By constructing suitable Lyapunov function and developing some new analysis techniques, a Lotka-Volterra predator-prey system with ratio-dependent functional responses and feedback controls is studied and a sufficient condition which guarantees the globally attractive of positive solution for the predator-prey model is obtained. Moreover, the numerical simulation to the system is given to illus...

In this work, in terms of the model parameters, sufficient conditions are established to construct a sequence of approximate observers for a two-species competitive Lotka–Volterra system. This iterative approach makes it possible to localize the solution of the system, and reveal its long-term behaviour. The main results are also illustrated by numerical simulations. 2007 Elsevier Inc. All righ...

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).

Abstract The global dynamics of the two-species Lotka–Volterra competition patch model with asymmetric dispersal is classified under assumptions that weak and weighted digraph connection matrix strongly connected cycle-balanced. We show in long time, either exclusion holds one species becomes extinct, or two reach a coexistence equilibrium, outcome determined by strength inter-specific rates. O...

A three species multi-delay Lotka-Volterra ratio-dependent predator-prey model with feedback controls and prey diffusion is investigated. By developing some new analysis methods, sufficient conditions are derived for the permanence of system.

We perform an analysis of a recent spatial version of the classical Lotka-Volterra model, where a finite scale controls individuals' interaction. We study the behavior of the predator-prey dynamics in physical spaces higher than one, showing how spatial patterns can emerge for some values of the interaction range and of the diffusion parameter.