Related papers: Rare extinction events in cyclic predator-prey gam…
This paper is concerned with a mathematical model of competition for resource where species consume noninteracting resources. This system of differential equations is formally obtained by renormalizing the MacArthur's competition model at…
We consider cyclic Lotka-Volterra models with three and four strategies where at every interaction agents play a strategy using a time-dependent probability distribution. Agents learn from a loss by reducing the probability to play a losing…
We study stochastic extinction for a class of Markov processes motivated by models in ecology and epidemiology. Extinction is often characterized by a boundedness condition and a condition on boundary Lyapunov exponents (invasion rates).…
We identify the phase of a cycle as a new critical factor for tipping points (critical transitions) in cyclic systems subject to time-varying external conditions. As an example, we consider how contemporary climate variability induces…
Discrete time, spatially extended models play an important role in ecology, modelling population dynamics of species ranging from micro-organisms to birds. An important question is how 'bottom up', individual-based models can be…
Extinction times in resampling processes are fundamental yet often intractable, as previous formulas scale as $2^M$ with the number of states $M$ present in the initial probability distribution. We solve this by treating multinomial updates…
Diffusion-driven instability and bifurcation analysis are studied in a predator-prey model with herd behavior and quadratic mortality by incorporating multiple Allee effect into prey species. The existence and stability of the equilibria of…
In this paper we study the long time behaviour of mean field games systems with fractional diffusion, modeling the case that the individual dynamics of the players is driven by independent jump processes and controlled through the drift…
The estimation of the probability of rare events is an important task in reliability and risk assessment. We consider failure events that are expressed in terms of a limit state function, which depends on the solution of a partial…
Coexistence of competing species is, due to unavoidable fluctuations, always transient. In this Letter, we investigate the ultimate survival probabilities characterizing different species in cyclic competition. We show that they often obey…
Coevolutionary dynamics is investigated in chemical catalysis, biological evolution, social and economic systems. The dynamics of these systems can be analyzed within the unifying framework of evolutionary game theory. In this Letter, we…
We show how the Equation-Free approach for mutliscale computations can be exploited to extract, in a computational strict and systematic way the emergent dynamical attributes, from detailed large-scale microscopic stochastic models, of…
Understanding the coexistence of diverse species in a changing environment is an important problem in community ecology. Bet-hedging is a strategy that helps species survive in such changing environments. However, studies of bet-hedging…
We study the dynamics of isolated interacting spin chains that are periodically driven by sudden quenches. Using full exact diagonalization of finite chains, we show that these systems exhibit three distinct regimes. For short driving…
We study a class of the stochastic May-Leonard models, with three species dominating each other in a cyclic nonhierarchical way, according to the rock-paper-scissors game. We introduce an unevenness in the system, by considering that one of…
Recent work of M.D. Johnston et al. has produced sufficient conditions on the structure of a chemical reaction network which guarantee that the corresponding discrete state space system exhibits an extinction event. The conditions consist…
We propose a minimal model of the dynamics of diversity -- replicator equations with extinction, invasion and mutation. We numerically study the behavior of this simple model and show that it displays completely different behavior from the…
Interacting particle systems with many degrees of freedom may undergo phase transitions to sustain atypical fluctuations of dynamical observables such as the current or the activity. This leads in some cases to symmetry-broken space-time…
In this paper, we consider a two-player two-strategy game with random payoffs in a population subdivided into $d$ demes, each containing $N$ individuals at the beginning of any given generation and experiencing local extinction and…
1 Sharp prediction of extinction times is needed in biodiversity monitoring and conservation management. 2 The Galton-Watson process is a classical stochastic model for describing population dynamics. Its evolution is like the matrix…