Abstract
The main aim of this paper is to investigate the combination synchronization phenomena of various fractional-order systems using the scaling matrix. For this purpose, the combination synchronization is performed by considering two drive systems and one response system. We show that the combination synchronization phenomenon is achieved theoretically. Moreover, numerical simulations are carried out to confirm and validate the obtained theoretical results.
Highlights
Fractional calculus is an old topic, going back to Riemann–Liouville, Leibniz, and Grünwald–Letnikov, where derivatives and integrals are considered of a real or complex order [1,2]
The fractional derivative is considered an excellent tool for explaining different processes with memory and anomalous diffusion problems compared to the classical derivative [7]
Numerical simulations for famous systems with Caputo–Hadamard derivatives were provided to clarify and verify the theoretical results obtained for the phenomenon of combination synchronization
Summary
Fractional calculus is an old topic, going back to Riemann–Liouville, Leibniz, and Grünwald–Letnikov, where derivatives and integrals are considered of a real or complex order [1,2]. Synchronization is a procedure in which two or more systems react with each other, leading to a joint development in some of their dynamic characteristics. Due to the growing interest in studying the synchronization phenomena for chaotic dynamical systems, many types of synchronization have been discovered in the literature [16,17,18,19,20]. Runzi et al [21] presented a new type of synchronization called combination synchronization. This type of synchronization consists of one response system and two drive systems.
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