相关论文: Subharmonic solutions for a class of predator-prey…

This paper ascertains the global topological structure of the set of subharmonics of arbitrary order of the periodic predator-prey model introduced in L\'opez-G\'omez, Ortega and Tineo in 1996. By constructing the iterates of the monodromy…

We prove the existence of infinitely many periodic solutions and complicated dynamics, due to the presence of a topological horseshoe, for the classical Volterra predator--prey model with a periodic harvesting. The proof relies on some…

The Lotka-Volterra predator-prey model still represents the paradigm for the description of the competition in population dynamics. Despite its extreme simplicity, it does not admit an analytical solution, and for this reason, numerical…

This paper is focused on local and global stability of a fractional-order predator-prey model with habitat complexity constructed in the Caputo sense and corresponding discrete fractional-order system. Mathematical results like positivity…

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…

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…

Many dynamical systems, such as the Lotka-Volterra predator-prey model and the Euler equations for the free rotation of a rigid body, are PT symmetric. The standard and well-known real solutions to such dynamical systems constitute an…

In this paper, we study a Lotka-Volterra model which contains two prey and one predator with the Beddington-DeAngelis functional responses. First, we establish a set of sufficient conditions for existence of positive periodic solutions.…

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…

We establish a criterion for the existence of a topological horseshoe in a class of planar systems generated by periodic switching between two subsystems, each admitting a family of closed orbits, where the mechanism for chaos arises from…

The method of generalized modeling has been applied successfully in many different contexts, particularly in ecology and systems biology. It can be used to analyze the stability and bifurcations of steady-state solutions. Although many…

A non-periodic version of the one-predator two-prey system model presented in [L.T.H. Nguyen, Q.H. Ta, T.V. T\d{a}, Existence and stability of periodic solutions of a Lotka-Volterra system, SICE International Symposium on Control Systems,…

The diffusive Holling-Tanner predator-prey model with no-flux boundary conditions and nonlocal prey competition is considered in this paper. We show the existence of spatial nonhomogeneous periodic solutions, which is induced by nonlocal…

In this paper we provide an elementary proof of the existence of canard solutions for a class of singularly perturbed predator-prey planar systems in which there occurs a transcritical bifurcation of quasi steady states. The proof uses a…

We present new a stability result for periodic solutions of the periodic predator prey Lotka Volterra model, based on boundaries for the average of the coexistence states. Our result complements previous one in the literature.

In this paper, by means of the Melnikov functions we consider bifurcations of harmonic or subharmonic solutions from a periodic solution of a planar Hamiltonian system under impulsive perturbation. We give some sufficient conditions under…

The broad application range of the predator-prey modelling enabled us to apply it to represent the dynamics of the work-employment system. For the adopted period, we conclude that this dynamics is chaotic in the beginning of the time series…

A self-similar hierarchical solution that is both dynamically and evolutionarily stable is found to the multi dimensional Lotka-Volterra equation with a single chain of prey-predator relations. This gives a simple and natural explanation to…

Stemming from the stochastic Lotka-Volterra or predator-prey equations, this work aims to model the spatial inhomogeneity by using stochastic partial differential equations (SPDEs). Compared to the classical models, the SPDE model is more…

In this paper, the existence of subharmonic solutions for a class of non-autonomous first-order Hamiltonian systems is investigated. We also study the minimality of periods for such solutions. Our results which extend and improve many…