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By generalizing a class of models recently introduced to account for protracted transients in biological systems, we identify a novel mechanism for hyperuniformity. In this model, competition of particles over a shared resource guides the…
We investigate travelling wave solutions in reaction-diffusion models of animal range expansion in the case that population diffusion is density-dependent. We find that the speed of the selected wave depends critically on the strength of…
We study local bifurcations of periodic solutions to time-periodic (systems of) integrodifference equations over compact habitats. Such infinite-dimensional discrete dynamical systems arise in theoretical ecology as models to describe the…
Understanding the organization of collective motion in biological systems is an ongoing challenge. In this Paper we consider a minimal model of self-propelled particles with variable speed. Inspired by experimental data from schooling fish,…
Understanding how patterns and travelling waves form in chemical and biological reaction-diffusion models is an area which has been widely researched, yet is still experiencing fast development. Surprisingly enough, we still do not have a…
We consider a collection of weakly interacting diffusion processes moving in a two-scale locally periodic environment. We study the large deviations principle of the empirical distribution of the particles' positions in the combined limit…
Flocking is a paradigmatic example of collective animal behaviour, where decentralized interaction rules give rise to a globally ordered state. In the emergence of order out of self-organization we find similarities between biological…
Systems with nonreciprocal interactions generically display time-dependent states. These are routinely observed in finite systems, from neuroscience to active matter, in which globally ordered oscillations exist. However, the stability of…
This paper concerns the spreading speed and asymptotical behaviors, which was left as an open problem in \cite{LLW22}, of a Fisher-KPP nonlocal diffusion model with a free boundary. Using a new lower solution, we get the exact finite…
The interplay between space and evolution is an important issue in population dynamics, that is in particular crucial in the emergence of polymorphism and spatial patterns. Recently, biological studies suggest that invasion and evolution…
Microorganisms living in microfluidic environments often form multi-species swarms, where they can leverage collective motions to achieve enhanced transport and spreading. Nevertheless, there is a general lack of physical understandings of…
In order to understand how nonlocal diffusion and pulse intervention affect dynamics of species, we focus on an age-structured nonlocal diffusion model in moving and heterogeneous environment, where nonlocal diffusion describes the long…
We analyze how temporal variability in local demography and dispersal combine to affect the rate of spread of an invading species. Our model combines state-structured local demography (specified by an integral or matrix projection model)…
The population dynamics that evolves in the radial symmetric geometry is investigated. The nonlinear reaction-diffusion model, which depends on population density, is employed as the governing equation for this system. The approximate…
We investigate how information spreads in three paradigmatic one-dimensional models with spatial disorder. The models we consider are unitarily related to a system of free fermions and are thus manifestly integrable. We demonstrate that…
This paper concerns wave propagation in a class of scalar reaction-diffusion-convection equations with $p$-Laplacian-type diffusion and monostable reaction. We introduce a new concept of a non-smooth traveling wave profile, which allows us…
The system decomposition theory has recently been developed for the dynamic analysis of nonlinear compartmental systems. The application of this theory to the ecosystem analysis has also been introduced in a separate article. Based on this…
We consider a spatially distributed population dynamics model with excitable predator-prey dynamics, where species propagate in space due to their taxis with respect to each other's gradient in addition to, or instead of, their diffusive…
Navigation of microorganisms is controlled by internal processes ultimately sensitive to mechanical or chemical signaling encountered along the path. In many natural environments, such as porous soils or physiological ducts, motile species…
Two hallmarks of non-equilibrium systems, from active colloids to animal herds, are agents motility and nonreciprocal interactions. Their interplay creates feedback loops leading to complex spatiotemporal dynamics crucial to understand and…