相关论文: The dynamics of weakly reversible population proce…

Fundamental properties of macroscopic gene-mating dynamic evolutionary systems are investigated. We focus on a single locus, any number of alleles in a two-gender dioecious population, for a large class of systems within population…

Correlations and other collective phenomena in a schematic model of heterogeneous binary agents (individual spin-glass samples) are considered on the complete graph and also on 2d and 3d regular lattices. The system's stochastic dynamics is…

The limiting slow dynamics of slow-fast, piecewise-linear, continuous systems of ODEs occurs on critical manifolds that are piecewise-linear. At points of non-differentiability, such manifolds are not normally hyperbolic and so the…

The behaviour of the 2D model system - the Ikeda map - is investigated in the weakly dissipative regime under external forcing on the incommensurate frequency. Coexistence of a large number of stable invariant curves is shown. Dependence of…

Evolutionary adaptation is the process that increases the fit of a population to the fitness landscape it inhabits. As a consequence, evolutionary dynamics is shaped, constrained, and channeled, by that fitness landscape. Much work has been…

The global asymptotic behavior of a stochastic Hopfield neural network model (HNNM) with delays is explored by studying the existence and structure of random attractors. It is first proved that the trajectory field of the stochastic delayed…

A class of models of biological population and communities with a singular equilibrium at the origin is analyzed; it is shown that these models can possess a dynamical regime of deterministic extinction, which is crucially important from…

To learn about the past from a sample of genomic sequences, one needs to understand how evolutionary processes shape genetic diversity. Most population genetic inference is based on frameworks assuming adaptive evolution is rare. But if…

We consider complex dynamical systems showing metastable behavior but no local separation of fast and slow time scales. The article raises the question of whether such systems exhibit a low-dimensional manifold supporting its effective…

Opinion dynamics is of paramount importance as it provides insights into the complex dynamics of opinion propagation and social relationship adjustment. It is assumed in most of the previous works that social relationships evolve much…

We describe a phase transition in continuum limits of interacting particle systems that exhibits a vertical bifurcation diagram. The transition is mediated by a competition short-range repulsion and long-range attraction. As a consequence…

Populations are made up of an integer number of individuals and are subject to stochastic birth-death processes whose rates may vary in time. Useful quantities, like the chance of ultimate fixation, satisfy an appropriate difference…

We construct a stochastic dynamical systems theory in which sustainability is a structural boundary property of a fully coupled Earth--Human--Production system. Each subsystem is modelled as a vector-valued process governed by stochastic…

This paper analyzes the global dynamics of 1-dimensional agent arrays with nearest neighbor linear couplings. The equations of motion are second order linear ODEs with constant coeffcients. The novel part of this research is that the…

We derive a formula for the quasi-potential of one-dimensional symmetric exclusion process in weak contact with reservoirs. The interaction with the boundary is so weak that, in the diffusive scale, the density profile evolves as the one of…

In any ecosystem, the conditions of the environment and the characteristics of the species that inhabit it are entangled, co-evolving in space and time. We introduce a model that couples active agents with a dynamic environment, interpreted…

We show that the social dynamics responsible for the formation of connected components that appear recurrently in face-to-face interaction networks, find a natural explanation in the assumption that the agents of the temporal network reside…

In a dissipative system, there exists the (global) attractor which has finite fractal dimensions. The flow on the attractor can be parametrized by a finite number of parameters (Temmam 1987). Using machine learning we demonstrate how to…

(Bi)multi-partite interaction patterns are commonly observed in real world systems which have inhibitory and excitatory couplings. We hypothesize these structural interaction pattern to be stable and naturally arising in the course of…

In this review, we describe the singular success of attractor neural network models in describing how the brain maintains persistent activity states for working memory, error-corrects, and integrates noisy cues. We consider the mechanisms…