Related papers: Analysis of a mutualism model with stochastic pert…
It is proved the existence and uniqueness of the global positive solution to the system of stochastic differential equations describing a non-autonomous stochastic predator-prey model with a modified version of Leslie-Gower and Holling-type…
Understanding the evolutionary stability of cooperation is a central problem in biology, sociology, and economics. There exist only a few known mechanisms that guarantee the existence of cooperation and its robustness to cheating. Here, we…
We study the behavior of an infinite system of ordinary differential equations modeling the dynamics of a metapopulation, a set of (discrete) populations subject to local catastrophes and connected via migration under a mean field rule; the…
The statistical properties of an ecosystem composed of species interacting via pairwise, random interactions and deterministic, concentration limiting self-interaction are studied analytically with tools of equilibrium statistical mechanics…
We propose a model of multispecies populations surviving on distributed resources. System dynamics are investigated under changes in abiotic factors such as the climate, as parameterized through environmental temperature. In particular, we…
The symbiotic branching model in $\mathbb{R}$ describes the behavior of two branching populations migrating in space $\mathbb{R}$ in terms of a corresponding system of stochastic partial differential equations. The system is parametrized…
We present a model for evolution and extinction in large ecosystems. The model incorporates the effects of interactions between species and the influences of abiotic environmental factors. We study the properties of the model by approximate…
This article aims to investigate sufficient conditions for the stability of stochastic differential equations with a random structure, particularly in contexts involving the presence of concentration points. The proof of asymptotic…
The role of species interactions in controlling the interplay between the stability of an ecosystem and its biodiversity is still not well understood. The ability of ecological communities to recover after a small perturbation of the…
We study how environmental stochasticity influences the long-term population size in certain one- and two-species models. The difficulty is that even when one can prove that there is persistence, it is usually impossible to say anything…
Theoretical ecologists have long sought to understand how the persistence of populations depends on biotic and abiotic factors. Classical work showed that demographic stochasticity causes the mean time to extinction to increase…
The effect of disturbance on a model ecosystem of sessile and mutually competitive species [Mathiesen et al. Phys. Rev. Lett. 107, 188101 (2011); Mitarai et al. Phys. Rev. E 86, 011929 (2012) ] is studied. The disturbance stochastically…
Frequency-dependent selection reflects the interaction between different species as they battle for limited resources in their environment. In a stochastic evolutionary game the species relative fitnesses guides the evolutionary dynamics…
Understanding under what conditions populations, whether they be plants, animals, or viral particles, persist is an issue of theoretical and practical importance in population biology. Both biotic interactions and environmental fluctuations…
Mutualistic networks are formed when the interactions between two classes of species are mutually beneficial. They are important examples of cooperation shaped by evolution. Mutualism between animals and plants plays a key role in the…
Stochastic feedback systems give rise to a variety of notions of stability. The conditions for the stability of the median, mean, and variance stability conditions differ. These conditions can be stated explicitly for scalar discrete-time…
This paper investigates the stochastic permanence of malaria and the existence of a stationary distribution for the stochastic process describing the disease dynamics over sufficiently longtime. The malaria system is highly random with…
The transient behavior of an ecosystem with N random interacting species in the presence of a multiplicative noise is analyzed. The multiplicative noise mimics the interaction with the environment. We investigate different asymptotic…
We study the stochastic dynamics of a system of interacting species in a stochastic environment by means of a continuous-time Markov chain with transition rates depending on the state of the environment. Models of gene regulation in systems…
A mutualist model with nonlocal diffusions and a free boundary is first considered. We prove that this problem has a unique solution defined $t\ge0$, and its dynamics are governed by a spreading-vanishing dichotomy. Some criteria for…