Related papers: Self-organized stochastic tipping in slow-fast dyn…
We present a neurobiologically--inspired stochastic cellular automaton whose state jumps with time between the attractors corresponding to a series of stored patterns. The jumping varies from regular to chaotic as the model parameters are…
Predicting the behavior of complex systems is critical in many scientific and engineering domains, and hinges on the model's ability to capture their underlying dynamics. Existing methods encode the intrinsic dynamics of high-dimensional…
We consider a white noise perturbation of dynamics in the neighborhood of a heteroclinic network. We show that under the logarithmic time rescaling the diffusion converges in distributon in a special topology to a piecewise constant process…
The brain is believed to operate in part by making predictions about sensory stimuli and encoding deviations from these predictions in the activity of "prediction error neurons." This principle defines the widely influential theory of…
Tipping points (TP) are abrupt transitions between metastable states in complex systems, most often described by a bifurcation or crisis of a multistable system induced by a slowly changing control parameter. An avenue for predicting TPs in…
Noise can shape the firing behaviors of neurons. Here, we show that noise acting on the fast variable of the Hedgehog burster can tune the spike counts of bursts via the self-induced stochastic resonance (SISR) phenomenon. Using the…
Transitions between multiple stable states of nonlinear systems are ubiquitous in physics, chemistry, and beyond. Two types of behaviors are usually seen as mutually exclusive: unpredictable noise-induced transitions and predictable…
A parabolic stochastic PDE is studied analytically and numerically, when a bifurcation parameter is slowly increased through its critical value. The aim is to understand the effect of noise on delayed bifurcations in systems with spatial…
Distributed optimization has become the default training paradigm in modern machine learning due to the growing scale of models and datasets. To mitigate communication overhead, local updates are often applied before global aggregation,…
Stochastic spreading models defined on complex network topologies are used to mimic the diffusion of diseases, information, and opinions in real-world systems. Existing theoretical approaches to the characterization of the models in terms…
We theoretically describe how weak signals may be efficiently transmitted throughout more than one frequency range in noisy excitable media by kind of stochastic multiresonance. This serves us here to reinterpret recent experiments in…
Self-sustained subthreshold oscillations in a discrete-time model of neuronal behavior are considered. We discuss bifurcation scenarios explaining the birth of these oscillations and their transformation into tonic spikes. Specific features…
A steadily increasing body of evidence suggests that the brain performs probabilistic inference to interpret and respond to sensory input and that trial-to-trial variability in neural activity plays an important role. The neural sampling…
A goal of data assimilation is to infer stochastic dynamical behaviors with available observations. We consider transition phenomena between metastable states for a stochastic system with (non-Gaussian) $\alpha-$stable L\'evy noise. With…
We analyze transport on a graph with multiple constraints and where the weight of the edges connecting the nodes is a dynamical variable. The network dynamics results from the interplay between a nonlinear function of the flow, dissipation,…
Slowing down phenomena occur in both deterministic and stochastic dynamical systems at the vicinity of phase transitions or bifurcations. An example is found in systems exhibiting a saddle-node bifurcation, which undergo a dramatic time…
The theory of stochastic resetting asserts that restarting a stochastic process can expedite its completion. In this paper, we study the escape process of a Brownian particle in an open Hamiltonian system that suffers noise-enhanced…
The influence of small random perturbations on a deterministic dynamical system with a locally stable equilibrium is considered. The perturbed system is described by the It\^{o} stochastic differential equation. It is assumed that the noise…
We consider particles that are conditioned to initial and final states. The trajectory of these particles is uniquely shaped by the intricate interplay of internal and external sources of randomness. The internal randomness is aptly…
Coupling dynamics of the states of the nodes of a network to the dynamics of the network topology leads to generic absorbing and fragmentation transitions. The coevolving voter model is a typical system that exhibits such transitions at…