Related papers: A predator-2 prey fast-slow dynamical system for r…
We address the question of an averaging principle for a general class of multi-scale hybrid predator-prey models. We consider prey-predator models where the kinetic of the prey population, described by a differential equation, is faster…
We consider a heteroclinic network in the framework of winnerless competition of species. It consists of two levels of heteroclinic cycles. On the lower level, the heteroclinic cycle connects three saddles, each representing the survival of…
We study a chemotaxis system that includes two competitive prey and one predator species in a two-dimensional domain, where the movement of prey (resp. predators) is driven by chemicals secreted by predators (resp. prey), called mutually…
A two-dimensional homomorphic logistic map that preserves features of the Lotka-Volterra equations was proposed. To examine chaos, iteration plots of the population, Lyapunov exponents calculated from Jacobian eigenvalues of the $2$D…
In this work, we consider a system of differential equations modeling the dynamics of some populations of preys and predators, moving in space according to rapidly oscillating time-dependent transport terms, and interacting with each other…
Various field and laboratory experiments show that prey refuge plays a significant role in the stability of prey-predator dynamics. On the other hand, theoretical studies show that delayed system exhibits a much more realistic dynamics than…
Dispersal between different habitats influences the dynamics and stability of populations considerably. Furthermore, these effects depend on the local interactions of a population with other species. Here, we perform a general and…
Spatially extended population dynamics models that incorporate intrinsic noise serve as case studies for the role of fluctuations and correlations in biological systems. Including spatial structure and stochastic noise in predator-prey…
We consider planar systems of predator-prey models with small predator death rate $\epsilon>0$. Using geometric singular perturbation theory and Floquet theory, we derive characteristic functions that determines the location and the…
In this paper, we complete the global qualitative analysis of a quartic family of planar vector fields corresponding to a rational Holling-type dynamical system which models the dynamics of the populations of predators and their prey in a…
In this paper, we investigate the emergence of a ratio-dependent predator-prey system with Michaelis-Menten-type functional response and reaction-diffusion. We derive the conditions for Hopf, Turing and Wave bifurcation on a spatial domain.…
We introduce a new model for large scale evolution and extinction in which species are organized into food chains. The system evolves by two processes: origination/speciation and extinction. In the model, extinction of a given species can…
We integrate dual-process theories of human cognition with evolutionary game theory to study the evolution of automatic and controlled decision-making processes. We introduce a model where agents who make decisions using either automatic or…
We study the spreading of families in two-dimensional multispecies predator-prey systems, in which species cyclically dominate each other. In each time step randomly chosen individuals invade one of the nearest sites of the square lattice…
In this paper we consider a model of a nutrient-prey-predator system in a chemostat with general functional responses, using the input concentration of nutrient as the bifurcation parameter. We study the changes in the existence of isolated…
We consider the model of spatially distributed population consisting of two species with "\textsl{predator\,--\,prey}" interaction; each of the species occupies two stations. Transfer of individuals between the stations (migration) is not…
In this paper, we consider the dynamics of a predator-prey system of Gause type with cooperative hunting among predators and Holling III functional response. The known work numerically shows that the system exhibits saddle-node and Hopf…
Double Hopf bifurcation analysis can be used to reveal some complicated dynamical behavior in a dynamical system, such as the existence or coexistence of periodic orbits, quasi-periodic orbits, or even chaos. In this paper, an algorithm for…
In this paper, we study the dynamics of a discrete Kolmogorov predator-prey model with Ricker-type prey growth. We give the sufficient and necessary condition to guarantee the existence and uniqueness of the positive fixed point. Using the…
We study the discrete-time dynamical systems associated to a stage-structured wild and sterile mosquito population. We describe all fixed points of the evolution operator (which depends on five parameters) of mosquito population and show…