# Synchronization and Application of a Novel Hyperchaotic System Based on Adaptive Observers
## 1 Introduction
They synchronized the proposed system with a reduced number of amplifiers. This synchronization has been used in secure communication applications. [PERSON] et al. [15] proposed a 4-dimensional hyperchaotic system based on cosine function. The authors have demonstrated the dynamic analysis and synchronization of the new system. They also presented an FPGA-based implementation of their proposed hyperchaotic system. [PERSON] et al. [28] proposed a new nonlinear 4-dimensional hyperchaotic system. They showed in their publication that the proposed system has hidden attractors. Then, they applied it on FPAA to show the accuracy of their proposed system. [PERSON] et al. [29] proposed a new 4-dimensional hyperchaotic system with hidden attractors and existing attractors without an equilibrium point. They performed active control-based synchronization of the proposed system. Nowadays, secure and effective information communication is increasing and gaining in importance. In this context, chaotic systems and in particular hyperchaotic systems have the potential to offer new and effective solutions for communication security. Recent studies have underscored the challenges in synchronizing hyperchaotic systems, particularly in practical applications involving parameter uncertainty. In systems with parameter uncertainty, achieving synchronization is notably challenging. To address this difficulty, the use of adaptive-based observers is considered a viable solution for designing such systems. The innovations presented in this study and the contributions of this work to the literature are listed as follows:  
* First, a new hyperchaotic system is proposed as an addition to the literature. Comprehensive dynamic analysis of the system is carried out. As a result of the dynamic analysis, it is observed that the proposed system exhibits hyperchaotic behavior. * Adaptive observer-based synchronization of the new system is designed. While performing the synchronization, parameter uncertainty is also taken into account. As a result of the design, it is observed that the synchronization errors reach zero in a short time, while at the same time the parameter uncertainty is eliminated. * The adaptive observer-based synchronization method is tested in a secure communication application where chaotic system synchronization is usually used. The transmitted signal is first masked by the transmitting hyperchaotic system and then transmitted to the receiving hyperchaotic system. * The analysis shows that the transmitted signal is successfully extracted from the masked signal received by the receiving hyperchaotic system within a short period of time. In Section 2, the mathematical model of the proposed hyperchaotic system is introduced and the necessary dynamic analysis methods are applied. In Section 3, the circuit simulation is performed. In Section 4, adaptive observer-based synchronization of the new hyperchaotic system is implemented and simulated. In Section 5, the realized synchronization is used in a secure communication application. Section 6 presents the conclusions.