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A fundamental problem in evolutionary ecology research is to explain how different species coexist in natural ecosystems. This question is directly related with species trophic competition. However, competition theory, based on the…
Lotka Volterra model and its modified forms have long become a major area of interest for periodic motions in nonlinear systems with competitive species. The model given by Volterra shows that its periodicity is dependent on initial…
We investigate the Volterra ecosystem driven by correlated noises. The competition of the predators induces an increasing in population density of the predators. The competition of the preys, however, leads the predators to decay. The…
We study the equilibria of a large Lokta-Volterra system of coupled differential equations in the case where the interaction coefficients form a large random matrix. In the case where this random matrix follows an elliptic model , we study…
We perform individual-based Monte Carlo simulations in a community consisting of two predator species competing for a single prey species, with the purpose of studying biodiversity stabilization in this simple model system. Predators are…
Decision making is a fundamental capability of living organisms, and has recently been gaining increasing importance in many engineering applications. Here, we consider a simple decision-making principle to identify an optimal choice in…
We present new a stability result for periodic solutions of the periodic predator prey Lotka Volterra model, based on boundaries for the average of the coexistence states. Our result complements previous one in the literature.
Bacteria and their viruses ("bacteriophages") coexist in natural environments forming complex infection networks. Recent empirical findings suggest that phage-bacteria infection networks often possess a nested structure such that there is a…
We consider a dynamical system obtained by the random switching between $N$ Lotka-Volterra food chains. Our key assumption will be that at least two vector fields only differ on the resources allocated to the growth rate of the first…
The global dynamics of the two-species Lotka-Volterra competition patch model with asymmetric dispersal is classified under the assumptions of weak competition and the weighted digraph of the connection matrix is strongly connected and…
The possible control of competitive invasion by infection of the invader and multiplicative noise is studied. The basic model is the Lotka-Volterra competition system with emergent carrying capacities. Several stationary solutions of the…
Classical ecological models predict that large, diverse communities should be unstable, presenting a central challenge to explaining the stable biodiversity seen in nature. We revisit this long-standing problem by extending the generalized…
This paper mainly focuses on the sign of the wave speed in the Lotka-Volterra competition system of bistable type, also known as the strong-strong competition case. The traveling wave solution of the system is crucial for understanding the…
New observations are opening the possibility of characterising habitable environments in exoplanetary systems, with the recent example of the candidate hycean world K2-18 b. This motivates an exploration of the possible ecological…
Dynamical systems are a valuable asset for the study of population dynamics. On this topic, much has been done since Lotka and Volterra presented the very first continuous system to understand how the interaction between two species -- the…
In this note, we study the long time behavior of Lotka-Volterra systems whose coefficients vary randomly. Benam and Lobry established that randomly switching between two environments that are both favorable to the same species may lead to…
We investigate the Lotka-Volterra model for predator-prey competition with a finite carrying capacity that varies periodically in time, modeling seasonal variations in nutrients or food resources. In the absence of time variability, the…
We introduce and analyze a spatial Lotka-Volterra competition model with local and nonlocal interactions. We study two alternative classes of nonlocal competition that differ in how each species' characteristics determine the range of the…
When three species compete cyclically in a well-mixed, stochastic system of $N$ individuals, extinction is known to typically occur at times scaling as the system size $N$. This happens, for example, in rock-paper-scissors games or…
In apparent contradiction to competition theory, the number of known, co-existing plankton species far exceeds their explicable biodiversity - a discrepancy termed the Paradox of the Plankton. We introduce a new game-theoretic model for…