Related papers: Chemotactic predator-prey dynamics
We consider a system of three random walkers (a `cheetah' surrounded by two `antelopes') diffusing in one dimension. The cheetah and the antelopes diffuse, but the antelopes experience in addition a deterministic relative drift velocity,…
We introduce mesoscopic and macroscopic model equations of chemotaxis with anomalous subdiffusion for modelling chemically directed transport of biological organisms in changing chemical environments with diffusion hindered by traps or…
Chase-escape percolation is a variation of the standard epidemic spread models. In this model, each site can be in one of three states: unoccupied, occupied by a single prey, or occupied by a single predator. Prey particles spread to…
This article adopts game theory to build a model for explaining the predation behavior of animals.We assume that both the prey and the preydator have two stratigies in this game,the active one and the passive one.By calculating the outcome…
We study chemotaxis in a porous medium using as a model a biased ("hungry") random walk on a percolating cluster. In close resemblance to the 1980s arcade game Pac-Man, the hungry random walker consumes food, which is initially distributed…
Reaction dynamics involving subdiffusive species is an interesting topic with only few known results, especially when the motion of different species is characterized by different anomalous diffusion exponents. Here we study the reaction…
We present a theory of chemokinetic search agents that regulate directional fluctuations according to distance from a target. A dynamic scattering effect reduces the probability to penetrate regions with high fluctuations and thus search…
We present a spatial, individual-based predator-prey model in which dispersal is dependent on the local community. We determine species suitability to the biotic conditions of their local environment through a time and space varying fitness…
In this paper, conformal fractional order discretization [20, 24, 25] is used to analyze bifurcation analysis and stability of a predator-prey system. A continuous model has been discretized into a discrete one while preserving the…
The movement of organisms and cells can be governed by occasional long distance runs, according to an approximate L\'evy walk. For T cells migrating through chronically-infected brain tissue, runs are further interrupted by long pauses, and…
Two density-dependent branching processes are considered to model predator-prey populations. For both models, preys are considered to be the main food supply of predators. Moreover, in each generation the number of individuals of each…
Due to the conventional distinction between ecological (rapid) and evolutionary (slow)timescales, ecological and population models to date have typically ignored the effects of evolution. Yet the potential for rapid evolutionary change has…
Animal cells can sense chemical gradients without moving, and are faced with the challenge of migrating towards a target despite noisy information on the target position. Here we discuss optimal search strategies for a chaser that moves by…
An investigation of the mesoscopic dynamics of chemical systems whose mass action equation gives rise to a deterministic chaotic attractor is carried out. A reactive lattice-gas model for the three-variable autocatalator is used to provide…
Cyclic predator-prey models with four or six species are studied on a square lattice when the invasion rates are varied. It is found that the cyclic invasions maintain a self-organizing pattern as long as the deviation of the invasion…
We study the adaptive dynamics of predator-prey systems modeled by a dynamical system in which the traits of predators and prey are allowed to evolve by small mutations. When only the prey are allowed to evolve, and the size of the…
Chemotaxis along helical paths towards a target releasing a chemoattractant is found in sperm cells and many microorganisms. We discuss the stochastic differential geometry of the noisy helical swimming path of a chiral swimmer. A chiral…
We employ partial integro-differential equations to model trophic interaction in a spatially extended heterogeneous environment. Compared to classical reaction-diffusion models, this framework allows us to more realistically describe the…
We numerically investigate the motion of active artificial microswimmers diffusing in a fuel concentration gradient. We observe that, in the steady state, their probability density accumulates in the low-concentration regions, whereas a…
Dynamical properties of numerically approximated discrete systems may become inconsistent with those of the corresponding continuous-time system. We present a qualitative analysis of the dynamical properties of two species Lotka-Volterra…