TITLE:
Finite-Time Fast Synchronization of Chaotic Systems with Application to Secure Communications
AUTHORS:
Zhaowei Cai, Jiancheng Zhang, Xiaohua Wu, Ningbo Pang
KEYWORDS:
Fast Chaotic Synchronization, Secure Communication, Finite-Time Observer, Observer Matching Condition, Strongly Observable Condition
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.14 No.5,
May
19,
2026
ABSTRACT: This paper presents a fast chaotic synchronization and secure communication method by constructing a finite-time reduced-order observer under the drive-response configuration. As the output of the drive system, the drive signal usually contains a message signal which is inaccessible to the response system, which hinders the reduced-order observer design. To overcome this limitation, a new equivalent system is obtained by constructing a new output which does not contain the unknown message signal. Then, the observer matching condition and the strongly observable condition are developed, and they are proven to be maintained in the new equivalent system. Thereafter, a finite-time observer (FTO) with reduced-order as well as FTO-based message signal recovery methods are developed, which result in the simultaneous chaotic synchronization and secure communication. One of the advantages of the FTO-based chaotic synchronization and secure communication method over the conventional asymptotic convergence observer method is that both the chaotic synchronization and the message signal recovery can be reached in an arbitrarily pre-defined time, and thus it can achieve a faster as well as a higher quality secure communication. Finally, simulation results are given to illustrate the effectiveness of the proposed techniques.