Related papers: Maximal Sensitive Dependence and the Optimal Path …
A path information is defined in connection with different possible paths of irregular dynamic systems moving in its phase space between two points. On the basis of the assumption that the paths are physically differentiated by their…
We propose a method for approximating solutions to optimization problems involving the global stability properties of parameter-dependent continuous-time autonomous dynamical systems. The method relies on an approximation of the…
Deterministic evolutionary game dynamics can lead to stable coexistences of different types. Stochasticity, however, drives the loss of such coexistences. This extinction is usually accompanied by population size fluctuations. We…
We consider continuous state branching processes that are perturbed by a Brownian motion. These processes are constructed as the unique strong solution of a stochastic differential equation. The long-term extinction and explosion behaviours…
The sensitivity of trajectories over finite time intervals t to perturbations of the initial conditions can be associated with a finite-time Lyapunov exponent lambda, obtained from the elements M_{ij} of the stability matrix M. For globally…
We consider multitype Markovian branching processes evolving in a Markovian random environment. To determine whether or not the branching process becomes extinct almost surely is akin to computing the maximal Lyapunov exponent of a sequence…
Understanding the mechanisms governing population extinctions is of key importance to many problems in ecology and evolution. Stochastic factors are known to play a central role in extinction, but the interactions between a population's…
Highly-diverse ecosystems exhibit a broad distribution of population sizes and species turnover, where species at high and low abundances are exchanged over time. We show that these two features generically emerge in the fluctuating phase…
In infectious disease modelling, the expected time from endemicity to extinction (of infection) may be analysed via WKB approximation, a method with origins in mathematical physics. The method is very general, but its uptake to date may…
We analyze the long term behavior of interacting populations which can be controlled through harvesting. The dynamics is assumed to be discrete in time and stochastic due to the effect of environmental fluctuations. We present extinction…
We consider a system of two stochastic differential equations (SDEs) with competing two-way interactions driven by Brownian motions and spectrally positive $\alpha$-stable random measures. Such a SDE system can be identified as a…
We consider excursions for a class of stochastic processes describing a population of discrete individuals experiencing density-limited growth, such that the population has a finite carrying capacity and behaves qualitatively like the…
We investigate the formation of stable ecological networks where many species share the same resource. We show that such stable ecosystem naturally occurs as a result of extinctions. We obtain an analytical relation for the number of…
In a complex community, species continuously adapt to each other. On rare occasions, the adaptation of a species can lead to the extinction of others, and even its own. "Adaptive dynamics" is the standard mathematical framework to describe…
Stochastic models are widely used to investigate the spread of epidemics in a complex environment. This paper extends a deterministic SAIRS epidemic model to a stochastic case with limited patient capacity and exposure. We first study the…
When four species compete stochastically in a cyclic way, the formation of two teams of mutually neutral partners is observed. In this paper we study through numerical simulations the extinction processes that can take place in this system…
The extinction time of an isolated population can be exponentially reduced by a periodic modulation of its environment. We investigate this effect using, as an example, a stochastic branching-annihilation process with a time-dependent…
The analysis of spatial extremes requires the joint modeling of a spatial process at a large number of stations and max-stable processes have been developed as a class of stochastic processes suitable for studying spatial extremes. Spatial…
Using the tools of the Markov Decision Processes, we justify the dynamic programming approach to the optimal impulse control of deterministic dynamical systems. We prove the equivalence of the integral and differential forms of the…
In multi-period stochastic optimization problems, the future optimal decision is a random variable whose distribution depends on the parameters of the optimization problem. We analyze how the expected value of this random variable changes…