Related papers: Predators-prey models with competition Part I: exi…
Apparent competition is an indirect interaction between species that share natural resources without any mutual aggression but negatively affect each other if there is a common enemy. The negative results of the apparent competition are…
We introduce a new model of competition on growing networks. This extends the preferential attachment model, with the key property that node choices evolve simultaneously with the network. When a new node joins the network, it chooses…
The literature posits that an introduced predator population, is able to drive it's target pest population extinct, if supplemented with high quality additional food of quantity $\xi > \xi_{critical}$, \cite{SP11, SPV18, SPD17, SPM13}. We…
Many theoretical models have been formulated to better understand the coevolutionary patterns that emerge from antagonistic interactions. These models usually assume that the attacks by the exploiters are random, so the effect of victim…
In this monograph, we introduce a new model in population dynamics that describes two species sharing the same environmental resources in a situation of open hostility. The interactions among these populations are described not in terms of…
We consider a stochastic individual based model where each predator searches during a random time and then manipulates its prey or rests. The time distributions may be non-exponential. An age structure allows to describe these interactions…
In the study of the evolution of cooperation, resource limitations are usually assumed just to provide a finite population size. Recently, however, agent-based models have pointed out that resource limitation may modify the original…
A nonautonomous periodic chemostat model with delays modelling $n$ species in competition is considered. Sufficient conditions on the coefficients and consumption functions for the species are given, for both the extinction of the species…
Classical understanding of the outcome of the struggle for existence results in the Darwinian survival of the fittest. Here we show that the situation may be different, more complex and arguably more interesting. Specifically, we show that…
We examine the two-dimensional extension of the model of Kessler and Sander of competition between two species identical except for dispersion rates. In this class of models, the spatial inhomogeneity of reproduction rates gives rise to an…
In freshwater ecosystems, aquatic insects that ontogenetically shift their habitat from aquatic to terrestrial play vital roles as prey subsidies that move nutrients and energy from aquatic to terrestrial food webs. As a result, these…
We investigate existence of stationary solutions to an aggregation/diffusion system of PDEs, modelling a two species predator-prey interaction. In the model this interaction is described by non-local potentials that are mutually…
To understand the spreading and interaction of prey and predator, in this paper we study the dynamics of the diffusive Lotka-Volterra type prey-predator model with different free boundaries. These two free boundaries, which may intersect…
An age-structured predator-prey system with diffusion and Holling-Tanner-type nonlinearities is considered. Regarding the intensity of the fertility of the predator as bifurcation parameter, we prove that a branch of positive coexistence…
Predicting competitive outcomes typically requires fitting dynamical models to data, from which interaction strengths and coexistence indicators such as invasion criteria can be produced. Methods that allow to propagate parameter…
We consider a predator-prey population model with prey gathering together for defense purposes. A transmissible unrecoverable disease affects the prey. We characterize the system behavior, establishing that ultimately either only the…
This manuscript considers a Neumann initial-boundary value problem for the predator-prey system $$ \left\{ \begin{array}{l} u_t = D_1 u_{xx} - \chi_1 (uv_x)_x + u(\lambda_1-u+a_1 v), \\[1mm] v_t = D_2 v_{xx} + \chi_2 (vu_x)_x +…
In a diverse population, where many species are present, competitors can fight for surviving at individual and collective levels. In particular, species, which would beat each other individually, may form a specific alliance that ensures…
Most modern systems strive to learn from interactions with users, and many engage in exploration: making potentially suboptimal choices for the sake of acquiring new information. We initiate a study of the interplay between exploration and…
We introduce a new predator-prey model by replacing the growth and predation constant by a square matrix, and the population density as a population vector. The classical Lotka-Volterra model describes a population that either modulates or…