Related papers: Demographic noise and piecewise deterministic Mark…

We analyze dynamical systems subjected to an additive noise and their deterministic limit. In this work, we will introduce a notion by which a stochastic system has something like a Markov partition for deterministic systems. For a chosen…

Noise and spatial degrees of freedom characterize most ecosystems. Some aspects of their influence on the coevolution of populations with cyclic interspecies competition have been demonstrated in recent experiments [e.g. B. Kerr et al.,…

We describe a continuous-time modelling framework for biological population dynamics that accounts for demographic noise. In the spirit of the methodology used by statistical physicists, transitions between the states of the system are…

Strong positive feedback is considered a necessary condition to observe abrupt shifts of ecosystems. A few previous studies have shown that demographic noise -- arising from the probabilistic and discrete nature of birth and death processes…

Noise, through its interaction with the nonlinearity of the living systems, can give rise to counter-intuitive phenomena such as stochastic resonance, noise-delayed extinction, temporal oscillations, and spatial patterns. In this paper we…

Necessary and sufficient conditions are given for a substochastic semigroup on $L^1$ obtained through the Kato--Voigt perturbation theorem to be either stochastic or strongly stable. We show how such semigroups are related to piecewise…

Consider the problem of interference mitigation in the identification of the dynamics of multidimensional control systems in the class of linear stationary models for single realizations of the observed signals. A concepts uncorrelated…

System-environment interactions are intrinsically nonlinear and dependent on the interplay between many degrees of freedom. The complexity may be even more pronounced when one aims to describe biologically motivated systems. In that case,…

A new sufficient condition is proved for the existence of stochastic semigroups generated by the sum of two unbounded operators. It is applied to one-dimensional piecewise deterministic Markov processes, where we also discuss the existence…

The influence of an external random field on the competition process in a nonlinear open spatially extended system is analyzed numerically. A three-component model is chosen as the competition model in which a "weak" species can move in…

In this paper, we seek to understand the behavior of dynamical systems that are perturbed by a parameter that changes discretely in time. If we impose certain conditions, we can study certain embedded systems within a hybrid system as…

We study a system whose dynamics are governed by predictions of its future states. A general formalism and concrete examples are presented. We find that the dynamical characteristics depend on how to shape the predictions as well as on how…

Stochastic phenomena in which the noise amplitude is proportional to the fluctuating variable itself, usually called {\it multiplicative noise}, appear ubiquitously in physics, biology, economy and social sciences. The properties of…

We employ a typical genetic circuit model to explore how noise can influence the dynamic structure. With the increase of a key interactive parameter, the model will deterministically go through two bifurcations and three dynamic structure…

Density dependent Markov population processes with countably many types can often be well approximated over finite time intervals by the solution of the differential equations that describe their average drift, provided that the total…

In animal groups, individual decisions are best characterised by probabilistic rules. Furthermore, animals of many species live in small groups. Probabilistic interactions among small numbers of individuals lead to a so called intrinsic…

Microbial populations in the natural environment are likely to experience growth conditions very different from those of a typical laboratory xperiment. In particular, removal rates of biomass and substrate are unlikely to be balanced under…

A natural phenomenon occurring in a living system is an outcome of the dynamics of the specific biological network underlying the phenomenon. The collective dynamics have both deterministic and stochastic components. The stochastic nature…

We investigate the lifetime of dynamical regimes under the impact of noise motivated by low-dimensional models of the atmosphere. One may expect that the inclusion of noise tends to make the system leave prescribed regions of the state…

We present a novel approach allowing the study of rare events like fixation under fluctuating environments, modeled as extrinsic noise, in evolutionary processes characterized by the dominance of one species. Our treatment consists of…