Spiral patterns and biodiversity in lattice-free Lotka-Volterra models

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 ...

Bilinear Forms of Integrable Lattices Related to Toda and Lotka-Volterra Lattices

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...

Population Dynamics of Stochastic Lattice Lotka–Volterra Models

Lattice 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...

The 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...