相关论文: Networks of piecewise linear neural mass models

We propose a general framework to extract microscopic interactions from raw configurations with deep neural networks. The approach replaces the modeling Hamiltonian by the neural networks, in which the interaction is encoded. It can be…

Diffusion-driven instability is a fundamental mechanism underlying pattern formation in spatially extended systems. In almost all existing works, diffusion across the links of the underlying network is modeled through scalar weights,…

We quantify the finite size effects in a stochastic network made up of rate neurons, for several kinds of recurrent connectivity matrices. This analysis is performed by means of a perturbative expansion of the neural equations, where the…

The problem of synchronization in heterogeneous networks of linear systems with nonlinear delayed diffusive coupling is considered. The network is presented in new coordinates mean-field dynamics and synchronization errors. Thus the problem…

The random transitions of ion channels between conducting and non-conducting states generate a source of internal fluctuations in a neuron, known as channel noise. The standard method for modeling fluctuations in the states of ion channels…

To understand the structural dynamics of a large-scale social, biological or technological network, it may be useful to discover behavioral roles representing the main connectivity patterns present over time. In this paper, we propose a…

The stability of synchronous states is analysed in the context of two populations of inhibitory and excitatory neurons, characterized by different pulse-widths. The problem is reduced to that of determining the eigenvalues of a suitable…

A recurrent neural network with noisy input is studied analytically, on the basis of a Discrete Time Master Equation. The latter is derived from a biologically realizable learning rule for the weights of the connections. In a numerical…

The process of training an artificial neural network involves iteratively adapting its parameters so as to minimize the error of the network's prediction, when confronted with a learning task. This iterative change can be naturally…

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…

Many real-world scale-free networks, such as neural networks and online communication networks, consist of a fixed number of nodes but exhibit dynamic edge fluctuations. However, traditional models frequently overlook scenarios where the…

Simultaneous recordings from many neurons hide important information and the connections characterizing the network remain generally undiscovered despite the progresses of statistical and machine learning techniques. Discerning the presence…

For a class of coupled limit cycle oscillators, we give a condition on a linear coupling operator that is necessary and sufficient for exponential stability of the synchronous solution. We show that with certain modifications our method of…

We study a generic family of nonlinear dynamics on undirected networks generalising linear consensus. We find a compact expression for its equilibrium points in terms of the topology of the network and classify their stability using the…

The process of pattern formation for a multi-species model anchored on a time varying network is studied. A non homogeneous perturbation superposed to an homogeneous stable fixed point can amplify, as follows a novel mechanism of…

The nonlinear evolution of current filaments generated by the Weibel-type filamentation instability is a topic of prime interest in space and laboratory plasma physics. In this paper, we investigate the stability of a stationary periodic…

Phase control of parametric modulation in coupled oscillator networks enables sculpting of dynamical states with desired spatiotemporal symmetries. Symmetry-aware Floquet analysis successfully predicts such states in linear systems, but…

Characterizing the emergence of chaotic dynamics of complex networks is an essential task in nonlinear science with potential important applications in many fields such as neural control engineering, microgrid technologies, and ecological…

Real-world complex systems such as ecological communities and neuron networks are essential parts of our everyday lives. These systems are composed of units which interact through intricate networks. The ability to predict sudden changes in…

Understanding neural dynamics is a central topic in machine learning, non-linear physics and neuroscience. However, the dynamics is non-linear, stochastic and particularly non-gradient, i.e., the driving force can not be written as gradient…