Abstract
In this paper we are interested in the fractional-order form of Chua’s system. A discretization process will be applied to obtain its discrete version. Fixed points and their asymptotic stability are investigated. Chaotic attractor, bifurcation and chaos for different values of the fractional-order parameter are discussed. We show that the proposed discretization method is different from other discretization methods, such as predictor-corrector and Euler methods, in the sense that our method is an approximation for the right-hand side of the system under study.
Highlights
In recent years differential equations with fractional order have attracted many researchers’ attention because of their applications in many areas of science and engineering; see, for example, [, ], and [ ]
The need for fractional-order differential equations stems in part from the fact that many phenomena cannot be modeled by differential equations with integer derivatives
The non-local property of fractional differential equations means that the state of a system depends on its current state and on its historical states. This property is very close to the real world, and fractional differential equations have become popular and have been applied to dynamical systems
Summary
Introduction In recent years differential equations with fractional order have attracted many researchers’ attention because of their applications in many areas of science and engineering; see, for example, [ , ], and [ ]. For stability conditions and synchronization of a system of fractional-order differential equations, one can see [ – ]. We recall the basic definitions (Caputo) and properties of fractional order differentiation and integration. To solve fractional-order differential equations, there are two famous methods: frequency domain methods [ ] and time domain methods [ ].
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