5 Sistemas Lotka-Volterra 10 5.1 Modelo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 5.2 Análisis de Estabilidad . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 5.2.1 Equilibrios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 5.2.2 Primer Método de Lyapunov . . . . . ...

In this paper we prove the existence of non-stationary periodic solutions of delay Lotka-Volterra equations. In the proofs we use the S-degree due to Dylawerski et al. [2].

We provide two examples of the appearance heavy-tailed distributions in social sciences applications. Among these are laws Pareto and Lotka some new ones. The illustrated through construction suitable toy models.

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 theory of optimal foraging predicts abrupt changes in consumer behavior which lead to discontinuities in the functional response. Therefore population dynamical models with optimal foraging behavior can be appropriately described by di erential equations with discontinuous right{hand sides. In this paper we analyze the behavior of three di erent Lotka{Volterra predator{prey systems with opt...

As exemplified by classic Lotka–Volterra theory, there are several canonical outcomes possible to a two species (interference) competitive interaction: coexistence, initial condition-dependent competitive exclusion of one species, or the global exclusion of one species. Evolutionary versions of Lotka–Volterra dynamics have been investigated in order to see the role that evolutionary adaptation ...

We analyse the asymptotic behaviour of integro-differential equations modelling N populations in interaction, where interactions are modelled by non-local terms involving linear combinations of the total number of individuals in each population. These models have already been shown to be suitable for the modelling of drug resistance in cancer. They also generalise the usual Lotka-Volterra ordin...

We investigate the existence, uniqueness and Gaussian curvature of the invariant carrying simplices of 3 species autonomous totally competitive Lotka-Volterra systems. Explicit examples are given where the carrying simplex is convex or concave, but also where the curvature is not single-signed. Our method monitors the curvature of an evolving surface that converges uniformly to the carrying sim...

A food web in a chemostat is considered in which an arbitrary number of competitor populations compete for a single, essential, nonreproducing, growth-limiting substrate, and an arbitrary number of predator populations prey on some or all of the competitor populations. Although any number of predator populations may prey on the same competitor population, each predator population preys on only ...