Related papers: Capture of the Lamb: Diffusing Predators Seeking a…
Mathematical modelling and numerical simulations of interaction populations are crucial topics in systems biology. The interactions of ecological models may occur among individuals of the same species or individuals of different species.…
We propose a minimal model of predator-swarm interactions which captures many of the essential dynamics observed in nature. Different outcomes are observed depending on the predator strength. For a "weak" predator, the swarm is able to…
This paper is concerned with continuous-time pursuit and evasion games. Typically, we have a lion and a man in a metric space: they have the same speed, and the lion wishes to catch the man while the man tries to evade capture. We are…
In this work, we investigate the system of three species ecological model involving one predator-prey subsystem coupling with a generalist predator with negative effect on the prey. Without diffusive terms, all global dynamics of its…
The escape probability $\xi_{x}$ from a site $x$ of a one-dimensional disordered lattice with trapping is treated as a discrete dynamical evolution by random iterations over nonlinear maps parametrized by the right and left jump…
We propose a dynamical trapping system composed of multiple chasers subject to target-tracking forces utilizing the velocity and position information of a single escaping target. To successfully capture the target, dividing chasers into…
Spreading processes play an increasingly important role in modeling for diffusion networks, information propagation, marketing and opinion setting. We address the problem of learning of a spreading model such that the predictions generated…
We consider the following generalization of the classical pursuit-evasion problem, which we call k-capture. A group of n pursuers (hyenas) wish to capture an evader (lion) who is free to move in an m-dimensional Euclidean space, the…
We study the escape behavior of a lamb to safe haven pursued by a hungry lion. Identifying the system with a pair of vicious Brownian walkers we evaluate the probability density function for the vicious pair and from there we estimate the…
Diffusion to capture is an ubiquitous phenomenon in many fields in biology and physical chemistry, with implications as diverse as ligand-receptor binding on eukaryotic and bacterial cells, nutrient uptake by colonies of unicellular…
We study the survival of a prey that is hunted by N predators. The predators perform independent random walks on a square lattice with V sites and start a direct chase whenever the prey appears within their sighting range. The prey is…
In this paper we introduce a formal method for the derivation of a predator's functional response from a system of fast state transitions of the prey or predator on a time scale during which the total prey and predator densities remain…
The dynamics of a prey-predator system with foraging facilitation among predators are investigated. The analysis involves the computation of many semi-algebraic systems of large degrees. We apply the pseudo-division reduction, real-root…
Diffusions are a successful technique to sample from high-dimensional distributions. The target distribution can be either explicitly given or learnt from a collection of samples. They implement a diffusion process whose endpoint is a…
The population size ("abundance") of wildlife species has central interest in ecological research and management. Distance sampling is a dominant approach to the estimation of wildlife abundance for many vertebrate animal species. One…
If one isolated species is supposed to evolve following the logistic mapping, then we are tempted to think that the dynamics of two species can be expressed by a coupled system of two discrete logistic equations. As three basic…
Poaching poses significant threats to wildlife and biodiversity. A valuable step in reducing poaching is to forecast poacher behavior, which can inform patrol planning and other conservation interventions. Existing poaching prediction…
We develop a mathematical model of extinction and coexistence in a generic predator-prey ecosystem composed of two herbivores in asymmetrical competition and a hunter exerting a predatory pressure on both species. With the aim of…
We have previously discussed the one-dimensional multitrap system of finite range and found the somewhat unexpected result that the larger is the number of imperfect traps the higher is the transmission through them. We discuss in this work…
We study a generalization of the standard trapping problem of random walk theory in which particles move subdiffusively on a one-dimensional lattice. We consider the cases in which the lattice is filled with a one-sided and a two-sided…