The Lotka-Volterra equations are a system of equations proposed to provide a simplified model of twospecies predator-prey population dynamics. In this paper, we investigate the problem of adaptive chaos control and synchronization of a generalized Lotka-Volterra system discovered by Samardzija and Greller (1988). The Samardzija-Greller model is a two-predator, one-prey generalization of the Lot...

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...

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 interac...

3 Example: Differentiating the Lotka-Volterra ODE system 2 3.1 The Lotka-Volterra ODE system . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 3.2 The derivatives of the Lotka-Volterra ODE system . . . . . . . . . . . . . . . . . . 3 3.3 Integration of the original and augmented Lotka-Volterra ODE system with the Runge-Kutta method . . . . . . . . . . . . . . . . . . . . . . . . . . . ....

For permanent and partially permanent, uniformly bounded Lotka-Volterra systems, we apply the Split Lyapunov function technique developed for competitive Lotka-Volterra systems to find new conditions that an interior or boundary fixed point of a Lotka-Volterra system with general species-species interactions is globally asymptotically stable. Unlike previous applications of the Split Lyapunov t...

Hirota’s bilinear technique is applied to some integrable lattice systems related to the Bäcklund transformations of the 2DToda, Lotka-Volterra and relativistic LotkaVolterra lattice systems, which include the modified Lotka-Volterra lattice system, the modified relativistic Lotka-Volterra lattice system, and the generalized BlaszakMarciniak lattice systems. Determinant solutions are constructe...

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 ...

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...

In recent years, non-autonomous delay differential equations have been used in the study of population dynamics, ecology and epidemic. Among those equations, a famous model for population is the Lotka-Volterra competition system. Due to the various seasonal effects present in real life situation, it is reasonable and practical to study the Lotka-Volterra competition system with periodic coeffic...

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 po...