A1 Vertaisarvioitu alkuperäisartikkeli tieteellisessä lehdessä
Three-Species Lotka-Volterra Model with Respect to Caputo and Caputo-Fabrizio Fractional Operators
Tekijät: Khalighi Moein, Eftekhari Leila, Hosseinpour Soleiman, Lahti Leo
Kustantaja: MDPI
Julkaisuvuosi: 2021
Lehti: Symmetry
Tietokannassa oleva lehden nimi: SYMMETRY-BASEL
Lehden akronyymi: SYMMETRY-BASEL
Artikkelin numero: ARTN 368
Vuosikerta: 13
Numero: 3
Sivujen määrä: 22
eISSN: 2073-8994
DOI: https://doi.org/10.3390/sym13030368
Julkaisun avoimuus kirjaamishetkellä: Avoimesti saatavilla
Julkaisukanavan avoimuus : Kokonaan avoin julkaisukanava
Rinnakkaistallenteen osoite: https://research.utu.fi/converis/portal/detail/Publication/55080266
Rinnakkaistallenteen lisenssi: CC BY
Rinnakkaistallennetun julkaisun versio: Kustantajan versio
In this paper, we apply the concept of fractional calculus to study three-dimensional Lotka-Volterra differential equations. We incorporate the Caputo-Fabrizio fractional derivative into this model and investigate the existence of a solution. We discuss the uniqueness of the solution and determine under what conditions the model offers a unique solution. We prove the stability of the nonlinear model and analyse the properties, considering the non-singular kernel of the Caputo-Fabrizio operator. We compare the stability conditions of this system with respect to the Caputo-Fabrizio operator and the Caputo fractional derivative. In addition, we derive a new numerical method based on the Adams-Bashforth scheme. We show that the type of differential operators and the value of orders significantly influence the stability of the Lotka-Volterra system and numerical results demonstrate that different fractional operator derivatives of the nonlinear population model lead to different dynamical behaviors.
Avainsanat:
Adam-Bashforth method, Caputo-Fabrizio operator, Lotka-Volterra differential equations, stability analysis
Ladattava julkaisu This is an electronic reprint of the original article. |  |
