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We introduce oscillatory analogues of fractional Brownian motion, sub-fractional Brownian motion and other related long range dependent Gaussian processes, we discuss their properties, and we show how they arise from particle systems with…

We investigate the instabilities and bifurcations of traveling pulses in a model excitable medium; in particular we discuss three different scenarios for the loss of stability resp. the disappearance of stable pulses. In numerical…

The spatiotemporal evolution of the out-of-time-order correlator (OTOC) measures the propagation and scrambling of local quantum information. For the transverse field Ising model with open boundaries, the local operator $\sigma^{x}$ shows…

This paper is concerned with the existence and the stability of travelling wave solutions to a bistable reaction-diffusion equation with a jump discontinuious point on nonlinear term. Sub-super solution method is used throughout this paper.…

Oscillons are extremely long lived, oscillatory, spatially localized field configurations that arise from generic initial conditions in a large number of non-linear field theories. With an eye towards their cosmological implications, we…

In this paper, we extend our earlier work to provide additional evidence for an alternative scenario to explain the nature of so-called `explosive events'. The bi-directed, fast Doppler motion of explosive events observed spectroscopically…

Based on a recent work on traveling waves in spatially nonlocal reaction-diffusion equations, we investigate the existence of traveling fronts in reaction-diffusion equations with a memory term. We will explain how such memory terms can…

An alternative explanation to the mechanism behind self-sustained oscillations of ions in direct current (DC) glow discharges is provided. Such description is distinguished from the one provided by the fluid models, where oscillations are…

Self-oscillations underlie many natural phenomena such as heartbeat, ocean waves, and the pulsation of variable stars. From pendulum clocks to the behavior of animal groups, self-oscillation is one of the keys to the understanding of…

In coupled reaction-diffusion systems, modes with two different length scales can interact to produce a wide variety of spatiotemporal patterns. Three-wave interactions between these modes can explain the occurrence of spatially complex…

Previous experimental studies have shown that when a layer of solid particles is explosively dispersed, the particles often develop a non-uniform spatial distribution. The instabilities within the particle bed and at the particle layer…

We revisit the problem of diffusion in a driven system consisting of an inertial Brownian particle moving in a symmetric periodic potential and subjected to a symmetric time-periodic force. We reveal parameter domains in which diffusion is…

We explore a mechanism of pattern formation arising in processes described by a system of a single reaction-diffusion equation coupled with ordinary differential equations. Such systems of equations arise from the modeling of interactions…

We performed an extensive numerical study of a two-dimensional reaction-diffusion system of the activator-inhibitor type in which domain patterns can form. We showed that both multidomain and labyrinthine patterns may form spontaneously as…

Reaction diffusion systems describe the behaviour of dynamic, interacting, particulate systems. Quantum stochastic processes generalise Brownian motion and Poisson processes, having operator valued It\^{o} calculus machinery. Here it is…

We investigate different emergent dynamics namely oscillation quenching and revival of oscillation in a global network of identical oscillators coupled with diffusive (positive) delay coupling as it is perturbed by symmetry breaking…

The recently introduced Theory of the Adjacent Possible (TAP) is a model of combinatorial innovation aiming to explain the "hockey-stick" upward trend of human technological evolution, where an explosion in the number of produced items with…

In natural settings, intermittent dynamics are ubiquitous and often arise from a coupling between external driving and spatial heterogeneities. A well-known example is the generation of transient, turbulent puffs of fluid through a pipe…

Zonal flows are well known to arise spontaneously out of turbulence. We show that for statistically averaged equations of the stochastically forced generalized Hasegawa-Mima model, steady-state zonal flows and inhomogeneous turbulence fit…

We study pattern-forming instabilities in reaction-advection-diffusion systems. We develop an approach based on Lyapunov-Bloch exponents to figure out the impact of a spatially periodic mixing flow on the stability of a spatially…