Related papers: Exponential Synchronization of 2D Cellular Neural …
In this work we study the synchronization of ring-structured cellular neural networks modeled by the lattice FitzHugh-Nagumo equations with boundary feedback. Through the uniform estimates of solutions and the analysis of dissipative…
In this work a new mathematical model for complex neural networks is presented by the partly diffusive FitzHugh-Nagumo equations with ensemble boundary coupling. We analyze the dissipative dynamics and boundary coupling dynamics of the…
A new mathematical model of neural networks described by diffusive FitzHugh-Nagumo equations with memristors and linear synaptic coupling is proposed and investigated. The existence of absorbing set for the solution semiflow in the energy…
A new mathematical model for complex neural networks of the partly diffusive Hindmasrh-Rose equations with boundary coupling is proposed. Through analysis of absorbing dynamics for the solution semiflow, the asymptotic synchronization of…
A new model of neural networks described by the memristive and diffusive Hindmarsh-Rose equations is proposed. Globally dissipative dynamics is shown with absorbing sets in the state spaces. Through sharp and uniform grouping estimates and…
In this article, we are interested in the behavior of a fully connected network of $N$ neurons, where $N$ tends to infinity. We assume that the neurons follow the stochastic FitzHugh-Nagumo model, whose specificity is the non-linearity with…
In this work, we present a new mathematical model of a boundary coupled neuron network described by the partly diffusive Hindmarsh-Rose equations. We prove the global absorbing property of the solution semiflow and then the main result on…
We discuss the synchronization of coupled neurons which are modelled as FitzHugh-Nagumo systems. As smallest entity in a larger network, we focus on two diffusively coupled subsystems, which can be interpreted as two mutually interacting…
The paper addresses the problem of parameter estimation (or identification) in dynamical networks composed of an arbitrary number of FitzHugh-Nagumo neuron models with diffusive couplings between each other. It is assumed that only the…
We study synchronization in heterogeneous FitzHugh-Nagumo networks. It is well known that heterogeneities in the nodes hinder synchronization when becoming too large. Here, we develop a controller to counteract the impact of these…
A new mathematical model of memristive neural networks described by the partly diffusive reaction-diffusion equations with weak synaptic coupling is proposed and investigated. Under rather general conditions it is proved that there exists…
We investigate the dynamics of a limit of interacting FitzHugh-Nagumo neurons in the regime of large interaction coefficients. We consider the dynamics described by a mean-field model given by a nonlinear evolution partial differential…
We consider an idealized network, formed by N neurons individually described by the FitzHugh-Nagumo equations and connected by electrical synapses. The limit for N to infinity of the resulting discrete model is thoroughly investigated, with…
We study synchronization in delay-coupled neural networks of heterogeneous nodes. It is well known that heterogeneities in the nodes hinder synchronization when becoming too large. We show that an adaptive tuning of the overall coupling…
Efforts to automate the reconstruction of neural circuits from 3D electron microscopic (EM) brain images are critical for the field of connectomics. An important computation for reconstruction is the detection of neuronal boundaries. Images…
The stochastic FitzHugh-Nagumo (FHN) model is a two-dimensional nonlinear stochastic differential equation with additive degenerate noise, whose first component, the only one observed, describes the membrane voltage evolution of a single…
Lipschitz Bound Estimation is an effective method of regularizing deep neural networks to make them robust against adversarial attacks. This is useful in a variety of applications ranging from reinforcement learning to autonomous systems.…
We characterize numerically the regime of anticipated synchronization in the coupled FitzHugh-Nagumo model for neurons. We consider two neurons, coupled unidirectionally (in a master-slave configuration), subject to the same random external…
First time in six decades, uncountable infinite exact solutions of FitzHugh-Nagumo model with diffusion have been found. FitzHugh-Nagumo model is a nonlinear dynamical system applicable to neurosciences, chemical kinetics, cell division,…
We examine the response of type II excitable neurons to trains of synaptic pulses, as a function of the pulse frequency and amplitude. We show that the resonant behavior characteristic of type II excitability, already described for harmonic…