Related papers: Coexistence in discrete time Multi-type competing …
We deal with strongly competing multispecies systems of Lotka-Volterra type with homogeneous Neumann boundary conditions in dumbbell-like domains. Under suitable non-degeneracy assumptions, we show that, as the competition rate grows…
We establish a link between metastability and a discrete time-crystalline phase in a periodically driven open quantum system. The mechanism we highlight requires neither the system to display any microscopic symmetry nor the presence of…
An ecosystem is a nonlinear dynamical system, its orbits giving rise to the observed complexity in the system. The diverse components of the ecosystem interact in discrete time to give rise to emergent features that determine the trajectory…
Random walkers characterized by random positions and random velocities lead to normal diffusion. A random walk was originally proposed by Einstein to model Brownian motion and to demonstrate the existence of atoms and molecules. Such a…
The two-type Richardson model describes the growth of two competing infections on $\mathbb{Z}^d$. At time 0 two disjoint finite sets $\xi_1,\xi_2\subset \mathbb{Z}^d$ are infected with type 1 and type 2 infection respectively. An uninfected…
This paper demonstrates that simple yet important characteristics of coevolution can occur in evolutionary algorithms when only a few conditions are met. We find that interaction-based fitness measurements such as fitness (linear) ranking…
We propose a new model of permanent monogamous pair formation in zoological populations with multiple types of females and males. According to this model, animals randomly encounter members of the opposite sex at their so-called firing…
We consider the model of Deijfen et al. for competing growth of two infection types in R^d, based on the Richardson model on Z^d. Stochastic ball-shaped infection outbursts transmit the infection type of the center to all points of the ball…
We investigate the effects of spatial heterogeneity on the coexistence of competing species in the case when the heterogeneity is dynamically generated by environmental flows with chaotic mixing properties. We show that one of the effects…
Interacting populations often create complicated spatiotemporal behavior, and understanding it is a basic problem in the dynamics of spatial systems. We study the two-species case by simulations of a host--parasitoid model. In the case of…
We study two new models of two particle species invading a surface from opposite sides. Collisions of particles of different species lead to the formation of congestion fronts. One of the models implements a reversible process whereas in…
Dynamical systems of N particles in \R^{D} interacting by a singular pair potential of mean field type are considered. The systems are assumed to be of gradient type and the existence of a macroscopic limit in the many particle limit is…
The cohesive collective motion (flocking, swarming) of autonomous agents is ubiquitously observed and exploited in both natural and man-made settings, thus, minimal models for its description are essential. In a model with continuous space…
We consider a model of a discrete time "interacting particle system" on the integer line where infinitely many changes are allowed at each instance of time. We describe the model using chameleons of two different colours, {\it viz}., red…
We study properties of a $p-$type subcritical branching process in random environment initiated at moment zero by a vector $\mathbf{z}=\left( z_{1},..,z_{p}\right) $\ of particles of different types. Assuming that the process belongs to the…
In this paper, we proposed a stochastic model which describes two species of particles moving in counterflow. The model generalizes the theoretical framework describing the transport in random systems since particles can work as mobile…
We study a system of two coupled transport equations with freezing. The solutions freeze in time when they are equal. We prove existence and uniqueness of continuous solutions if the initial conditions are continuous. We discuss several…
Phase separation, i.e., the coexistence of two different phases, is observed in many systems away from the coexistence curve of a first-order transition, leading to a stable heterogeneous phase or region. Examples include various quantum…
A random walk problem with particles on discrete double infinite linear grids is discussed. The model is based on the work of Montroll and others. A probability connected with the problem is given in the form of integrals containing…
The paper deals with a class of cooperative functional differential equations (FDEs) with infinite delay, for which sufficient conditions for persistence and permanence are established. Here, the persistence refers to all solutions with…