Chaotic behaviour of fractional predator-prey dynamical system. (English) Zbl 1489.92119
Summary: 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.
MSC:
| 92D25 | Population dynamics (general) |
| 34A08 | Fractional ordinary differential equations |
| 26A33 | Fractional derivatives and integrals |
| 65T60 | Numerical methods for wavelets |
Keywords:
predator-prey model; rabies model; Bernstein wavelet; Euler approach; operational matrix; Caputo derivative; fractional differential equationsReferences:
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