Related papers: Mean field approximation for noisy delay coupled e…

In this paper, we deepen the analysis of continuous time Fictitious Play learning algorithm to the consideration of various finite state Mean Field Game settings (finite horizon, $\gamma$-discounted), allowing in particular for the…

This paper is concerned with a linear-quadratic mean field Stackelberg stochastic differential game with partial information and common noise, which contains a leader and a large number of followers. To be specific, the followers face a…

Mean field games (MFGs) offer a powerful framework for modeling large-scale multi-agent systems. This paper addresses MFGs formulated in continuous time with discrete state spaces, where agents' dynamics are governed by continuous-time…

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…

We formulate the MFG limit for $N$ interacting agents with a common noise as a single quasi-linear deterministic infinite-dimensional partial differential second order backward equation. We prove that any its (regular enough) solution…

We consider synchronization by noise for stochastic partial differential equations which support traveling pulse solutions, such as the FitzHugh-Nagumo equation. We show that any two pulse-like solutions which start from different positions…

We consider pulse-coupled Leaky Integrate-and-Fire neural networks with randomly distributed synaptic couplings. This random dilution induces fluctuations in the evolution of the macroscopic variables and deterministic chaos at the…

We consider a general multidimensional stochastic differential delay equation (SDDE) with state-dependent colored noises. We approximate it by a stochastic differential equation (SDE) system and calculate its limit as the time delays and…

Here we present a study of stochastic resonance in an extended FitzHugh-Nagumo system with a field dependent activator diffusion. We show that the system response (here measured through the output signal-to-noise ratio) is enhanced due to…

In this paper, we study the long-time behavior of mean field game (MFG) systems influenced by a common noise. While classical results establish the convergence of deterministic MFG towards stationary solutions under suitable monotonicity…

We analytically study the input-output properties of a neuron whose active dendritic tree, modeled as a Cayley tree of excitable elements, is subjected to Poisson stimulus. Both single-site and two-site mean-field approximations incorrectly…

We consider a network of randomly coupled rate-based neurons influenced by external and internal noise. We derive a second-order stochastic mean-field model for the network dynamics and use it to analyze the stability and bifurcations in…

Neuronal excitability is the phenomena that describes action potential generation due to a stimulus input. Commonly, neuronal excitability is divided into two classes: Type I and Type II, both having different properties that affect…

We consider the coaction of two distinct noise sources on the activation process of a single and two interacting excitable units, which are mathematically described by the Fitzhugh-Nagumo equations. We determine the most probable activation…

We study the mean field game problem for a nervous system consisting of a large number of neurons with mean-field interaction. In this system, each neuron can modulate its spiking activity by controlling its membrane potential to…

This paper focuses on exploring the convergence properties of a generic player's trajectory and empirical measures in an N-player Linear-Quadratic-Gaussian Nash game, where Brownian motion serves as the common noise. The study establishes…

We consider the effect of distributed delays in neural feedback systems. The avian optic tectum is reciprocally connected with the nucleus isthmi. Extracellular stimulation combined with intracellular recordings reveal a range of signal…

In this note, we clarify the well-posedness of the limit equations to the mean-field $N$-neuron models proposed in Baladron et al. and we prove the associated propagation of chaos property. We also complete the modeling issue in Baladron et…

By using a semi-analytical dynamical mean-field approximation previously proposed by the author [H. Hasegawa, Phys. Rev. E, {\bf 70}, 066107 (2004)], we have studied the synchronization of stochastic, small-world (SW) networks of…

We study the interplay between diversity and noise in a 3D network of FitzHugh-Nagumo elements, with topology and dimensions chosen to model a pancreatic beta-cell cluster, as an example of an excitable cell network. Our results show that…