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Oscillator networks display intricate synchronization patterns. Determining their stability typically requires incorporating the symmetries of the network coupling. Going beyond analyses that appeal only to a network's automorphism group,…
Advances in neural recording methods enable sampling from populations of thousands of neurons during the performance of behavioral tasks, raising the question of how recorded activity relates to the theoretical models of computations…
This paper tackles the problem of nonlinear systems, with sublinear growth but unbounded control, under perturbation of some time-varying state constraints. It is shown that, given a trajectory to be approximated, one can find a neighboring…
Here we numerically study a model of excitable media, namely, a network with occasionally quiet nodes and connection weights that vary with activity on a short-time scale. Even in the absence of stimuli, this exhibits unstable dynamics,…
This paper reports the analysis of the dynamics of a model of pulse-coupled oscillators with global inhibitory coupling. The model is inspired by experiments on colonies of bacteria-embedded synthetic genetic circuits. The total population…
We study the collective behaviour of an ensemble of coupled motile elements whose interactions depend on time and are alternatively attractive or repulsive. The evolution of interactions is driven by individual internal variables with…
We demonstrate that strongly asymmetric limit cycles can be observed in the system of three identical ring oscillators (3-gene networks known as Repressilators) globally coupled by signal molecule diffusion added to the model in a way like…
Limit cycles are self-sustained, closed trajectories in phase space representing (un)-stable, periodic behavior in nonlinear dynamical systems. They underpin diverse natural phenomena, from neuronal firing patterns to engineering…
This work concerns a many-body deterministic model that displays life-like properties as emergence, complexity, self-organization, spontaneous compartmentalization, and self-regulation. The model portraits the dynamics of an ensemble of…
Finding the conditions that foster synchronization in networked oscillatory systems is critical to understanding a wide range of biological and mechanical systems. However, the conditions proved in the literature for synchronization in…
In this study, we investigate the continuous time dynamics of Recurrent Neural Networks (RNNs), focusing on systems with nonlinear activation functions. The objective of this work is to identify conditions under which RNNs exhibit perpetual…
A sufficiently connected topology linking the constituent units of a complex system is usually seen as a prerequisite for the emergence of collective phenomena such as synchronization. We present a random network of heterogeneous phase…
We study analytically the dynamics of a network of sparsely connected inhibitory integrate-and-fire neurons in a regime where individual neurons emit spikes irregularly and at a low rate. In the limit when the number of neurons N tends to…
We study emergent oscillatory behavior in networks of diffusively coupled nonlinear ordinary differential equations. Starting from a situation where each isolated node possesses a globally attracting equilibrium point, we give, for an…
Canards, special trajectories that follow invariant repelling slow manifolds for long time intervals, have been frequently observed in slow-fast systems of either biological, chemical and physical nature. Here, collective canard explosions…
We present continuum models that describe the evolution of the position of a random walker on a growing network using four different growth algorithms. Three of these involve a random element, including one in which the motility rate of the…
We consider a random process on recursive trees, with three types of events. Vertices give birth at a constant rate (growth), each edge may be removed independently (fragmentation of the tree) and clusters (or trees) are frozen with a rate…
Networks of chaotic units with static couplings can synchronize to a common chaotic trajectory. The effect of dynamic adaptive couplings on the cooperative behavior of chaotic networks is investigated. The couplings adjust to the activities…
Scrambling of information in a quantum many-body system, quantified by the out-of-time-ordered correlator (OTOC), is a key manifestation of quantum chaos. A regime of exponential growth in the OTOC, characterized by a Lyapunov exponent, has…
We study a family of binary state, socially-inspired contagion models which incorporate imitation limited by an aversion to complete conformity. We uncover rich behavior in our models whether operating with either probabilistic or…