Related papers: Evolution of states in a continuum migration model
A model is proposed that describes the evolution of a mixed state of a quantum system for which gain and loss of energy or amplitude are present. Properties of the model are worked out in detail. In particular, invariant subspaces of the…
A new approach to understanding evolution [Val09], namely viewing it through the lens of computation, has already started yielding new insights, e.g., natural selection under sexual reproduction can be interpreted as the Multiplicative…
The deterministic dynamics of randomly connected neural networks are studied, where a state of binary neurons evolves according to a discreet-time synchronous update rule. We give a theoretical support that the overlap of systems' states…
Populations exhibiting partial migration consist of two groups of individuals: Those that mi- grate between habitats, and those that remain fixed in a single habitat. We propose several discrete-time population models to investigate the…
We consider a class of stochastic dynamical systems, called piecewise deterministic Markov processes, with states $(x, \s)\in \O\times \G$, $\O$ being a region in $\bbR^d$ or the $d$--dimensional torus, $\G$ being a finite set. The…
An infinite system of point particles placed in $\mathds{R}^d$ is studied. The particles are of two types; they perform random walks in the course of which those of distinct types repel each other. The interaction of this kind induces an…
We study the ergodic property of a continuous-state branching process with immigration and competition. The exponential ergodicity in a weighted total variation distance is proved under natural assumptions. The main theorem applies to…
This paper studies the long-term behaviour of a continuous time Markov chain formed by two non-negative integer valued components that evolve subject to a competitive interaction. In the absence of interaction the Markov chain is just a…
In this paper, we consider $n$-type Markov branching processes with immigration and resurrection. The uniqueness criteria are first established. Then, a new method is found and the explicit expression of extinction probability is…
It has been argued that any evolution law taking pure states to mixed states in quantum field theory necessarily gives rise to violations of either causality or energy-momentum conservation, in such a way as to have unacceptable…
Populations interact non-linearly and are influenced by environmental fluctuations. In order to have realistic mathematical models, one needs to take into account that the environmental fluctuations are inherently stochastic. Often,…
We prove sharp universal upper bounds on the number of steady and asymptotic states of discrete- and continuous-time Markovian evolutions of open quantum systems. We show that the bounds depend only on the dimension of the system and not on…
We study a general class of translation invariant quantum Markov evolutions for a particle on $\bbZ^d$. The evolution consists of free flow, interrupted by scattering events. We assume spatial locality of the scattering events and…
We consider a stationary continuous model of random size population with non-neutral mutations using a continuous state branching process with non-homogeneous immigration. We assume the type (or mutation) of the immigrants is random given…
We study a class of swarming problems wherein particles evolve dynamically via pairwise interaction potentials and a velocity selection mechanism. We find that the swarming system undergoes various changes of state as a function of the…
Studying the behaviour of Markov processes at boundary points of the state space has a long history, dating back all the way to William Feller. With different motivations in mind entrance and exit questions have been explored for different…
Cooperative interactions pervade in a broad range of many-body populations, such as ecological communities, social organizations, and economic webs. We investigate the dynamics of a population of two equivalent species A and B that are…
We consider spatial population dynamics given by Markov birth-and-death process with constant mortality and birth influenced by establishment or fecundity mechanisms. The independent and density dependent dispersion of spreading are…
We consider time-continuous Markovian discrete-state dynamics on random networks of interacting agents and study the large population limit. The dynamics are projected onto low-dimensional collective variables given by the shares of each…
We examine to what extent the tempo and mode of environmental fluctuations matter for the growth of structured populations. The models are switching, linear ordinary differential equations $x'(t)=A(\sigma(\omega t))x(t)$ where…