Statistical mechanics of relative species abundance (RSA) patterns in biological networks is presented. The theory is based on multispecies replicator dynamics equivalent to the LotkaVolterra equation, with diverse interspecies interactions. Various RSA patterns observed in nature are derived from a single parameter related to productivity or maturity of a community. The abundance distribution ...

A metapopulation model with explicit local dynamics is studied. Unlike many patch-based metapopulation models which assume that the local population within each patch is at its equilibrium, our model incorporates population changes in local patches that interact with metapopulation dynamics. The model keeps track of the fractions of patches that have species 1 only, species 2 only, or both spec...

Of concern is the effect of a small spatially inhomogeneous perturbation of the reproduction rate of the first species in a two-species LotkaVolterra competition-diffusion problem with spatially homogeneous reaction terms. Apart from this perturbation and the diffusion rates, the two species are assumed to be identical. Our main result shows that the first species can always invade, whereas the...

We develop from basic principles a two-species differential equations model which exhibits mutualistic population interactions. The model is similar in spirit to a commonly cited model (Dean 1983), but corrects problems with singularities in that model. In addition, we investigate our model in more depth. The behavior of the system is investigated by varying the intrinsic growth rate for each o...

In this paper, we establish sufficient conditions under which Lotka-Volterra cooperative systems are permanent for the n-dimensional case. We improve the result of [G. Lu and Z. Lu, Permanence for two species LotkaVolterra systems with delays, Math. Biosci. Engi. 5 (2008), 477-484] for the 2-dimensional case in that no restrictions of the size of time delays are needed. When the interval of tim...

Global dynamical behaviors of the competitive Lotka-Volterra system even in 3-dimension are not fully understood. The Lyapunov function can provide us such knowledge once it is constructed. In this paper, we construct explicitly the Lyapunov function in three examples of the competitive LotkaVolterra system for the whole state space: (1) the general 2-dimensional case; (2) a 3-dimensional model...

Lotka-Volterra population biology models are important models that describe the interaction between various biological species considered as predator-prey system. This work describes a Lotka-Volterra population biology model with negative feedback. We show that for this biological model, the predator and prey species have stable coexistence. Then we shall propose ecological monitoring of the po...

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...

The present study combines the theory and the experimental data to predict the changes on intestinal bacterial populations during ingestion of beneficial probiotic bacteria. Our proposed model is a modified version of the LotkaVolterra model, which takes the probiotic administration into account. Using the linear stability analysis of the model, the conditions for coexistence of the probiotics ...

This talk concerns numerical approximations of oscillating patterns in reaction-diffusion systems. Stability analysis on a test reactiondiffusion system with oscillating solution allows comparisons in terms of stability regions and stepsize restrictions of some time integrators. Moreover, a dissipation and dispersion analysis are also carried out, see [1]. We consider the well known and commonl...