Related papers: Synchronization of Boundary Coupled Hindmarsh-Rose…
This paper presents a framework for the study of convergence when the nodes' dynamics may be both piecewise smooth and/or nonidentical across the network. Specifically, we derive sufficient conditions for global convergence of all node…
The cooperative behavior of neurons and neuronal areas associated with the synchronization behavior proves to be a fundamental neural mechanism. In addition, abnormal levels of synchronization have been related to unhealthy 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…
The rate coding response of a single peripheral sensory neuron in the asymptotic, near-equilibrium limit can be derived using information theory, asymptotic Bayesian statistics and a theory of complex systems. Almost no biological knowledge…
Synchronous firing of neurons is thought to play important functional roles such as feature binding and switching of cognitive states. Although synchronization has mainly been investigated using model neurons with simple connection topology…
This paper is concerned with the global existence and stability of solution to the quasi linear hyperbolic-parabolic chemotaxis system on the half-line,which was proposed in[1] to primarily describe the formation of coherent vascular…
Networks of model neurons with balanced recurrent excitation and inhibition produce irregular and asynchronous spiking activity. We extend the analysis of balanced networks to include the known dependence of connection probability on the…
We propose a boundary neuron method with random features (BNM-RF) for solving partial differential equations. The method approximates the unknown boundary function by a shallow network within the boundary integral formulation. With randomly…
We study the asymptotic behavior for asymmetric neuronal dynamics in a network of linear Hopfield neurons. The interaction between the neurons is modeled by random couplings which are centered i.i.d. random variables with finite moments of…
Synchronization underlies phenomena including memory and perception in the brain, coordinated motion of animal flocks, and stability of the power grid. These synchronization phenomena are often modeled through networks of phase-coupled…
We present a study on the emergence of a variety of spatio temporal patterns among neurons that are connected in a multiplex framework, with neurons on two layers with different functional couplings. With the Hindmarsh-Rose model for the…
There is a strong nexus between the network size and the computational resources available, which may impede a neuroscience study. In the meantime, rescaling the network while maintaining its behavior is not a trivial mission. Additionally,…
In this work we are interested in a mathematical model of the collective behavior of a fully connected network of finitely many neurons, when their number and when time go to infinity. We assume that every neuron follows a stochastic…
A unified approach for analyzing synchronization in coupled systems of autonomous differential equations is presented in this work. Through a careful analysis of the variational equation of the coupled system we establish a sufficient…
We investigate singularly perturbed elliptic problems with multiplicative nonlocal diffusion terms subject to Robin boundary conditions. The diffusion depends on a global quantity of the solution, which introduces a nonlocal coupling…
In this work, we propose a nonlinear stochastic model of a network of stochastic spiking neurons. We heuristically derive the mean-field limit of this system. We then design a Monte Carlo method for the simulation of the microscopic system,…
In this paper, we present a novel deep learning approach, deeply-fused nets. The central idea of our approach is deep fusion, i.e., combine the intermediate representations of base networks, where the fused output serves as the input of the…
We study the asymptotic law of a network of interacting neurons when the number of neurons becomes infinite. Given a completely connected network of neurons in which the synaptic weights are Gaussian correlated random variables, we describe…
Characterizing the in uence of network properties on the global emerging behavior of interacting elements constitutes a central question in many areas, from physical to social sciences. In this article we study a primary model of disordered…
We investigate localized wave solutions in a network of Hindmarsh-Rose neural model taking into account the long-range diffusive couplings. We show by a specific analytical technique that the model equations in the infrared limit (wave…