Related papers: Transient localized wave patterns and their applic…
Sheared incompressible flows are usually considered non-dispersive media. As a consequence, the frequency evolution in transients has received much less attention than the wave energy density or growth factor. By carrying out a large number…
In this paper, we study the traveling wave solutions to the density-suppressed motility model describing the ``self-trapping'' mechanism that induces spatio-temporal pattern formations observed in the experiment. We establish the existence…
State transition between the Peregrine rogue wave and w-shaped traveling wave induced by higher-order effects and background frequency is studied. We find that this intriguing transition, described by an exact explicit rational solution, is…
We study the middle cerebral artery blood flow velocity (MCAfv) in humans using transcranial Doppler ultrasonography (TCD). The time series of the axial flow velocity averaged over a cardiac beat interval is found to exhibit clear…
Many neuronal systems and models display a certain class of mixed mode oscillations (MMOs) consisting of periods of small amplitude oscillations interspersed with spikes. Various models with different underlying mechanisms have been…
We prove a principle of linearized stability for traveling wave solutions to neural field equations posed on the real line. Additionally, we provide the existence of a finite dimensional invariant center manifold close to a traveling wave,…
An inhomogeneous anisotropic physical model of the brain cortex is presented that predicts the emergence of non--evanescent (weakly damped) wave--like modes propagating in the thin cortex layers transverse to both the mean neural fiber…
Traveling wavetrains in generalized two-species predator-prey models and two-component reaction-diffusion equations are considered. The stability of the fixed points of the traveling wave ODEs (in the usual "spatial" variable) is…
We study the existence and nonexistence of traveling waves of general diffusive Kermack-McKendrick SIR models with standard incidence where the total population is not constant. The three classes, susceptible $S$, infected $I$ and removed…
The recent theoretical discovery of families of travelling wave solutions in pipe flow at Reynolds numbers lower than the transitional range naturally raises the question of their relevance to the turbulent transition process. Here a series…
By event-driven molecular dynamics simulations we investigate magneto-transport in a two-dimensional model with randomly distributed scatterers close to the field-induced localization transition. This transition is generated by percolating…
We analyze the effects of noise on the traveling wave dynamics in neural fields. The noise influences the dynamics on two scales: first, it causes fluctuations in the wave profile, and second, it causes a random shift in the phase of the…
The mechanisms underlying cardiac fibrillation have been investigated for over a century, but we are still finding surprising results that change our view of this phenomenon. The present study focuses on the transition from normal rhythm to…
In this paper, we present a cell motility model that takes into account the cell membrane effect. The model introduced is an incompressible Darcy free boundary problem. This model involves a nonlinear term in the boundary condition to model…
Modal linear stability analysis has proven very successful in the analysis of coherent structures of turbulent flows. Formally, it describes the evolution of a disturbance in the limit of infinite time. In this work we apply modal linear…
Traveling waves are ubiquitous in nature and control the speed of many important dynamical processes, including chemical reactions, epidemic outbreaks, and biological evolution. Despite their fundamental role in complex systems, traveling…
Competitive neural networks are often used to model the dynamics of perceptual bistability. Switching between percepts can occur through fluctuations and/or a slow adaptive process. Here, we analyze switching statistics in competitive…
Thanks to novel, powerful brain activity recording techniques, we can create data-driven models from thousands of recording channels and large portions of the cortex, which can improve our understanding of brain-states neuromodulation and…
The review is concerned with the nonlinear Schr\"odinger equation (NLSE) in the presence of disorder. Disorder leads to localization in the form of the localized Anderson modes (AM), while nonlinearity is responsible for the interaction…
In this paper, we investigate the existence, uniqueness, and spectral stability of traveling waves arising from a single threshold neural field model with one spatial dimension, a Heaviside firing rate function, axonal propagation delay,…