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A fractional model for predator-prey with omnivore

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dc.contributor.author Bonyah E.
dc.contributor.author Atangana A.
dc.contributor.author Elsadany A.A.
dc.date.accessioned 2022-10-31T15:05:31Z
dc.date.available 2022-10-31T15:05:31Z
dc.date.issued 2019
dc.identifier.issn 10541500
dc.identifier.other 10.1063/1.5079512
dc.identifier.uri http://41.74.91.244:8080/handle/123456789/453
dc.description Bonyah, E., Department of Mathematics Education, University of Education, Winneba, Kumasi Campus, Kumasi, Ghana; Atangana, A., Institute for Groundwater Studies, University of the Free State, Bloemfontein, 9301, South Africa; Elsadany, A.A., Mathematics Department, College of Sciences and Humanities Studies Al-Kharj, Prince Sattam Bin Abdulaziz University, Al-Kharj, Saudi Arabia, Department of Basic Science, Faculty of Computers and Informatics, Suez Canal University, Ismailia, 41522, Egypt en_US
dc.description.abstract We consider the model of interaction of predator and prey with omnivore using three different waiting time distributions. The first waiting time is induced by the power law distribution which is the generator of Pareto statistics. The second waiting time is induced by exponential decay law with a particular property of Delta Dirac distribution when the fractional order tends to 1, this distribution is link to the Poison distribution. While the last waiting distribution, induced by the Mittag-Leffler distribution, presents a crossover from exponential to power law. For each model, we presented the conditions under which the existence of unique set of exact solutions is reached using the fixed-point Picard's method. Making use of a recent suggested numerical scheme, we solved each model numerically and some numerical simulations were generated for different values of fractional orders. We noticed a new attractor which can be considered as a combination of the Brownian motion and power law distribution in the model with the Atangana-Baleanu fractional derivative. With the aim to capture more attractors, we modified the model and presented also some numerical simulations. Our new model provides more attractors than the existing one even for fractional differential cases. We presented finally the Maximal Lyapunov exponent and the bifurcation diagrams. The comparative study shows that modeling with non-local and non-singular kernel fractional derivative leads to more attractors as this kernel is able to capture more physical problems. � 2019 Author(s). en_US
dc.publisher American Institute of Physics Inc. en_US
dc.title A fractional model for predator-prey with omnivore en_US
dc.type Article en_US


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