Related papers: On dynamical systems of quadratic stochastic opera…
Statistical systems are conceived from the standpoint of statistical mechanics, as made of a (generally large) number of identical units and exhibiting a (generally large) number of different configurations (microstates), among which only…
Operator splitting methods allow to split the operator describing a complex dynamical system into a sequence of simpler subsystems and treat each part independently. In the modeling of dynamical problems, systems of (possibly coupled)…
Many systems in biology, physics and engineering can be described by systems of ordinary differential equation containing many parameters. When studying the dynamic behavior of these large, nonlinear systems, it is useful to identify and…
Stochastic differential equations are widely used in various fields; in particular, the usefulness of duality relations has been demonstrated in some models such as population models and Brownian momentum processes. In this study, a…
This contribution is concerned with mathematical models for the dynamics of the genetic composition of populations evolving under recombination. Recombination is the genetic mechanism by which two parent individuals create the mixed type of…
The language of operator algebras is of great help for the formulation of questions and answers in quantum statistical mechanics. In Chapter 1 we present a minimal mathematical introduction to operator algebras, with physical applications…
In this paper we consider quadratic stochastic operators designed on finite Abelian groups. It is proved that such operators have the property of regularity.
The study of density-dependent stochastic population processes is important from a historical perspective as well as from the perspective of a number of existing and emerging applications today. In more recent applications of these…
A two-type two-sex branching process is introduced with the aim of describing the interaction of predator and prey populations with sexual reproduction and promiscuous mating. In each generation and in each species the total number of…
In this article we present the modeling of bi-stability view problems described by the activity or firing rates of two interacting population of neurons. Starting from the study of a complex system, the sys-tem of stochastic differential…
Recent experimental advances have inspired the development of theoretical tools to describe the non-equilibrium dynamics of quantum systems. Among them an exact representation of quantum spin systems in terms of classical stochastic…
Dynamical systems are used to model a variety of phenomena in which the bifurcation structure is a fundamental characteristic. Here we propose a statistical machine-learning approach to derive lowdimensional models that automatically…
Stochastic dynamic models have been extensively used for the description of processes with uncertainties arising in the operations research, behavioral sciences, and many other application areas. A large class of the problems from these…
We identify the conditions under which a stochastic driving inducing energy changes on a system coupled to a thermal bath can be treated as a work source. When these conditions are met, the work statistics satisfies the Crooks fluctuation…
Motivated by a general principle governing regulation mechanisms in biological cells, we investigate a general interaction scheme between different populations of particles and specific particles, referred to as agents. Assuming that each…
Single species population models and discrete stochastic gene frequency models are two standards of mathematical biology important for the evolution of populations. An agent based model is presented which reproduces these models and then…
Background. It is assumed that the introduction of stochastic in mathematical model makes it more adequate. But there is virtually no methods of coordinated (depended on structure of the system) stochastic introduction into deterministic…
We consider q-state Potts models coupled by their energy operators. Restricting our study to self-dual couplings, numerical simulations demonstrate the existence of non-trivial fixed points for 2 <= q <= 4. These fixed points were first…
A recent characterisation of Fock-adapted contraction operator stochastic cocycles on a Hilbert space, in terms of their associated semigroups, yields a general principle for the construction of such cocycles by approximation of their…
The scope of the paper is the theoretical analysis of the time rate in which a dynamical system reaches a stable stationary state or stable oscillations. The method used for the analysis is based on the so-called iterative time profiles,…