Related papers: Seizure intervention via diffusion mechanisms
We study nonlinear stability of spatially homogeneous oscillations in reaction-diffusion systems. Assuming absence of unstable linear modes and linear diffusive behavior for the neutral phase, we prove that spatially localized perturbations…
Recent advances in transport properties measurements of disordered materials and lattice simulations, using superconducting qubits, have rekindled interest in Anderson localization, motivating our study of highly disordered quantum…
We study the spike statistics of neurons in a network with dynamically balanced excitation and inhibition. Our model, intended to represent a generic cortical column, comprises randomly connected excitatory and inhibitory leaky…
A probabilistic model describes a system in its observational state. In many situations, however, we are interested in the system's response under interventions. The class of structural causal models provides a language that allows us 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…
We study the diffusive dynamics of a Brownian particle in proximity of a flat surface under non-equilibrium conditions, which are created by an anisotropic thermal environment with different temperatures being active along distinct spatial…
The dynamics of a packages diffusion process within a selforganized network is analytically studied by means of an extended $f$% -spin facilitated kinetic Ising model (Fredrickson-Andersen model) using a Fock-space representation for the…
This study investigates the asymptotic dynamics of solutions to the Fokker-Planck-Kolmogorov (FPK) equation, with a specific focus on ship roll stability in dynamic sea conditions. Utilizing a fourth-order filter, we conduct a thorough…
Identification of nonlinear dynamical systems is crucial across various fields, facilitating tasks such as control, prediction, optimization, and fault detection. Many applications require methods capable of handling complex systems while…
Differential equation-based physiological models of sleep-wake networks describe sleep-wake regulation by simulating the activity of wake- and sleep-promoting neuronal populations and the modulation of these populations by homeostatic and…
Controlling dopant transport with high spatial precision is crucial for improving the semiconductor functionality, reliability, and scalability. Although prior models of noise-assisted diffusion have been largely confined to idealized one…
The model reduction of a mesoscopic kinetic dynamics to a macroscopic continuum dynamics has been one of the fundamental questions in mathematical physics since Hilbert's time. In this paper, we consider a diagram of the diffusion limit…
Spatial pattern formation in excitable fluctuating media was researched analytically from the point of view of the order parameters concept. The reaction-diffusion system in external noise is considered as a model of such medium. Stochastic…
From a simple model for the driven motion of a planar interface under the influence of a diffusion field we derive a damped nonlinear oscillator equation for the interface position. Inside an unstable regime, where the damping term is…
We introduce and analyze a class of neural network models motivated by the Drosophila central complex nervous system, designed to capture the emergence and dynamics of orientation-selective activity bumps. Starting from a biologically…
We investigate a driven, one-dimensional system of colloidal particles in a periodically currogated narrow channel subject to a time-delayed feedback control. Our goal is to identify conditions under which the control induces oscillatory,…
Many mathematical models of interacting agents assume that individual interactions scale down in proportion to the network size, ensuring that the combined input received from the network does not diverge. In theoretical neuroscience,…
The analysis of noise-induced escape in populations of bistable elements is challenging, because nonlinearity, coupling, and noise all play essential roles. We show that the interplay of these three factors yields three qualitatively…
We consider a heterogeneous, globally coupled population of excitatory quadratic integrate-and-fire neurons with excitability adaptation due to a metabolic feedback associated with ketogenic diet, a form of therapy for epilepsy. Bifurcation…
We propose a discrete time dynamical system (a map) as phenomenological model of excitable and spiking-bursting neurons. The model is a discontinuous two-dimensional map. We find condition under which this map has an invariant region on the…