The convergence conditions for a class of generalized Persidskii systems and their discretized dynamics are introduced, which can be checked through linear (matrix) inequalities. case almost periodic this with input is also studied. proposed results applied to Lotka–Volterra model opinion dynamics.

It is known that a limit cycle (or periodic coexistence) can occur in a competitor–competitor–mutualist Lotka–Volterra system  ẋ1 = x1(r1 − a11x1 − a12x2 + a13x3), ẋ2 = x2(r2 − a21x1 − a22x2 + a23x3), ẋ3 = x3(r3 + a31x1 + a32x2 − a33x3), where ri , ai j are positive real constants [X. Liang, J. Jiang, The dynamical behavior of type-K competitive Kolmogorov systems and its applications to 3-di...

We consider a periodic Lotka–Volterra competition system without instantaneous negative feedbacks (i.e., pure-delay systems) ẋi (t)= xi(t) [ ri (t)− n ∑ j=1 aij (t)xj ( t − τij (t) )] , i = 1,2, . . . , n. (∗) We establish some 3/2-type criteria for global attractivity of a positive periodic solution of the system, which generalize the well-known Wright’s 3/2 criteria for the autonomous delay l...

In this paper we study the global dynamics of 3–dimensional predator prey Lotka–Volterra systems, which describes two predators competing for food or shared one resource. From theoretical analysis on all parameters of this system, we show that if the resource for prey is limited, then there exist some values of parameters such that two predators and one prey coexist and their population are asy...

We show that a number of models in virus dynamics, epidemiology and plant biology can be presented as ``damped" versions the Lotka-Volterra predator-prey model, by analogy to damped harmonic oscillator. The deepens with use Lyapunov functions, which allow us characterize their dynamics even make some estimates.

Using an LMI (linear matrix inequality) optimization approach, a stability criterion is obtained for the local stability of the positive equilibrium of a Lotka–Volterra system with delays. © 2004 Elsevier Ltd. All rights reserved.