Related papers: Aging by near-extinctions in many-variable interac…
The GREM-like trap model is a continuous time Markov jump process on the leaves of a finite volume $L$-level tree whose transition rates depend on a trapping landscape built on the vertices of the whole tree. We prove that the natural…
Lotka-Volterra (LV) equations play a key role in the mathematical modeling of various ecological, biological and chemical systems. When the number of species (or, depending on the viewpoint, chemical components) becomes large, basic but…
In the framework of recently introduced frustrated lattice gas models, we study the out of equilibrium dynamical processes during the compaction process in granular media. We find irreversible-reversible cycles in agreement with recent…
Ergodicity breaking and aging effects are fundamental challenges in out-of-equilibrium systems. Various mechanisms have been proposed to understand the non-ergodic and aging phenomena, possibly related to observations in systems ranging…
Non-autonomous differential equations exhibit a highly intricate dynamics, and various concepts have been introduced to describe their qualitative behavior. In general, it is rare to obtain time dependent invariant compact attracting sets…
Understanding how stochastic and non-linear deterministic processes interact is a major challenge in population dynamics theory. After a short review, we introduce a stochastic individual-centered particle model to describe the evolution in…
Cyclic dominance of species has been identified as a potential mechanism to maintain biodiversity, see e.g. B. Kerr, M. A. Riley, M. W. Feldman and B. J. M. Bohannan [Nature {\bf 418}, 171 (2002)] and B. Kirkup and M. A. Riley [Nature {\bf…
In this letter we study a reference model in theoretical ecology, the disordered Lotka-Volterra model for ecological communities, in the presence of finite demographic noise. Our theoretical analysis, which takes advantage of a mapping to…
Over the past century, nonlinear difference and differential equations have been used to understand conditions for species coexistence. However, these models fail to account for random fluctuations due to demographic and environmental…
In this paper we present the simplest individual level model of predator-prey dynamics and show, via direct calculation, that it exhibits cycling behavior. The deterministic analogue of our model, recovered when the number of individuals is…
The rapid advancement of environmental sequencing technologies, such as metagenomics, has significantly enhanced our ability to study microbial communities. The eubiotic composition of these communities is crucial for maintaining ecological…
In this paper, we study the significance of ecological interactions and separation of birth and death dynamics in stochastic heterogeneous populations via general birth-death processes. Interactions can manifest through the birth dynamics,…
The aging dynamics of a simple model glass is numerically investigated observing how it takes place in the potential energy landscape $V$. Partitioning the landscape in basins of minima of $|\nabla V|^2$, we are able to elucidate some…
Slow relaxation occurs in many physical and biological systems. `Creep' is an example from everyday life: when stretching a rubber band, for example, the recovery to its equilibrium length is not, as one might think, exponential: the…
Ecological interaction networks are rarely homogeneous: species naturally form communities with distinct interaction structures, resulting in block-structured variance and correlation profiles in the interaction matrix. We study the…
For years, a main focus of ecological research has been to better understand the complex dynamical interactions between species which comprise food webs. Using the connectance properties of a widely explored synthetic food web called the…
A class of models for large-scale evolution and mass extinctions is presented. These models incorporate environmental changes on all scales, from influences on a single species to global effects. This is a step towards a unified picture of…
Macroevolution is considered as a problem of stochastic dynamics in a system with many competing agents. Evolutionary events (speciations and extinctions) are triggered by fitness records found by random exploration of the agents' fitness…
We study the persistence and extinction of species in a simple food chain that is modelled by a Lotka-Volterra system with environmental stochasticity. There exist sharp results for deterministic Lotka-Volterra systems in the literature but…
Analyzing coexistence and survival scenarios of Lotka-Volterra (LV) networks in which the total biomass is conserved is of vital importance for the characterization of long-term dynamics of ecological communities. Here, we introduce a…