SOME CHAOTIC MATHEMATICAL MODELS WITH STOCHASTIC RESETTING

Ilknur Koca and Abdon Atangana
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Ilknur Koca: Department of Accounting and Financial Management, Seydikemer High School of Applied Sciences, Mugla Sıtkı Kocman University, Mugla, Turkey
Abdon Atangana: ��Institute for Groundwater Studies, Faculty of Natural and Agricultural Sciences, University of the Free State, Bloemfontein 9301, South Africa‡Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan

FRACTALS (fractals), 2022, vol. 30, issue 08, 1-23

Abstract: A system of three nonlinear equations that depict chaotic behavior was considered in this work. We looked at four cases: one with a power-law property; one with a fading memory effect; one with a transition from stretched exponential to power-law; and one with a stochastic component. We have presented a detailed analysis of stability and we have suggested a number similar to the reproductive number in the case of epidemiology. At this stage, we did not provide a physical meaning for such a number. However, such a number may be useful. A numerical scheme based on the Lagrange polynomial interpolation was used to solve the respective models numerically. Numerical simulations were performed for different values of fractional orders and densities of randomness and piecewise ideas.

Keywords: Stochastic Chaotic Models; Fractional Differential Operators; New Number; Lagrange Polynomial Interpolation (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1142/S0218348X22402125

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