Related papers: Punctuated equilibrium in an evolving bacterial po…
The existence and local stability of some non-negative equilibrium points of a class of SIRS infectious disease models with non-linear infection and treatment rates are investigated under the condition that the total population is a…
Motivated by the results of recent laboratory experiments (Yoshida et al. Nature, 424, 303-306 (2003)) as well as many earlier field observations that evolutionary changes can take place in ecosystems over relatively short ecological time…
We present a two-species population model in a well-mixed environment where the dynamics involves, in addition to birth and death, changes due to environmental factors and inter-species interactions. The novel dynamical components are…
A biologically motivated model for spatio-temporal coexistence of two competing species is studied by mean-field theory and numerical simulations. In d>1 dimensions the phase diagram displays an extended region where both species coexist,…
We introduce a comprehensive analytical benchmark, relying on Fokker-Planck formalism, to study microbial dynamics in presence of both biotic and abiotic forces. In equilibrium, we observe a balance between the two kinds of forces, leading…
Noise-induced transitions between metastable fixed points in systems evolving on multiple time scales are analyzed in situations where the time scale separation gives rise to a slow manifold with bifurcation. This analysis is performed…
The generalized stochastic Loewner evolution (SLE) driven by reversible Langevin dynamics was theoretically investigated in the context of non-equilibrium statistical mechanics. The recent study of the authors revealed that the Loewner…
The well-posedness of a multi-population dynamical system with an entropy regularization and its convergence to a suitable mean-field approximation are proved, under a general set of assumptions. Under further assumptions on the evolution…
A nonlinearly coupled system of bouncing balls is shown to exhibit features like self-organised-criticality (SOC) and punctuated equilibrium (PE) in suitable parameter domains. The temporal evolution of the non-stationary amplitudes is…
In this paper we review various information-theoretic characterizations of the approach to equilibrium in biological systems. The replicator equation, evolutionary game theory, Markov processes and chemical reaction networks all describe…
A central feature of complex systems is the relevance and entanglement of different levels of description. For instance, the dynamics of ecosystems can be alternatively described in terms of large ecological processes and classes of…
In this paper, we investigate a class of nonlinear impulsive stochastic differential evolution equations with infinite delay in Banach space. Based on the Krasnoselskii's fixed point theorem, sufficient conditions of the existence of the…
We propose a model of chemostat where the bacterial population is individually-based, each bacterium is explicitly represented and has a mass evolving continuously over time. The substrate concentration is represented as a conventional…
Bacterial assemblies exhibit rich collective behaviors that control their biological functions, making them a relevant object of study from an active matter physics perspective. Dense bacterial suspensions self-organize into distinct…
At Alife VI, Mark Bedau proposed some evolutionary statistics as a means of classifying different evolutionary systems. Ecolab, whilst not an artificial life system, is a model of an evolving ecology that has advantages of mathematical…
In this work we study the stability of the equilibria reached by ecosystems formed by a large number of species. The model we focus on are Lotka-Volterra equations with symmetric random interactions. Our theoretical analysis, confirmed by…
The population dynamics and stability of ecosystems of interacting species is studied from the perspective of non-equilibrium thermodynamics by assuming that species, through their biotic and abiotic interactions, are units of entropy…
Arguing about the equilibrium distribution of continuous-time Markov chains can be vital for showing properties about the underlying systems. For example in biological systems, bistability of a chemical reaction network can hint at its…
The paper considers some concepts of nonuniform asymptotic stability for skew-evolution semiflows on Banach spaces. The obtained results clarify differences between the uniform and nonuniform cases. Some examples are included to illustrate…
Starting from common assumptions, we build a rate equation model for multi-strain disease dynamics in terms of immune repertoire classes. We then move to a strain-level description where a low-order closure reminiscent of a pair…