Related papers: Integrate-and-fire models with an almost periodic …
Up to now, modern Machine Learning is mainly based on fitting high dimensional functions to enormous data sets, taking advantage of huge hardware resources. We show that biologically inspired neuron models such as the…
We present a mathematical analysis of a networks with Integrate-and-Fire neurons and adaptive conductances. Taking into account the realistic fact that the spike time is only known within some \textit{finite} precision, we propose a model…
This paper investigates the existence of almost periodic traveling fronts for Fisher-KPP lattice equations in one-dimensional almost periodic media. By the Lyapunov exponent of the linearized operator near the unstable steady state, we give…
Spike correlations between neurons are ubiquitous in the cortex, but their role is at present not understood. Here we describe the firing response of a leaky integrate-and-fire neuron (LIF) when it receives a temporarily correlated input…
Spiking Neural Networks (SNNs) are valued for their ability to process spatio-temporal information efficiently, offering biological plausibility, low energy consumption, and compatibility with neuromorphic hardware. However, the commonly…
We briefly review and highlight the consequences of rigorous and exact results obtained in \cite{cessac:10}, characterizing the statistics of spike trains in a network of leaky Integrate-and-Fire neurons, where time is discrete and where…
Fixed-time stable dynamical systems are capable of achieving exact convergence to an equilibrium point within a fixed time that is independent of the initial conditions of the system. This property makes them highly appealing for designing…
Resolving fluid transport at engine surfaces is required to predict transient heat loss, which is becoming increasingly important for the development of high-efficiency internal combustion engines (ICE). The limited number of available…
An analytical description of the response properties of simple but realistic neuron models in the presence of noise is still lacking. We determine completely up to the second order the firing statistics of a single and a pair of leaky…
The search for Lyapunov functions is a crucial task in the analysis of nonlinear systems. In this paper, we present a physics-informed neural network (PINN) approach to learning a Lyapunov function that is nearly maximal for a given stable…
We study the stability properties of a class of time-varying nonlinear systems. We assume that non-strict input-to-state stable (ISS) Lyapunov functions for our systems are given and posit a mild persistency of excitation condition on our…
Analysis of transient stability of strongly nonlinear post-fault dynamics is one of the most computationally challenging parts of Dynamic Security Assessment. This paper proposes a novel approach for assessment of transient stability of the…
Nonlinear Noisy Leaky Integrate and Fire (NNLIF) models for neurons networks can be written as Fokker-Planck-Kolmogorov equations on the probability density of neurons, the main parameters in the model being the connectivity of the network…
We construct an exactly solvable circuit of interacting memristors and study its dynamics and fixed points. This simple circuit model interpolates between decoupled circuits of isolated memristors, and memristors in series, for which exact…
We develop a formalism to analyze the behaviour of pulse--coupled identical phase oscillators with a specific attention devoted to the onset of partial synchronization. The method, which allows describing the dynamics both at the…
We provide general methods for explicitly constructing strict Lyapunov functions for fully nonlinear slowly time-varying systems. Our results apply to cases where the given dynamics and corresponding frozen dynamics are not necessarily…
In contexts where data samples represent a physically stable state, it is often assumed that the data points represent the local minima of an energy landscape. In control theory, it is well-known that energy can serve as an effective…
In order to ease the analysis of error propagation in neuromorphic computing and to get a better understanding of spiking neural networks (SNN), we address the problem of mathematical analysis of SNNs as endomorphisms that map spike trains…
We study the global dynamics of integrate and fire neural networks composed of an arbitrary number of identical neurons interacting by inhibition and excitation. We prove that if the interactions are strong enough, then the support of the…
Machine learning techniques have demonstrated their effectiveness in achieving autonomy and optimality for nonlinear and high-dimensional dynamical systems. However, traditional black-box machine learning methods often lack formal stability…