Abstract
Isochronal function projective synchronization between chaotic and time-delayed chaotic systems with unknown parameters is investigated in this article. Based on Lyapunov stability theory, adaptive controllers and parameter updating laws are designed to achieve the isochronal function projective synchronization between chaotic and time-delayed chaotic systems. The scheme is applied to realize the synchronization between time-delayed Lorenz systems and time-delayed hyper-chaotic Chen systems, respectively. Numerical simulations are also presented to show the effectiveness of the proposed method.Mathematics Subject Classification 2000: 34C28; 34D20; 37N35.
Highlights
In the last few years, chaos synchronization has gained a lot of attention for its potential applications in some engineering applications, such as image processing, chemical and biological systems, information science and in particular secure communication
Among all types of chaos synchronization, projective synchronization phenomenon is of great significance for its potential application in secure communication
In 1999, Mainieri and Rehacek [14] first proposed the concept of projective synchronization, which is characterized that the drive and the response systems could be synchronized up to a scaling factor
Summary
In the last few years, chaos synchronization has gained a lot of attention for its potential applications in some engineering applications, such as image processing, chemical and biological systems, information science and in particular secure communication. Note that projective synchronization [26,27] between time-delayed chaotic systems was extensively investigated. Results about isochronal function projective synchronization between chaotic and time-delayed chaotic systems are still few. Isochronal function projective synchronization scheme between chaotic and timedelayed chaotic systems with unknown parameters is proposed. To consider the isochronal synchronization between chaotic and time-delayed chaotic systems, take the drive system as follows y = F(y)θr + G(y − τ )βr + f (y). Isochronal function projective synchronization between systems (1) and (2) will occur under the control (4) and parameter updating laws (6). The synchronization result could hold between chaotic and delayed chaotic systems with different structures under appropriate controllers and parameter updating laws
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