相关论文: Dynamics of exponential linear map in functional s…
Hypergraphs have been a useful tool for analyzing population dynamics such as opinion formation and the public goods game occurring in overlapping groups of individuals. In the present study, we propose and analyze evolutionary dynamics on…
This paper combines the decomposition technique ($\sigma$-stability) in random functional analysis with the deterministic theory of asymptotically pointwise contractions to provide a complete self-contained derivation of a fixed point…
Evolution by Natural Selection is a process by which progeny inherit some properties from their progenitors with small variation. These properties are subject to Natural Selection and are called adaptive traits and carriers of the latter…
Valiant's (2007) model of evolvability models the evolutionary process of acquiring useful functionality as a restricted form of learning from random examples. Linear threshold functions and their various subclasses, such as conjunctions…
We consider a class of cubic stochastic operators that are motivated by models for evolution of frequencies of genetic types in populations. We take populations with three mutually exclusive genetic types. The long term dynamics of single…
We study linear response for families of skew-product dynamical systems with contracting fibres. Our approach is based on a sectional transfer operator acting on families of probability measures along the fibres. The operator allows to…
The theoretical and numerical understanding of the key concept of topological entropy is an important problem in dynamical systems. Most studies have been carried out on maps (discrete-time systems). We analyse a scenario of global changes…
The pull-back, push-forward and multiplication of smooth functions can be extended to distributions if their wave front set satisfies some conditions. Thus, it is natural to investigate the topological properties of these operations between…
Random population dynamics with catastrophes (events pertaining to possible elimination of a large portion of the population) has a long history in the mathematical literature. In this paper we study an ergodic model for random population…
In \cite{ CLEVACKTHI, CLEVACK} an attempt is made to find a comprehensive mathematical framework in which to investigate the problems of well-posedness, asymptotic analysis and parameter estimation for fully nonlinear evolutionary game…
We study two-dimensional, two-piece, piecewise-linear maps having two saddle fixed points. Such maps reduce to a four-parameter family and are well known to have a chaotic attractor throughout open regions of parameter space. The purpose of…
We study the continuity of pullback and uniform attractors for non-autonomous dynamical systems with respect to perturbations of a parameter. Consider a family of dynamical systems parameterised by a complete metric space $\Lambda$ such…
The object of study is a soft random geometric graph with vertices given by a Poisson point process on a line and edges between vertices present with probability that has a polynomial decay in the distance between them. Various aspects of…
In a previous paper we considered a sequence of maps on a complete metric space $(X,d)$ and derived an extension of the Banach fixed point theorem. We showed that backward trajectories of maps $X\to X$ converge under mild conditions and…
A novel approach towards construction of absolutely continuous distributions over the unit interval is proposed. Considering two absolutely continuous random variables with positive support, this method conditions on their convolution to…
We obtain a Liouville property for stationary diffusions in random environment which are small, isotropic perturbations of Brownian motion in spacial dimension greater than two. Precisely, we prove that, on a subset of full probability, the…
In this paper, the dynamics of a phytoplankton-zooplankton system with linear functional responses are examined. For the continuous-time model, the global asymptotic stability of the fixed points is demonstrated by constructing Lyapunov…
In the Entropic Dynamics (ED) approach the essence of quantum theory lies in its probabilistic nature while the Hilbert space structure plays a secondary and ultimately optional role. The dynamics of probability distributions is driven by…
We present a stylized model with feedback loops for the evolution of a population's wealth over generations. Individuals have both talent and wealth: talent is a random variable distributed identically for everyone, but wealth is a random…
We consider an ordinary differential equation with a unique hyperbolic attractor at the origin, to which we add a small random perturbation. It is known that under general conditions, the solution of this stochastic differential equation…