Lyapunov functions for Lotka { Volterra predator { prey models with optimal foraging behavior
نویسنده
چکیده
The theory of optimal foraging predicts abrupt changes in consumer behavior which lead to discontinuities in the functional response. Therefore population dynamical models with optimal foraging behavior can be appropriately described by di erential equations with discontinuous right{hand sides. In this paper we analyze the behavior of three di erent Lotka{Volterra predator{prey systems with optimal foraging behavior. We examine a predator{prey model with alternative food, a two{patch model with mobile predators and resident prey, and a two{patch model with both predators and prey mobile. We show that in the studied examples, optimal foraging behavior changes the neutral stability intrinsic to Lotka{Volterra systems to the existence of a bounded global attractor. The analysis is based on the construction and use of appropriate Lyapunov functions for models described by discontinuous di erential equations.
منابع مشابه
The Stability of Some Systems of Harvested Lotka-Volterra Predator-Prey Equations
Some scientists are interesting to study in area of harvested ecological modelling. The harvested population dynamics is more realistic than other ecological models. In the present paper, some of the Lotka-Volterra predator-prey models have been considered. In the said models, existing species are harvested by constant or variable growth rates. The behavior of their solutions has been analyzed ...
متن کاملThe Efficiency of Harvested Factor; Lotka-Volterra Predator-Prey Model
Scientists are interested in find out “how to use living resources without damaging the ecosystem at the same time?” from nineteen century because the living resources are limited. Thus, the harvested rate is used as the control parameters. Moreover, the study of harvested population dynamics is more realistic. In the present paper, some predator-prey models in which two ecologically inte...
متن کاملThe Lotka-Volterra Predator-Prey Equations
One may find out the application of mathematics in the areas of ecology, biology, environmental sciences etc. Mathematics is particulary used in the problem of predator-prey known as lotka-Volterra predator-prey equations. Indeed, differential equations is employed very much in many areas of other sciences. However, most of natural problems involve some unknown functions...
متن کاملAn Analysis on The Lotka-Volterra Food Chain Model: Stability
The food chain refers to a natural system by which energy is transmitted from one organism to another. In fact, a food chain consists of producers, consumers and decomposition. Presence of complex food web increase the stability of the ecosystem. Classical food chain theory arises from Lotka-Volterra model. In the present paper, the dynamics behavior of three level food chain is studied. A syst...
متن کاملGlobal Existence and Convergence of Solutions to a Cross-Diffusion Cubic Predator-Prey System with Stage Structure for the Prey
We study a cubic predator-prey system with stage structure for the prey. This system is a generalization of the two-species Lotka-Volterra predator-prey model. Firstly, we consider the asymptotical stability of equilibrium points to the system of ordinary differential equations type. Then, the global existence of solutions and the stability of equilibrium points to the system of weakly coupled ...
متن کامل