Related papers: Durrett-Levin spatial model of allelopathy
The present study investigates the interaction of an equidistant three-level atom and a single-mode cavity field that has been initially prepared in a generalized coherent state. The atom-field interaction is considered to be, in general,…
We propose a new stochastic epidemiological model defined in a continuous space of arbitrary dimension, based on SIS dynamics implemented in a spatial $\Lambda$-Fleming-Viot (SLFV) process. The model can be described by as little as three…
This study introduces an innovative framework for merging ecological and epidemiological modeling via the formulation of a sophisticated predator-prey model that addresses the intricacies of disease dynamics, the Allee effect, and defensive…
We introduce and study a nonlinear discrete dynamical system describing the evolution of a resource distribution among interacting agents. The model generalizes several classical mean-field and opinion-dynamics frameworks and is defined on…
A simple cellular automata model for a two-group war over the same territory is presented. It is shown that a qualitative advantage is not enough for a minority to win. A spatial organization as well a definite degree of aggressiveness are…
In biological systems, active agents such as actomyosin and cells move and interact on curved surfaces, exhibiting diverse phenomena. These observations have motivated studies of how curvature shapes their collective behavior. Here, using a…
One of the most important branches of nonlinear control theory is the so-called sliding-mode. Its aim is the design of a (nonlinear) feedback law that brings and maintains the state trajectory of a dynamic system on a given sliding surface.…
We investigate classes of interacting systems that allow for a mapping to disordered noninteracting systems. As we show, such a mapping is possible for interacting systems with a suppressed density of states at the chemical potential,…
We analyze an interacting particle system with a Markov evolution of birth-and-death type. We have shown that a local competition mechanism (realized via a density dependent mortality) leads to a globally regular behavior of the population…
Physical processes rarely occur in isolation, rather they influence and interact with one another. Thus, there is great benefit in modeling potential dependence between both spatial locations and different processes. It is the interaction…
Scalar field cosmologies with a generalized harmonic potential are investigated in flat and negatively curved Friedmann-Lema\^itre-Robertson-Walker and Bianchi I metrics. An interaction between the scalar field and matter is considered.…
We investigate the survivor distributions of a spatially extended model of competitive dynamics in different geometries. The model consists of a deterministic dynamical system of individual agents at specified nodes, which might or might…
Symmetry invariant local interaction of a many body system leads to global constraints. We obtain explicit forms of the global macroscopic condition assuring that at the microscopic level the evolution respects the overall symmetry.
With the development of network science, Turing pattern has been proven to be formed in discrete media such as complex networks, opening up the possibility of exploring it as a generation mechanism in the context of biology, chemistry, and…
Age-structured models capture the dynamic behavior of populations over time and result in nonlinear integro-partial differential equations (IPDEs). These processes arise in various fields such as biotechnology, economics, or demography.…
The two-dimensional Ising model with competing short range ferromagnetic interactions and long range antiferromagnetic interactions is perhaps the most simple one containing the minimal microscopic ingredients necessary for an appropriate…
Dominance is usually considered a constant value that describes the relative difference in fitness or phenotype between heterozygotes and the average of homozygotes at a focal polymorphic locus. However, the observed dominance can vary with…
Contact processes (CP's) with particle creation requiring a minimal neighborhood (restrictive or threshold CP's) present a novel sort of discontinuous absorbing transitions, that revealed itself robust under the inclusion of different…
An organism that is newly introduced into an existing population has a survival probability that is dependent on both the population density of its environment and the competition it experiences with the members of that population.…
We study the general properties of stochastic two-species models for predator-prey competition and coexistence with Lotka-Volterra type interactions defined on a $d$-dimensional lattice. Introducing spatial degrees of freedom and allowing…