A Simple Noise Model With Memory for Biological Systems

Abstract

Received () Revised () Accepted () A noise source model, consisting of a pulse sequence at random times with memory, is presented. By varying the memory we can obtain variable randomness of the stochastic process. The delay time between pulses, i. e. the noise memory, produces different kinds of correlated noise ranging from white noise, without delay, to quasi-periodical process, with delay close to the average period of the pulses. The spectral density is calculated. This type of noise could be useful to describe physical and biological systems where some delay is present. In particular it could be useful in population dynamics. A simple dynamical model for epidemiological infection with this noise source is presented. We find that the time behavior of the illness depends on the noise parameters. Specifically the amplitude and the memory of the noise affect the number of infected people.

Stability in a system subject to noise with regulated periodicity

“…The stochastic nature of living systems and the related noiseinduced effects range from bioinformatics [4,5], to population dynamics [6][7][8][9], to virus dynamics and epidemics [10,11].…”

“…Specifically, random variations of species concentrations in natural ecosystems [1,2,[11][12][13], the role of molecular noise in the growth of bacteria that are present in food products [14], and the stochastic dynamics of diseases connected with genetic mutations [15] are fundamental aspects that cannot be neglected when seeking a better understanding of the dynamics of complex living systems. In particular, in these systems the random variations of temperature, food resources, and other environmental parameters can be described using models in which multiplicative noise sources are present [8,16,17].…”

“…[11,29] using a pulse noise model with memory. The pulse noise was the source of the spreading infection, and the memory reflected the presence of the incubation period.…”

Predator population depending on lemming cycles

“…This means that ξ(t) = f /T . The DTDP process 35 is a renewal pulse process with delay ζ 0 after each pulse.…”

The Bistable Potential: An Archetype for Classical and Quantum Systems

“…Systems exhibiting absorbing states and noise-induced phase transitions can be described by these equations. [10][11][12][13][14] The models based on MLE abound not only in physics, but also in biology, ecology, economy, or social sciences. The function of the order parameter g(x) takes different forms depending on the system investigated, ranging from a pure linear multiplicative noise term, often used in population dynamics, to more general expressions which represent the effects of both additive and multiplicative noise sources.…”