The Effects of Continuously Varying the Fractional Differential Order of Chaotic Nonlinear Systems |
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| Institution: | 1. Faculty of Education, Gaziosmanpaşa University, Tokat 60250, Turkey;2. Departamento de Matemáticas, Universidad Sergio Arboleda, Bogotá 110221, Colombia;1. Institute of Applied Mathematics, Baku State University, Az 1148, Z. Khalilov str. 23, Baku, Azerbaijan;2. Institute of Control Systems of ANAS, AZ1141, B. Vahabzadeh str. 9, Baku, Azerbaijan |
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| Abstract: | We consider nonlinear third order differential equations which are known to exhibit chaotic behaviour, and amend their order using fractional calculus techniques. By doing this we demonstrate that by continuously increasing the order of differentiation for those systems from 2 to 3, a period doubling route to chaos ensues. This period doubling begins at a system specific order value between 2 and 3. |
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