相关论文: Equilibrium in a large Lotka-Volterra system with …

For a population with any given number of types, we construct a new multivariate Moran process with frequency-dependent selection and establish, analytically, a correspondence to equilibrium Lotka-Volterra phenomenology. This…

In complex ecological communities, species may self-organize into clusters or clumps where highly similar species can coexist. The emergence of such species clusters can be captured by the interplay between neutral and niche theories. Based…

Spontaneous formation of transverse patterns is ubiquitous in nonlinear dynamical systems of all kinds. An aspect of particular interest is the active control of such patterns. In nonlinear optical systems this can be used for all-optical…

Game theory ideas provide a useful framework for studying evolutionary dynamics in a well-mixed environment. This approach, however, typically enforces a strictly fixed overall population size, deemphasizing natural growth processes. We…

We study a model ecosystem by means of dynamical techniques from disordered systems theory. The model describes a set of species subject to competitive interactions through a background of resources, which they feed upon. Additionally…

We investigate the Generalized Lotka-Volterra (GLV) equations, a central model in theoretical ecology, where species interactions are assumed to be fixed over time and heterogeneous (quenched noise). Recent studies have suggested that the…

Species coexistence is a complex, multifaceted problem. At an equilibrium, coexistence requires two conditions: stability under small perturbations; and feasibility, meaning all species abundances are positive. Which of these two conditions…

We investigate a model of high-dimensional dynamical variables with all-to-all interactions that are random and non-reciprocal. We characterize its phase diagram and show that the model can exhibit chaotic dynamics. We show that the…

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…

In this paper we study the long term dynamics of two prey species and one predator species. In the deterministic setting, if we assume the interactions are of Lotka-Volterra type (competition or predation), the long term behavior of this…

In this paper, we introduce a general framework to quantify dissimilarities between generalized Lotka-Volterra dynamical processes, ranging from classical predator-prey systems to multispecies communities interacting on networks. The…

It is known that the effect of species' density on species' growth is non-additive in real ecological systems. This challenges the conventional Lotka-Volterra model, where the interactions are always pairwise and their effects are additive.…

Complex ecological networks are often characterized by intricate interactions that extend beyond pairwise relationships. Understanding the stability of higher-order ecological networks is salient for species coexistence, biodiversity, and…

We consider a dynamical system obtained by the random switching between $N$ Lotka-Volterra food chains. Our key assumption will be that at least two vector fields only differ on the resources allocated to the growth rate of the first…

A system of nonlinear ordinary differential equations with forcing function is developed to model evolution processes in complex systems. In this system R, C, and P are the resource, consumption, and production functions correspondingly. F…

According to contemporary views, equilibrium constant is relevant only to true thermodynamic equilibria in isolated systems with one chemical reaction. The paper presents a novel formula that ties-up equilibrium constant and chemical system…

We study the dynamics of a predator-prey system in a random environment. The dynamics evolves according to a deterministic Lotka-Volterra system for an exponential random time after which it switches to a different deterministic…

We consider the problem of equilibration of a single oscillator system with dynamics given by the generalized Langevin equation. It is well-known that this dynamics can be obtained if one considers a model where the single oscillator is…

In self-gravitating stars, two dimensional or geophysical flows and in plasmas, long range interactions imply a lack of additivity for the energy; as a consequence, the usual thermodynamic limit is not appropriate. However, by contrast with…

Nonlinear Fokker-Planck equations play a major role in modeling large systems of interacting particles with a proved effectiveness in describing real world phenomena ranging from classical fields such as fluids and plasma to social and…