Math. Model. Nat. Phenom.
Volume 11, Number 5, 2016Bifurcations and Pattern Formation in Biological Applications
|Page(s)||158 - 174|
|Published online||07 December 2016|
Noise Induced Phenomena in the Dynamics of Two Competing Species
Dipartimento di Fisica e Chimica, Università di Palermo, Group of Interdisciplinary Theoretical Physics and CNISM, Unità di Palermo, Viale delle Scienze, Ed. 18, I-90128
2 Dipartimento di Scienze Veterinarie, Università di Messina Polo Universitario dell’Annunziata, 98168 Messina, Italy
3 Radiophysics Department, Lobachevsky State University, Nizhniy Novgorod, Russia
4 Istituto Nazionale di Fisica Nucleare, Sezione di Catania, Italy
5 Istituto per l’Ambiente Marino Costiero, CNR, U.O.S. di Capo Granitola, Via del Faro 3, I-91020 Campobello di Mazara (TP), Italy
* Corresponding author. E-mail: email@example.com
Noise through its interaction with the nonlinearity of the living systems can give rise to counter-intuitive phenomena. In this paper we shortly review noise induced effects in different ecosystems, in which two populations compete for the same resources. We also present new results on spatial patterns of two populations, while modeling real distributions of anchovies and sardines. The transient dynamics of these ecosystems are analyzed through generalized Lotka-Volterra equations in the presence of multiplicative noise, which models the interaction between the species and the environment. We find noise induced phenomena such as quasi-deterministic oscillations, stochastic resonance, noise delayed extinction, and noise induced pattern formation. In addition, our theoretical results are validated with experimental findings. Specifically the results, obtained by a coupled map lattice model, well reproduce the spatial distributions of anchovies and sardines, observed in a marine ecosystem. Moreover, the experimental dynamical behavior of two competing bacterial populations in a meat product and the probability distribution at long times of one of them are well reproduced by a stochastic microbial predictive model.
Mathematics Subject Classification: 82C05 / 82C31 / 60H10 / 34F15 / 92D25 / 92D40
Key words: noise induced phenomena / population dynamics / Langevin equation / multiplicative noise / stochastic resonance / predictive microbiology
© EDP Sciences, 2016
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