Chaotic behaviour of fractional predator-prey dynamical system. (June 2020)

• Record Type: Journal Article
• Authors: Kumar, Sunil; Kumar, Ranbir; Cattani, Carlo; Samet, Bessem
• Is Part Of: Chaos, solitons and fractals. Volume 135(2020)
• Publication Date: 2020-06
• Subjects: Predator-prey model -- Rabies model -- Bernstein wavelet -- Euler approach -- Operational matrix -- Caputo derivative -- Fractional differential equations; Chaotic behavior in systems -- Periodicals; Solitons -- Periodicals; Fractals -- Periodicals; Chaotic behavior in systems; Fractals; Solitons; Periodicals; 003.7
• DOI: 10.1016/j.chaos.2020.109811
• Languages: English
• ISSNs: 0960-0779

Abstract

Abstract: In this endeavour, Bernstein wavelet and Euler methods are used to solve a nonlinear fractional predator-prey biological model of two species. The theoretical results with their corresponding biological consequence due to Bernstein wavelet are considered and discussed. A test problem of predator-prey model with two different cases are examined to determined the capability of our proposed methods. We showed that the obtained solutions are the most powerful and, wherever it is possible the comparison, in a very good coincidence with the other numerical solution. Few numerical simulations are finding for predator and prey populations and new chaotic behaviours of predator-prey population model are also obtained by using the Euler method. Moreover, a comparison have been done between the capability of the Bernstein wavelet and the Euler approach. The numerical simulations and behaviours of Rabies model are depicted through graphically which is a special case of predator-prey model.