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This paper studies impulsive stabilization of nonlinear systems. We propose two types of event-triggering algorithms to update the impulsive control signals with actuation delays. The first algorithm is based on continuous event detection,…
We study the stability of the dynamics of a network of n neurons intercting linearly through a random gaussian matrix of excitatory and inhibitory type. Using the aproach developed in a previous paper we show some interesting properties of…
Most models of neurons incorporate a capacitor to account for the marked capacitive behavior exhibited by the cell membrane. However, such capacitance is widely considered constant, thereby neglecting the possible effects of time-dependent…
In exploring the simulation of human rhythmic perception and synchronization capabilities, this study introduces a computational model inspired by the physical and biological processes underlying rhythm processing. Utilizing a reservoir…
Systematic generalization aims to evaluate reasoning about novel combinations from known components, an intrinsic property of human cognition. In this work, we study systematic generalization of NNs in forecasting future time series of…
This paper models the dynamics of a large set of interacting neurons within the framework of statistical field theory. We use a method initially developed in the context of statistical field theory [44] and later adapted to complex systems…
We introduce a dynamical spatio-temporal model formalized as a recurrent neural network for forecasting time series of spatial processes, i.e. series of observations sharing temporal and spatial dependencies. The model learns these…
We develop a new framework for the study of complex continuous time dynamical systems based on viewing them as collections of interacting control modules. This framework is inspired by and builds upon the groupoid formalism of Golubitsky,…
Modeling dynamical systems plays a crucial role in capturing and understanding complex physical phenomena. When physical models are not sufficiently accurate or hardly describable by analytical formulas, one can use generic function…
Generative models of brain activity have been instrumental in testing hypothesized mechanisms underlying brain dynamics against experimental datasets. Beyond capturing the key mechanisms underlying spontaneous brain dynamics, these models…
Neurons fire irregularly on multiple timescales when stimulated with a periodic pulse train. This raises two questions: Does this irregularity imply significant intrinsic stochasticity? Can existing neuron models be readily extended to…
This paper builds on the connection between graph neural networks and traditional dynamical systems. We propose continuous graph neural networks (CGNN), which generalise existing graph neural networks with discrete dynamics in that they can…
Turn-taking behaviour is simulated in a coupled agents system. Each agent is modelled as a mobile robot with two wheels. A recurrent neural network is used to produce the motor outputs and to hold the internal dynamics. Agents are developed…
Metastability, characterized by a variability of regimes in time, is a ubiquitous type of neural dynamics. It has been formulated in many different ways in the neuroscience literature, however, which may cause some confusion. In this…
Today, complex networks have attracted increasing attention from various fields of science and engineering. It has been demonstrated that many complex networks display various synchronization phenomena. In this paper, we introduce a…
The review presents a parameter switching algorithm and his applications which allows numerical approximation of any attractor of a class of continuous-time dynamical systems depending linearly on a real parameter. The considered classes of…
This work reports a compact behavioral model for gated-synaptic memory. The model is developed in Verilog-A for easy integration into computer-aided design of neuromorphic circuits using emerging memory. The model encompasses various forms…
Research in multistable systems is a flourishing field with countless examples and applications across scientific disciplines. I present a catalog of multistable dynamical systems covering relevant fields of knowledge. This work is focused…
We construct and analyze a rate-based neural network model in which self-interacting units represent clusters of neurons with strong local connectivity and random inter-unit connections reflect long-range interactions. When sufficiently…
Learning the dynamics of complex systems features a large number of applications in data science. Graph-based modeling and inference underpins the most prominent family of approaches to learn complex dynamics due to their ability to capture…