Lotka-Volterra Population Biology Models with Negative Feedback and their Ecological Monitoring
نویسنده
چکیده
Lotka-Volterra population biology models are important models that describe the interaction between various biological species considered as predator-prey system. This work describes a Lotka-Volterra population biology model with negative feedback. We show that for this biological model, the predator and prey species have stable coexistence. Then we shall propose ecological monitoring of the population biology model by constructing a nonlinear exponential observer for the population biology model under study. The nonlinear observer design for the population biology model is constructed by applying Sundarapandian’s theorem (2002) and using only the dynamics of the Lotka-Volterra population biology model and the prey population size as the output function. Numerical example and MATLAB simulations are given to illustrate the ecological monitoring or the nonlinear observer design for the two-species LotkaVolterra population biology model with negative feedback.
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 کاملExtinction in Nonautonomous Discrete Lotka-Volterra Competitive System with Pure Delays and Feedback Controls
The coexistence and global stability of population models are of the interesting subjects in mathematical biology. Many authors have argued that the discrete time models are governed by differential equations which are more appropriate than the continuous ones to describe the dynamics of population when the population has nonoverlapping generations, a lot has been done on discrete Lotka-Volterr...
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 کاملLattice Lotka - Volterra models and negative cross - di usion
Negative cross-diiusion has been identiied as a factor increasing the possibility of spatio-temporal instabilities in Lotka-Volterra equations. But such terms have been considered as quite rare in ecological modeling, since imply deceitful prey-predator relationships. We show that negative cross-diiusion appears naturally in reaction diiusion equations obtained using a simple mean eld decouplin...
متن کاملConvergence in Lotka-Volterra-type delay systems without instantaneous feedbacks
Synopsis Most of the convergence results appearing so far for delayed Lotka-Volterra-type systems require that undelayed negative feedback dominate both delayed feedback and interspecific interactions. Such a requirement is rarely met in real systems. In this paper we present convergence criteria for systems without instantaneous feedback. Roughly, our results suggest that in a Lotka-Volterra-t...
متن کامل