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Periodic solutions for a discrete time predator-prey system with monotone functional responses
, Article Comptes Rendus Mathematique ; Volume 345, Issue 4 , 2007 , Pages 199-202 ; 1631073X (ISSN) ; Hesaaraki, M ; Sharif University of Technology
2007
Abstract
In this Note, sharp sufficient conditions for the existence of periodic solutions of a nonautonomous discrete time semi-ratio-dependent predator-prey system with functional responses are derived. In our results this system with any monotone functional response bounded by polynomials in R+, always has at least one ω-periodic solution. In particular, this system with the most popular functional responses Michaelis-Menten, Holling type-II and III, sigmoidal, Ivlev and some other monotone response functions, always has at least one ω-periodic solution. To cite this article: M. Fazly, M. Hesaaraki, C. R. Acad. Sci. Paris, Ser. I 345 (2007). © 2007 Académie des sciences
Solutions od Reaction-Diffusion Predator-Prey Systems
, M.Sc. Thesis Sharif University of Technology ; Hesaraki, Mahmoud (Supervisor)
Abstract
The dynamics of a reaction–diffusion predator–prey system with strong Allee effect in the prey population is considered. Nonexistence of non constant positive steady state solutions are shown to identify the ranges of parameters of spatial pattern formation. Bifurcations of spatially homogeneous and non homogeneous periodic solutions as well as non constant steady state solutions are studied.
These results show that the impact of the Allee effect essentially increases the system spatiotemporal complexity
These results show that the impact of the Allee effect essentially increases the system spatiotemporal complexity
, M.Sc. Thesis Sharif University of Technology ; Hesaraki, Mahmoud (Supervisor)
Abstract
In this thesis, a model of predator-prey with a continuous threshold harvesting with refuge and without refuge the prey is formulated; and its dynamics, also, its direct effects on ecosystem such as the stability properties of some periodic solutions and coexistence eqilibria are surveyed. Numerical and theoretical analyses are used to investigate boundedness of solutions, stability of eqilibria, periodic orbits, bifurcations and heteroclinic orbits
A Lyapunov Functional for a Predator-Prey Model with Nonlinear Predation Rate and Periodic Solutions
, M.Sc. Thesis Sharif University of Technology ; Hesaraki, Mahmoud (Supervisor)
Abstract
In this thesis we consider the dynamics of a general predator-prey model which generalizes several known predator-prey, assuming that the intrinsic growth rate of the pray, the predation rate, and the removal functions are given in an unspecified form. Using the Lyapunov method, we derive sufficient conditions for the stability of the equilibria. also, we consider a delayed periodic predator- prey model and sufficient conditions are derived for the existence, uniqueness and global asymptotic stability of positive periodic solutions of the model.
Persistence in Seasonally Forced Epidemiological Models and Seasonally Varying Predator-Prey Models Via the Basic Reproduction Number
, M.Sc. Thesis Sharif University of Technology ; Hesaraki, Mahmoud (Supervisor)
Abstract
In this study, we will examine persistence of various kinds of seasonally forced epidemiological models and seasonally varying predator-prey models. The results of our study regarding persistence of the models will be shown via basic reproduction number. We will show that, in the framework of our study and under some conditions, persistence is obtained as long as the basic reproduction number is bigger than one. We will also prove that, in the framework of our study and under sufficient conditions, if the basic reproduction number is smaller than one, the species under discussion won’t survive in the predator-prey models, and the disease(s) would go extinct in the epidemiological...
Solutions of Reaction-Diffiusion Predator-Prey Systems
, M.Sc. Thesis Sharif University of Technology ; Hesaraki, Mahmoud (Supervisor)
Abstract
Consider the following Two Reaction-Diffusion System with Predator-Prey interactions.
{ █(ut = Du Δu + f (u) "" bϕ(u)v x ∈ Ω ,t>0 ,@ @vt = Dv Δv + g(v) + cϕ(u)v x ∈ Ω ,t>0 ,)┤
The main purposes of Thesis are as follow: The effect of a protection zone in the diffusive Leslie predator–prey model, Non-existence of non-constant positive steady states of two Holling type-II predator–prey systems: Strong interaction case, In the first chapter, my work is devoted to investigate the change of behavior of diffusive Leslie predator–prey model with large intrinsic predator growth rate, when a simple protection zone Ω_0 for the prey is introduced. In other word, the...
{ █(ut = Du Δu + f (u) "" bϕ(u)v x ∈ Ω ,t>0 ,@ @vt = Dv Δv + g(v) + cϕ(u)v x ∈ Ω ,t>0 ,)┤
The main purposes of Thesis are as follow: The effect of a protection zone in the diffusive Leslie predator–prey model, Non-existence of non-constant positive steady states of two Holling type-II predator–prey systems: Strong interaction case, In the first chapter, my work is devoted to investigate the change of behavior of diffusive Leslie predator–prey model with large intrinsic predator growth rate, when a simple protection zone Ω_0 for the prey is introduced. In other word, the...