Contractivity and global stability for discrete models of Lotka-Volterra type

Persistence and Global Stability in Discrete Models of Pure-delay Nonautonomous Lotka-Volterra Type

In this paper, for the above discrete system of pure-delay type, by improving the former work (2002, J. Math. Anal. Appl. 273, 492-511) which extended the averaged condition offered by S. Ahmad and A. C. Lazer (2000, Nonlinear Analysis 40, 37-49), we offer conditions of persistence, and considering a Lyapunov-like discrete function to the above discrete system, we establish sufficient condition...

Global stability of a Lotka-Volterra type predator-prey model with stage structure and time delay

A delayed Lotka–Volterra type predator–prey model with stage structure for predator is investigated. It is assumed in the model that the individuals in the predator population may belong to one of two classes: the immatures and the matures, the age to maturity is presented by a time delay, and that the immature predators do not have the ability to prey. By analyzing characteristic equations and...

Dynamics of a discrete Lotka-Volterra model

Generalized Lotka-Volterra (GLV) Models

The Generalized Lotka-Volterra (GLV) model: wi(t+ 1) = λwi(t) + aw̄(t)− cw̄(t)wi(t) , i = 1, ......, N 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 ∼ wdw (α ≥ 1) and truncated Levy flights fluctuations Lα(w̄).

Lotka-Volterra competition models for sessile organisms.

Markov models are widely used to describe the dynamics of communities of sessile organisms, because they are easily fitted to field data and provide a rich set of analytical tools. In typical ecological applications, at any point in time, each point in space is in one of a finite set of states (e.g., species, empty space). The models aim to describe the probabilities of transitions between stat...