A way to model stochastic perturbations in population dynamics models with bounded realizations

Abstract : In this paper, we analyze the use of the Ornstein-Uhlenbeck process to model dynamical systems subjected to bounded noisy perturbations. In order to discuss the main characteristics of this new approach we consider some basic models in population dynamics such as the logistic equations and competitive Lotka-Volterra systems. The key is the fact that these perturbations can be ensured to keep inside some interval that can be previously fixed, for instance, by practitioners, even though the resulting model does not generate a random dynamical system. However, one can still analyze the forwards asymptotic behavior of these random differential systems. Moreover, to illustrate the advantages of this type of modeling, we exhibit an example testing the theoretical results with real data, and consequently one can see this method as a realistic one, which can be very useful and helpful for scientists.
Document type :
Journal articles
Complete list of metadatas

Cited literature [6 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-02105829
Contributor : Alain Rapaport <>
Submitted on : Sunday, April 21, 2019 - 10:23:42 PM
Last modification on : Saturday, May 11, 2019 - 1:19:50 AM

File

CCLR_250219.pdf
Publisher files allowed on an open archive

Identifiers

Collections

Citation

Tomas Caraballo, Renato Colucci, Javier López-De-La-Cruz, Alain Rapaport. A way to model stochastic perturbations in population dynamics models with bounded realizations. Communications in Nonlinear Science and Numerical Simulation, Elsevier, 2019, 77, pp.239-257. ⟨https://www.sciencedirect.com/science/article/pii/S1007570419301303⟩. ⟨10.1016/j.cnsns.2019.04.019⟩. ⟨hal-02105829⟩

Share

Metrics

Record views

55

Files downloads

25