A Lotka–Volterra type food chain model with stage structure and time delays

AbstractA three-species Lotka–Volterra type food chain model with stage structure and time delays is investigated. It is assumed in the model that the individuals in each species may belong to one of two classes: the immatures and the matures, the age to maturity is presented by a time delay, and that the immature predators (immature top predators) do not have the ability to feed on prey (predator). By using some comparison arguments, we first discuss the permanence of the model. By means of an iterative technique, a set of easily verifiable sufficient conditions are established for the global attractivity of the nonnegative equilibria of the model

Uniformly Strong Persistence for a Delayed Predator-Prey Model

An asymptotically periodic predator-prey model with time delay is investigated. Some sufficient conditions for the uniformly strong persistence of the system are obtained. Our result is an important complementarity to the earlier results

Harmless delays and global attractivity for nonautonomous predator-prey system with dispersion

AbstractIn this paper, we consider a nonautonomous predator-prey model with dispersion and a finite number of discrete delays. The system consists of two Lotka-Volterra patches and has two species: one can disperse between two patches, but the other is confined to one patch and cannot disperse. Our purpose is to demonstrate that the time delays are harmless for uniform persistence of the solutions of the system. Furthermore, we establish conditions under which the system admits a positive periodic solution which attracts all solutions

Permanence and Stability of an Age-Structured Prey-Predator System with Delays

An age-structured prey-predator model with delays is proposed and analyzed. Mathematical analyses of the model equations with regard to boundedness of solutions, permanence, and stability are analyzed. By using the persistence theory for infinite-dimensional systems, the sufficient conditions for the permanence of the system are obtained. By constructing suitable Lyapunov functions and using an iterative technique, sufficient conditions are also obtained for the global asymptotic stability of the positive equilibrium of the model

Periodic solutions of a delayed predator-prey model with stage structure for predator

A periodic time-dependent Lotka-Volterra-type predator-prey model with stage structure for the predator and time delays due to negative feedback and gestation is investigated. Sufficient conditions are derived, respectively, for the existence and global stability of positive periodic solutions to the proposed model

Interacting populations : hosts and pathogens, prey and predators

Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution June 2007The interactions between populations can be positive, neutral or negative. Predation and parasitism are both relationships where one species benefits from the interaction at the expense of the other. Predators kill their prey instantly and use it only for food, whereas parasites use their hosts both as their habitat and their food. I am particularly interested in microbial parasites (including bacteria, fungi, viri, and some protozoans) since they cause many infectious diseases. This thesis considers two different points in the population-interaction spectrum and focuses on modeling host-pathogen and predator-prey interactions. The first part focuses on epidemiology, i. e., the dynamics of infectious diseases, and the estimation of parameters using the epidemiological data from two different diseases, phocine distemper virus that affects harbor seals in Europe, and the outbreak of HIV/AIDS in Cuba. The second part analyzes the stability of the predator-prey populations that are spatially organized into discrete units or patches. Patches are connected by dispersing individuals that may, or may not differ in the duration of their trip. This travel time is incorporated via a dispersal delay in the interpatch migration term, and has a stabilizing effect on predator-prey dynamics.This work has been supported by the US National Science Foundation (DEB-0235692), the US Environmental Protection Agency (R-82908901), the Ocean Ventures Fund, and the Academic Programs Office

A Stage-structure Leslie-Gower Model with Linear Harvesting and Disease in Predator

The growth dynamics of various species are affected by various aspects. Harvesting interventions and the spread of disease in species are two important aspects that affect population dynamics and it can be studied. In this work, we consider a stage-structure Leslie–Gower model with linear harvesting on the both prey and predator. Additionally, we also consider the infection aspect in the predator population. The population is divided into four subpopulations: immature prey, mature prey, susceptible predator, and infected predator. We analyze the existences and stabilities of feasible equilibrium points. Our results shown that the harvesting in prey and the disease in predator impacts the behavioral of system. The situation in the system is more complex due to disease in the predator population. Some numerical simulations are given to confirm our results

A survey on stably dissipative Lotka-Volterra systems with an application to infinite dimensional Volterra equations

For stably dissipative Lotka{Volterra equations the dynamics on the attractor are Hamiltonian and we argue that complex dynamics can occur. We also present examples and properties of some infinite dimensional Volterra systems with applications related with stably dissipative Lotka-Volterra equations. We finish by mentioning recent contributions on the subject

Analysis of a Nonautonomous Delayed Predator-Prey System with a Stage Structure for the Predator in a Polluted Environment

A two-species nonautonomous Lotka-Volterra type model with diffusional migration among the immature predator population, constant delay among the matured predators, and toxicant effect on the immature predators in a nonprotective patch is proposed. The scale of the protective zone among the immature predator population can be regulated through diffusive coefficients Di(t), i=1,2. It is proved that this system is uniformly persistent (permanence) under appropriate conditions. Sufficient conditions are derived to confirm that if this system admits a positive periodic solution, then it is globally asymptotically stable