Abstract
This paper investigates the modified function projective synchronization between fractional-order chaotic systems, which are partially linear financial systems with uncertain parameters. Based on the stability theory of fractional-order systems and the Lyapunov matrix equation, a controller is obtained for the synchronization between fractional-order financial chaotic systems. Using the controller, the error systems converged to zero as time tends to infinity, and the uncertain parameters were also estimated so that the phenomenon of parameter distortion was effectively avoided. Numerical simulations demonstrate the validity and feasibility of the proposed method.
Highlights
In recent years, study on chaos is one of the most interesting research topics in real and physical systems [1–4]
In practice, the parameter distortion phenomenon frequently appears in fractional-order chaotic systems
Many projective synchronization methods of chaotic systems with unknown parameters have been proposed in recent years [23]
Summary
Study on chaos is one of the most interesting research topics in real and physical systems [1–4]. Chaos synchronization in fractional-order financial systems has been studied in recent years [20–22]. In practice, the parameter distortion phenomenon frequently appears in fractional-order chaotic systems. Parameters may be uncertain or drift with time in the chaotic synchronization between the response and drive systems because of various kinds of interferences. Many projective synchronization methods of chaotic systems with unknown parameters have been proposed in recent years [23]. Achieving synchronization and identifying parameters are very important in financial chaotic systems. We investigated fractional-order financial systems proposed by Chen [24]. Numerical simulation results showed that the proposed method effectively eliminated chaos and stabilized two financial systems.
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