Related papers: Transient localized wave patterns and their applic…
We consider reaction-diffusion equations that are stochastically forced by a small multiplicative noise term. We show that spectrally stable travelling wave solutions to the deterministic system retain their orbital stability if the…
Optimal information processing in peripheral sensory systems has been associated in several examples to the signature of a critical or near critical state. Furthermore, cortical systems have also been described to be in a critical state in…
We study the effects of noise on stationary pulse solutions (bumps) in spatially extended neural fields. The dynamics of a neural field is described by an integrodifferential equation whose integral term characterizes synaptic interactions…
During slow-wave sleep, the brain produces traveling waves of slow oscillations (SOs; $\leq 2$ Hz), characterized by the propagation of alternating high- and low-activity states. The question of internal mechanisms that modulate traveling…
The physical mechanism on meridians (acupuncture lines) is studied and a theoretical model is proposed. The meridians are explained as an alternating system responsible for the integration and the regulation of life in addition to the…
We consider a free boundary model of epithelial cell migration with logistic growth and nonlinear diffusion induced by mechanical interactions. Using numerical simulations, phase plane and perturbation analysis, we find and analyse…
A nonlinear PDE featuring flux limitation effects together with those of the porous media equation (nonlinear Fokker-Planck) is presented in this paper. We analyze the balance of such diverse effects through the study of the existence and…
We consider general reaction diffusion systems posed on rectangular lattices in two or more spatial dimensions. We show that travelling wave solutions to such systems that propagate in rational directions are nonlinearly stable under small…
In order to remain adaptable to a dynamic environment, neural activity must be simultaneously both sensitive and stable. To solve this problem, the brain has been hypothesised to sit near a critical boundary. Yet, precisely how criticality…
We study diffusion of Cosmic Rays (CRs) in turbulent magnetic fields using test particle simulations. Electromagnetic fields are produced in direct numerical MHD simulations of turbulence and used as an input for particle tracing, particle…
We review our recent theoretical results on multiple scattering of waves in nonlinear disordered media. In particular, we discuss angular correlations of scattered waves, coherent backscattering cone, and the new phenomenon of temporal…
Despite the significance of short-term memory in cognitive function, the process of encoding and sustaining the input information in neural activity dynamics remains elusive. Herein, we unveiled the significance of transient neural dynamics…
The theory of traveling waves and spreading speeds is developed for time-space periodic monotone semiflows with monostable structure. By using traveling waves of the associated Poincar\'e maps in a strong sense, we establish the existence…
Dynamical descriptions and modeling of natural systems have generally focused on fixed points, with saddles and saddle-based phase-space objects such as heteroclinic channels/cycles being central concepts behind the emergence of…
Wave propagation in complex media is a universal problem spanning optics, acoustics, mechanics, and condensed matter physics. While disorder usually causes strong scattering, recent theory predicts that a special class of correlated…
We show that chimera patterns can be induced by noise in nonlocally coupled neural networks in the excitable regime. In contrast to classical chimeras, occurring in noise-free oscillatory networks, they have features of two phenomena:…
Spiral waves are ubiquitous spatiotemporal patterns that occur in various excitable systems. In cardiac tissue, the formation of these spiral waves is associated with life-threatening arrhythmias, and, therefore, it is important to study…
The spin transfer torque (STT) can lead to steady precession of magnetization without any external applied field in magnetic spin valve where the magnetic layer have very different spin diffusion length. This effect is associated with an…
In the recent years, MRI-driven turbulent transport has been found to depend in a significant way on fluid viscosity $\nu$ and resistivity $\eta$ through the magnetic Prandtl number $Pm=\nu/\eta$. In particular, the transport decreases with…
The nonlinear Schroedinger equation in the presence of disorder is considered. The dynamics of an initially localized wave packet is studied. A subdiffusive spreading of the wave packet is explained in the framework of a continuous time…