Related papers: On Some Perturbation Approaches to Population Dyna…
We prove that a recently proposed homotopy perturbation method for the treatment of population dynamics is just the Taylor expansion of the population variables about initial time. Our results show that this perturbation method fails to…
This paper deals with the existence, multiplicity, minimal complexity and global structure of the subharmonic solutions to a class of planar Hamiltonian systems with periodic coefficients, being the classical predator-prey model of V.…
In this paper we present the simplest individual level model of predator-prey dynamics and show, via direct calculation, that it exhibits cycling behavior. The deterministic analogue of our model, recovered when the number of individuals is…
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…
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…
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…
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…
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…
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…
We present numerical results based on a simplified ecological system in evolution, showing features of extinction similar to that claimed for the biosystem on Earth. In the model each species consists of a population in interaction with the…
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…
The classical two-species non-linear Predator-Prey system, often used in population dynamics modeling, is expressed in terms of a single positive coupling parameter $\lambda$. Based on standard logarithmic transformations, we derive a novel…
Urban ecosystems exhibit complex predator-prey dynamics increasingly disrupted by anthropogenic disturbances (e.g., noise, habitat fragmentation). Classical Lotka-Volterra (LV) models fail to capture these human-induced stressors, and…
The existence of beyond mean field quasi-cycle oscillations in a simple spatial model of predator prey interactions is derived from a path integral formalism. The results agree substantially with those obtained from analysis of similar…
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…
The problem of determining dynamical models and trajectories that describe observed time-series data allowing for the understanding, prediction and possibly control of complex systems in nature is of a great interest in a wide variety of…
We show that a number of models in virus dynamics, epidemiology and plant biology can be presented as ``damped" versions of the Lotka-Volterra predator-prey model, by analogy to the damped harmonic oscillator. The analogy deepens with the…
Experiments in predator-prey systems show the emergence of long-term cycles. Deterministic model typically fails in capturing these behaviors, which emerge from the microscopic interplay of individual based dynamics and stochastic effects.…
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.…
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…