Related papers: Asymptotic regime in N random interacting species
Main aim of this topical issue is to report recent advances in noisy nonequilibrium processes useful to describe the dynamics of ecological systems and to address the mechanisms of spatio-temporal pattern formation in ecology both from the…
We investigate elementary cellular automata (ECA) from the point of view of (discrete) dynamical systems. By studying small lattice sizes, we obtain the complete phase space of all minimal ECA, and, starting from a maximal entropy…
In this paper we show that a variety of interacting particle systems with multiple species can be viewed as random walks on Hecke algebras. This class of systems includes the asymmetric simple exclusion process (ASEP), M-exclusion TASEP,…
Motivated by recent experiments in neuroscience which indicate that neuronal avalanches exhibit scale invariant behavior similar to self-organized critical systems, we study the role of noisy (non-conservative) local dynamics on the…
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…
When can complex ecological interactions drive an entire ecosystem into a persistent non-equilibrium state, where species abundances keep fluctuating without going to extinction? We show that high-diversity spatially-extended systems, in…
We study the effects of time-varying environmental noise on nonequilibrium phase transitions in spreading and growth processes. Using the examples of the logistic evolution equation as well as the contact process, we show that such temporal…
Bistable biological regulatory systems need to cope with stochastic noise to fine-tune their function close to bifurcation points. Here, we study stability properties of this regime in generic systems to demonstrate that cooperative…
The dynamics of an ensemble of bistable elements under the influence of noise and with global time-delayed coupling is studied numerically by using a Langevin description and analytically by using 1) a Gaussian approximation and 2) a…
Emergent non-reciprocal interactions violating Newton's third law are widespread in out-of-equilibrium systems. Phase separating mixtures with such interactions exhibit travelling states with no equilibrium counterpart. Using extensive…
In this thesis we aim to analyze and quantify the energetic and information contents that can be extracted from a dynamical system subject to the external environment. The latter is usually assumed to be deleterious for the feasibility of…
Nonreciprocal active matter systems typically feature an asymmetric role among interacting agents, such as a pursuer-evader relationship. We propose a multi-species nonreciprocal active matter model that is invariant under permutations of…
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…
We derive the stationary probability distribution for a non-equilibrium system composed by an arbitrary number of degrees of freedom that are subject to Gaussian colored noise and a conservative potential. This is based on a…
We investigate the emergent behavior of four types of generic dynamical systems under random environmental perturbations. Sufficient conditions for nearly-emergence in various scenarios are presented. Recent fundamental works of F. Cucker…
Populations interact non-linearly and are influenced by environmental fluctuations. In order to have realistic mathematical models, one needs to take into account that the environmental fluctuations are inherently stochastic. Often,…
We consider a dynamic version of the Neyman contagious point process that can be used for modelling the spacial dynamics of biological populations, including species invasion scenarios. Starting with an arbitrary finite initial…
We study a class of random processes on $N$ particles which can be interpreted as stochastic model of luminescence. Each particle can stay in one of two states: Excited state or ground state. Any particle at ground state is excited with a…
We first present a new stochastic version of the Cucker-Smale model of the emergent behavior in flocks in which the mutual communication between individuals is affected by random factor. Then, the existence and uniqueness of global solution…
We study the asymptotic behavior, as time t goes to infinity, of nonautonomous dynamical systems involving multiscale features. These systems model the emergence of various collective behaviors in game theory, as well as the asymptotic…