N-Systems Function Projective Combination Synchronization-A Review of Real and Complex Continuous Time Chaos Synchronization

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.