas. Excitable media models are typical examples with large state dimensions. Their statistical properties are often of great interest but are also very challenging to…