We consider nonlinear, probability measure{valued dynamical systems that generalise those classical Lotka{Volterra equations in which, to use ecological terminology, the total size of a nite number of populations of interacting species is conserved. In our generalisation there is a \di erent species" at each point of an arbitrary measurable space. Such in nitely{many{species analogues of the cl...

We analyze a probabilistic cellular automaton describing the dynamics of coexistence of a predator–prey system. The individuals of each species are localized over the sites of a lattice and the local stochastic updating rules are inspired by the processes of the Lotka–Volterra model. Two levels of meanfield approximations are set up. The simple approximation is equivalent to an extended patch m...

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...

For the majority of species, per capita growth rate correlates negatively with population density. Although the popular logistic equation for the growth of a single species incorporates this intraspecific competition, multi-trophic models often ignore self-limitation of the consumers. Instead, these models often assume that the predator-prey interactions are purely exploitative, employing simpl...

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...

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.

We use the normal form theory, averaging method, and integral manifold theorem to study the existence of limit cycles in Lotka-Volterra systems and the existence of invariant tori in quadratic systems in ℝ(3).

In this paper, we consider an autonomous Lotka-Volterra stochastic competitive system with feedback controls and infinite delays. Sufficient conditions which ensure the global stability of the system is considered. Some simulation figures are introduced to support the analytical findings.

Abstract This paper aims to developed a high-order and accurate method for the solution of one-dimensional Lotka-Volterra-diffusion with Numman boundary conditions. A fourth-order compact finite difference scheme spatial part combined implicit-explicit Runge Kutta in temporal are proposed. Furthermore, points discretized by using terms fourth order accuracy. key idea proposed is take full advan...

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).