Abstract
Synchronization of fractional‐order chaotic dynamical systems is receiving increasing attention owing to its interesting applications in secure communications of analog and digital signals and cryptographic systems. In this paper, a drive‐response synchronization method is studied for “phase and antiphase synchronization” of a class of fractional‐order chaotic systems via active control method, using the 3‐cell and Volta systems as an example. These examples are used to illustrate the effectiveness of the synchronization method.
Highlights
The theory of fractional calculus is a 300-year-old topic which can trace back to Leibniz, Riemann, Liouville, Grunwald, and Letnikov 1, 2
It has been found that some fractionalorder differential systems such as the fractional-order jerk model 3, the fractional-order Rossler system 4, and the fractional-order Arneodo system 5 can demonstrate chaotic behavior
The concept of synchronization can be extended to generalized synchronization 8, complete synchronization 9, lag synchronization, phase synchronization, antiphase synchronization, and so on
Summary
The theory of fractional calculus is a 300-year-old topic which can trace back to Leibniz, Riemann, Liouville, Grunwald, and Letnikov 1, 2. Synchronization of fractional-order chaotic systems has started to attract increasing attention due to its potential applications in secure communication and control processing 6, 7. Phase and anti-phase synchronization using is introduced, which is used to “phase and anti-phase synchronization” for a class of fractional-order chaotic systems using active control method 14. 2. Fractional Derivative and Numerical Algorithm of Fractional Differential Equation. We choose the Caputo version and use a predictorcorrector algorithm for fractional differential equations 18 , which is the generalization of. D∗αx t f t, x t , 0 ≤ t ≤ T, 2.4 x k 0 x0k , k 0, 1, . . . , m − 1
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