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The symbiotic branching model describes the dynamics of a spatial two-type population, where locally particles branch at a rate given by the frequency of the other type combined with nearest-neighbour migration. This model generalizes…
We study an abstract model for the co-evolution between mutating viruses and the adaptive immune system. In sequence space, these two populations are localized around transiently dominant strains. Delocalization or error thresholds exhibit…
Conflict destabilizes social interactions and impedes cooperation at multiple scales of biological organization. Of fundamental interest are the causes of turbulent periods of conflict. We analyze conflict dynamics in a monkey society model…
We present a novel approach to modeling market dynamics using ordinary differential equations that explicitly incorporates product competitiveness and consumer behavior. Our framework treats market segments as interacting populations in a…
We discuss a discrete-time model for motion of substance in a channel of a network. For the case of stationary motion of the substance and for the case of time-independent values of the parameters of the model we obtain a new class of…
Formation and competition of associations are studied in a six-species ecological model where each species has two predators and two prey. Each site of a square lattice is occupied by an individual belonging to one of the six species. The…
A model of six-species food web is studied in the viewpoint of spatial interaction structures. Each species has two predators and two preys, and it was previously known that the defensive alliances of three cyclically predating species…
Behavioral adoptions are influenced by peers in different ways. While some individuals may change after a single incoming influence, others need multiple cumulated attempts. These two mechanism, known as the simple and the complex…
Self-organisation of individuals within large collectives occurs throughout biology. Mathematical models can help elucidate the individual-level mechanisms behind these dynamics, but analytical tractability often comes at the cost of…
Game theory is the standard tool used to model strategic interactions in evolutionary biology and social science. Traditional game theory studies the equilibria of simple games. But is traditional game theory applicable if the game is…
A discrete delay is included to model the time between the capture of the prey and its conversion to viable biomass in the simplest classical Gause type predator-prey model that has equilibrium dynamics without delay. As the delay increases…
The biased interaction game described the operation of systems rooted in boundedly rational interactions under conditions of scarcity. The game explored the influence of bias and demonstrated how hierarchy and inequality are emergent system…
We introduce and solve a general model of dynamic response under external perturbations. This model captures a wide range of systems out of equilibrium including Ising models of physical systems, social opinions, and population genetics.…
The transient behavior of an ecosystem with N random interacting species in the presence of a multiplicative noise is analyzed. The multiplicative noise mimics the interaction with the environment. We investigate different asymptotic…
Many biological systems dynamically rearrange their components through a sequence of configurations in order to perform their functions. Such dynamic processes have been studied using network models that sequentially retrieve a set of…
The simplest model of a smart spatial redistribution of individuals is proposed. A single-species population is considered, to be composed of two discrete subpopulations inhabiting two stations; migration is a transfer between them. The…
In the present article, we demonstrate the emergence and existence of the spiral wave chimera-like transient pattern in coupled ecological systems, composed of prey-predator patches, where the patches are connected in a three-dimensional…
Many biological systems are governed by difference equations and exhibit discrete-time dynamics. Examples include the size of a population when generations are non-overlapping, and the incidence of a disease when infections are recorded at…
Honest signals and cues have been observed as part of interspecific and intraspecific communication among animals. Recent theories suggest that existing signaling systems have evolved through natural selection imposed by predators. Honest…
Temporal resolution of visual information processing is thought to be an important factor in predator-prey interactions, shaped in the course of evolution by animals' ecology. Here I show that light can be considered to have a dual role of…