Patent DD 288911. References[1] G. Reißig and M. Peschel. Systolische Schaltungsanordnung zur Sim-ulation von Systemen in Lotka–Volterra–Darstellung. Patent DD 288911, 3 Nov. 1989. (“Systolic array for the simulation of Lotka–Volterra–Systems”, in German).

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...

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 ...

In this paper, periodic solution of impulsive Lotka-Volterra recurrent neural networks with delays is studied. Using the continuation theorem of coincidence degree theory and analysis techniques, we establish criteria for the existence of periodic solution of impulsive Lotka-Volterra recurrent neural networks with delays.

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...

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...

Discrete-time Lotka-Volterra competition models are obtained by applying nonstandard finite difference (NSFD) schemes to the continuous-time counterparts of the model. The NSFD methods are noncanonical symplectic numerical schemes when applying to the predator-prey model x = x − xy and y = −y + xy. The local dynamics of the discrete-time model are analyzed and compared with the continuous model...

The classical Monad model for bacterial growth in a chemostnt, based on u Michaelis-Menten kinetic analog, is restated in terms of an approximate LotkaVolterra formulation. The parameters of these two formulations are explicitly related; the new model is easier to work with, but yields the same results as the original. The model is then extended to the case where multiple alternate substrates m...