Relaxation dynamics in the presence of pulse multiplicative noise sources with different correlation properties

Integrated random pulse process with positive and negative periodicity

A study of nonstationary processes that are integrals of stationary random sequences of delta pulses is presented. An integrated renewal process can be represented as the sum of a deterministic linear function of time and a Wiener process of the corresponding intensity. This intensity is determined by the mean value and variance of the waiting times of the pulse process and is greater for super-Poisson processes than for sub-Poisson ones. Linear growth over time of all cumulants is proved. An integrated random process with fixed time intervals can be replaced by the sum of a deterministic linear function and a random process with bounded variance. The analytical results are in good agreement with the numerical ones.

Effect of multiplicative noise on stationary stochastic process

An open system that can be analyzed using the Langevin equation with multiplicative noise is considered. The stationary state of the system results from a balance of deterministic damping and random pumping simulated as noise with controlled periodicity. The dependence of statistical moments of the variable that characterizes the system on parameters of the problem is studied. A nontrivial decrease in the mean value of the main variable with an increase in noise stochasticity is revealed. Applications of the results in several physical, chemical, biological, and technical problems of natural and humanitarian sciences are discussed.

Delayed bet-hedging resilience strategies under environmental fluctuations

Many biological populations, such as bacterial colonies, have developed through evolution a protection mechanism, called bet hedging, to increase their probability of survival under stressful environmental fluctuation. In this context, the concept of preadaptation refers to a common type of bet-hedging protection strategy in which a relatively small number of individuals in a population stochastically switch their phenotypes to a dormant metabolic state in which they increase their probability of survival against potential environmental shocks. Hence, if an environmental shock took place at some point in time, preadapted organisms would be better adapted to survive and proliferate once the shock is over. In many biological populations, the mechanisms of preadaptation and proliferation present delays whose influence in the fitness of the population are not well understood. In this paper, we propose a rigorous mathematical framework to analyze the role of delays in both preadaptation and proliferation mechanisms in the survival of biological populations, with an emphasis on bacterial colonies. Our theoretical framework allows us to analytically quantify the average growth rate of a bet-hedging bacterial colony with stochastically delayed reactions with arbitrary precision. We verify the accuracy of the proposed method by numerical simulations and conclude that the growth rate of a bet-hedging population shows a nontrivial dependency on their preadaptation and proliferation delays. Contrary to the current belief, our results show that faster reactions do not, in general, increase the overall fitness of a biological population.