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Analysis of mathematical models in ecology and epidemiology often focuses on asymptotic dynamics, such as stable equilibria and periodic orbits. However, many systems exhibit long transient behaviors where certain aspects of the dynamics…
We consider a model for a population in a heterogeneous environment, with logistic type local population dynamics, under the assumption that individuals can switch between two different nonzero rates of diffusion. Such switching behavior…
The problem of velocity selection for reaction fronts has been intensively investigated, leading to the successful marginal stability approach for propagation into an unstable state. Because the front velocity is controlled by the leading…
We study 2D fronts propagating up a co-moving reaction rate gradient in finite number reaction-diffusion systems. We show that in a 2D rectangular channel, planar solutions to the deterministic mean-field equation are stable with respect to…
We study the Brownian motion of a classical particle in one-dimensional inhomogeneous environments where the transition probabilities follow quasiperiodic or aperiodic distributions. Exploiting an exact correspondence with the…
The dynamics of two-dimensional thin premixed flames is addressed in the framework of mathematical models where the flow field on either side of the front is piecewise incompressible and vorticity-free. Flames confined in channels with…
The current paper is devoted to the investigation of wave propagation phenomenon in reaction-diffusion equations with ignition type nonlinearity in time heterogeneous and random media. It is proven that such equations in time heterogeneous…
The ecological invasion problem in which a weaker exotic species invades an ecosystem inhabited by two strongly competing native species is modelled by a three-species competition-diffusion system. It is known that for a certain range of…
This paper is devoted to reaction-diffusion equations with bistable nonlinearities depending periodically on time. These equations admit two linearly stable states. However, the reaction terms may not be bistable at every time. These may…
We present a general method for studying front propagation in nonlinear systems with a global constraint in the language of hybrid tank models. The method is illustrated in the case of semiconductor superlattices, where the dynamics of the…
Active matter systems display a fascinating range of dynamical states, including stationary patterns and turbulent phases. While the former can be tackled with methods from the field of pattern formation, the spatio-temporal disorder of the…
We address the hydrodynamics of operator spreading in interacting integrable lattice models. In these models, operators spread through the ballistic propagation of quasiparticles, with an operator front whose velocity is locally set by the…
In toroidal geometry, and prior to the establishment of a fully developed turbulent state, the so-called topological instability of the pressure-gradient-driven turbulence is observed. In this intermediate state, a narrow spectral band of…
We present a systematic derivation of the gradient flows associated to a broad class of interfacial energies, emphasizing the relation between intrinsic and extrinsic variations of the interface. We show that the intrinsic variables…
We show that propagation speeds in invasion processes modeled by reaction-diffusion systems are determined by marginal spectral stability conditions, as predicted by the marginal stability conjecture. This conjecture was recently settled in…
We study a reaction-diffusion equation with an integral term describing nonlocal consumption of resources. We show that a homogeneous equilibrium can lose its stability resulting in appearance of stationary spatial structures. It is a new…
We study three different lattice models in which two species of diffusing particles are driven in opposite directions by an electric field. We focus on dynamical phase transitions that involve phase separation into domains that may be…
We present numerical evidence of a novel propagation mode for superfast impact ionization fronts in high-voltage Si $p^+$-$n$-$n^+$ structures. In nonlinear dynamics terms, this mode corresponds to a pulled front propagating into an…
We numerically examine a bidisperse system of active and passive particles coupled to a resource substrate. The active particles deplete the resource at a fixed rate and move toward regions with higher resources, while all of the particles…
This paper investigates wave-packet dynamics in non-Hermitian lattice systems and reveals a surprising phenomenon: The simultaneous propagation of two distinct wavefronts, one traveling at the non-Hermitian velocity and the other at the…