The Lotka-Volterra equations can be used to model the behavior of complex systems in nature. Trajectories in a stable heteroclinic channel describe transient dynamics according to the winnerless competition principle in such a system. The existence of such a channel is guaranteed if the parameters of the Lotka-Volterra equations satisfy a number of conditions. We study under what conditions a h...

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...

A novel coordinate transformation is used to reduce a simple generalization of the Lotka-Volterra dynamical system to a single second-order autonomous ordinary differential equation. Formal analytic solutions to this differential equation are presented which are shown to reduce to the recently obtained solution to the LotkaVolterra system [C. M. Evans and G. L. Findley, J. Math. Chem. 25 (1999)...

Having attracted much attention in the past few years, predator-prey system provides a good mathematical model to present the correlation between predators and preys. This paper focuses on the robust stability of Lotka-Volterra predator-prey system with the fuzzy impulsive control model, and Takagi-Sugeno T-S fuzzy impulsive control model as well. Via the T-S model and the Lyapunov method, the ...

By using the theory of exponential dichotomy and Banach fixed point theorem, this paper is concerned with the problem of the existence and uniqueness of almost periodic solution in a harvesting Lotka-Volterra recurrent neural networks on time scales. To a certain extent, our work in this paper corrects the defect in [Y.G. Liu, B.B. Liu, S.H. Ling, The almost periodic solution of Lotka-Volterra ...

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 Generalized Lotka-Volterra (GLV) model: w i (t + 1) = w i (t) + a w(t) ? c w(t)w i (t) ; i = 1 provides a general method to simulate, analyze and understand a wide class of phenomena that are characterized by power-law probability distributions: P (w)dw w ?1? dw (1) and truncated Levy ights uctuations L (w).