Related papers: Autonomous models on a Cayley tree
We study the Potts model on locally tree-like random graphs of arbitrary degree distribution. Using a population dynamics algorithm we numerically solve the problem exactly. We confirm our results with simulations. Comparisons with a…
Dynamic regression trees are an attractive option for automatic regression and classification with complicated response surfaces in on-line application settings. We create a sequential tree model whose state changes in time with the…
We present a comprehensive pedagogical discussion of a family of models describing the propagation of a single particle in a multicomponent non-Markovian Gaussian random field. We report some exact results for single-particle Green's…
Most population models assume that individuals within a given population are identical, that is, the fundamental role of variation is ignored. Here we develop a general approach to modeling heterogeneous populations with discrete…
Adaptive networks appear in many biological applications. They combine topological evolution of the network with dynamics in the network nodes. Recently, the dynamics of adaptive networks has been investigated in a number of parallel…
Animals use various processes to inform themselves about their environment and make decisions about how to move and form their territory. In some cases, populations inform themselves of competing groups through observations at distances,…
A class of models for large-scale evolution and mass extinctions is presented. These models incorporate environmental changes on all scales, from influences on a single species to global effects. This is a step towards a unified picture of…
Evolutionary game theory has been successfully used to investigate the dynamics of systems, in which many entities have competitive interactions. From a physics point of view, it is interesting to study conditions under which a coordination…
The time process of transport on randomly evolving trees is investigated. By introducing the notions of living and dead nodes a model of random tree evolution is constructed which describes the spreading in time of objects corresponding to…
We present an individual based model of evolutionary ecology. The reproduction rate of individuals characterized by their genome depends on the composition of the population in genotype space. Ecological features such as the taxonomy and…
This paper is concerned with a reaction-diffusion single species model with harvesting on $n$-dimensional isotropically growing domain. The model on growing domain is derived and the corresponding comparison principle is proved. The…
A simple model of species origin resulted from dynamic features of a population, solely, is developed. The model is based on the evolution optimality in space distribution, and the selection is gone over the mobility. Some biological issues…
The displayed tree phylogenetic network model is shown to sit as a natural submodel of the graphical model associated to a directed acyclic graph (DAG). This representation allows to derive a number of results about the displayed tree…
We introduce an individual-based model for fiber elements having the ability to cross-link or unlink each other and to align with each other at the cross links. We first formally derive a kinetic model for the fiber and cross-links…
We explore the complex dynamical behavior of two simple predator-prey models of biological coevolution that on the ecological level account for interspecific and intraspecific competition, as well as adaptive foraging behavior. The…
The role of forest heterogeneity in the long-term, large-scale dynamics of forest fires is investigated by means of a cellular automata model and mean field approximation. Heterogeneity was conceived as trees (or acres of forest) with…
In this report, I will review some of the most used models in theoretical ecology along with appealing reformulations and recent results in terms of diversity, stability, and functioning of large well-mixed ecological communities.
We study the invariant measures of infinite systems of stochastic differential equations (SDEs) indexed by the vertices of a regular tree. These invariant measures correspond to Gibbs measures associated with certain continuous…
The stationary distribution of a sample taken from a Wright-Fisher diffusion with general small mutation rates is found using a coalescent approach. The approximation is equivalent to having at most one mutation in the coalescent tree to…
We propose dynamical systems trees (DSTs) as a flexible class of models for describing multiple processes that interact via a hierarchy of aggregating parent chains. DSTs extend Kalman filters, hidden Markov models and nonlinear dynamical…