Noise with memory as a model of lemming cycles

Stability in a system subject to noise with regulated periodicity

“…Throughout this paper, we suppose that at time t 0 = 0 there is a pulse so that W t n (τ ) = W t n (τ |t 0 ) [13]. The distributions are shown in Fig.…”

“…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].…”

“…[13]. Moreover, studies on population dynamics show that the competition among species can exhibit quasiperiodic properties and stochastic resonance phenomena [7,8].…”

Stochastic models for phytoplankton dynamics in Mediterranean Sea

“…This new approach is used to better analyze the real dynamics of phytoplankton populations, which are continuously exposed to random and deterministic changes in environmental variables. Indeed, it is worth recalling that marine ecosystems are complex systems, that is open systems characterized by nonlinear interactions between their parts and external perturbations (Goryachev et al, 2005;Maye et al, 2007), both deterministic and random, due to environmental variables (Grenfell et al, 1998;Zimmer, 1999;Bjornstad and Grenfell, 2001;Spagnolo et al, , 2003Spagnolo et al, , 2004Spagnolo et al, , 2005La Barbera and Spagnolo, 2002;Valenti et al, 2004aValenti et al, , 2006Caruso et al, 2005;Chichigina et al, 2005Chichigina et al, , 2011Fiasconaro et al, 2006;Chichigina, 2008;La Cognata et al, 2010). As a consequence, the study of a marine ecosystem has to be performed by considering also the effects of random perturbations, which can be treated as environmental noise sources.…”

Predator population depending on lemming cycles

“…Lemming number can be described from the mathematical point of view as a pulse sequence. 7 Pulses occur only at years of anomalous increase in population. The periodicity of the process can be regulated from quasi-periodic process to random pulse process.…”