Related papers: Phase Space Formulation of Population Dynamics in …
We introduce the evolving categories multinomial (ECM) distribution for multivariate count data taken over time. This distribution models the counts of individuals following iid stochastic dynamics among categories, with the number and…
To describe population dynamics, it is crucial to take into account jointly evolution mechanisms and spatial motion. However, the models which include these both aspects, are not still well-understood. Can we extend the existing results on…
We present a simple model for describing the dynamics of the interaction between a homogeneous population or society, and the natural resources and reserves that the society needs for its survival. The model is formulated in terms of…
Human dynamics and sociophysics suggest statistical models that may explain and provide us with better insight into social phenomena. Here we tackle the problem of determining the distribution of the population density of a social space…
The composition of ecological communities varies not only between different locations but also in time. Understanding the fundamental processes that drive species towards rarity or abundance is crucial to assessing ecosystem resilience and…
The large deviation principle on phase space is proved for a class of Markov processes known as random population dynamics with catastrophes. In the paper we study the process which corresponds to the random population dynamics with linear…
The environment in which a population evolves can have a crucial impact on selection. We study evolutionary dynamics in finite populations of fixed size in a changing environment. The population dynamics are driven by birth and death…
Owing to the analogies between the problem of wealth redistribution with taxation in a multi-agent society, we introduce and discuss a kinetic model describing the statistical distributions in time of the sizes of groups of biological…
The assembly and persistence of ecological communities can be understood as the result of the interaction and migration of species. Here we study a single community subject to migration from a species pool in which inter-specific…
Any epidemiological compartmental model with constant population is shown to be a Hamiltonian dynamical system in which the total population plays the role of the Hamiltonian function. Moreover, some particular cases within this large class…
A class of models is introduced describing the evolution of population species whose carrying capacities are functionals of these populations. The functional dependence of the carrying capacities reflects the fact that the correlations…
Biodiversity widely observed in ecological systems is attributed to the dynamical balance among the competing species. The time-varying populations of the interacting species are often captured rather well by a set of deterministic…
We distinguish a mechanical representation of the world in terms of point masses with positions and momenta and the chemical representation of the world in terms of populations of different individuals, each with intrinsic stochasticity,…
Real-world optimisation problems are often dynamic. Previously good solutions must be updated or replaced due to changes in objectives and constraints. It is often claimed that evolutionary algorithms are particularly suitable for dynamic…
This article presents a general description of dynamical systems using the language of enriched functors and enriched natural transformations. This framework is essential to establish the equivalence of three descriptions of dynamics -- a…
We introduce a model of Poincar\'e mappings which represents hierarchical structure of phase spaces for systems with many degrees of freedom. The model yields residence time distribution of power type, hence temporal correlation remains…
This paper presents a new approach to behavioral-social dynamics of human crowds. First order models are derived based on mass conservation at the macroscopic scale, while methods of the kinetic theory are used to model the decisional…
Proposed to study the dynamics of physiological systems in which the evolution depends on the state in a previous time, the Mackey-Glass model exhibits a rich variety of behaviors including periodic or chaotic solutions in vast regions of…
The Hamiltonian Mean Field model describes a system of N fully-coupled particles showing a second-order phase transition as a function of the energy. The dynamics of the model presents interesting features in a small energy region below the…
A novel theory of hybrid quantum-classical systems is developed, utilizing the mathematical framework of constrained dynamical systems on the quantum-classical phase space. Both, the quantum and the classical descriptions of the respective…