Abstract
As an important branch in the field of chaos, chaos synchronization (CHS) has attracted great attentions since it was firstly proposed. In this review article, numerous types of continuous time CHS are presented for the past 29 years. Previous CHS are divided into two major parts: one is CHS in real number field, and the other is CHS in complex number field. Some classic types of CHS, controllers and corresponding stability theories are preliminarily reviewed. Besides, a new type of chaos synchronization is proposed, which is called N-systems combination function projective synchronization (NCOFPS). Interestingly and importantly, most of these proposed types of CHS belong to NCOFPS. Then, time delay function projective synchronization (TDFPS) is also proposed, which is one of the types of NCOFPS and never studied in existed papers. And TDFPS controller, corresponding mathematical proof are obtained and simulation experiments illustrate the effectiveness of investigated controller. This paper provides a generalized view to catch the development of CHS in different fields. Finally, we give the conclusions and prospects of CHS.
Highlights
Since the first specific chaotic system was proposed by Lorenz in 1963 [1], chaos, as the third great physical revolution after the generation of relativity and quantum mechanics, have made significant historical progress in recent years
The types of chaos synchronization (CHS) are changed into two major categories, real CHS and complex CHS
Complete synchronization means that two chaotic systems accomplish accordance with time
Summary
Since the first specific chaotic system was proposed by Lorenz in 1963 [1], chaos, as the third great physical revolution after the generation of relativity and quantum mechanics, have made significant historical progress in recent years It is the interdisciplinary and multidisciplinary field of science [2], which promotes connections between different disciplines and demonstrates the complexity of human society and nature. Zhang et al.: N-Systems Function Projective Combination Synchronization rotating fluids, analyzing the characters of detuned lasers and modeling thermal convection process [8]–[11] It was another major breakthrough in chaos. Time delay function projective synchronization (TDFPS) is investigated It is a special case of NCOFPS and is never reported in existed works.
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