Novel nonlinear system family generated from coupling effect of Sin-Cosine function

TL;DR

This paper introduces a new family of nonlinear systems derived from the coupling of sine and cosine functions, revealing chaotic and fractal behaviors with potential applications in secure communication and signal processing.

Contribution

The paper reports the discovery and mathematical classification of the Sine-Cosine Nonlinear System Family (SCNSF), a novel class of systems with unique chaotic and fractal properties.

Findings

SCNSF exhibits chaotic behavior in real numbers.

SCNSF shows rich fractal patterns in complex domain.

Potential applications in secure communication and encryption.

Abstract

The Sine-Cosine function, which is widely adopted in mathematics and physics, has attracted our attention due to its unique properties. By delving into the coupling effect of the Sine-Cosine function, we discover a previously unreported class of nonlinear systems, namely the Sine-Cosine Nonlinear System Family (SCNSF). This discovery is motivated by the need to expand the repertoire of nonlinear systems and understand the complex behaviors that can emerge from the combination of basic trigonometric functions. The SCNSF has both chaotic characteristics in the real number domain and fractal characteristics in the complex number domain. The classification and general mathematical description of SCNSF provide a solid theoretical foundation for further research. The proposal of three types of classic systems within SCNSF and the investigation of their chaotic properties and hardware implementation open up new avenues for practical applications. The large chaotic range exhibited by these systems implies their potential applications in various fields such as secure communication and chaotic circuit design. Moreover, the discovery of the chaos generation mechanism based on the coupling effect of the Sine-Cosine function deepens our understanding of the origin of chaos. In the complex number domain, the high parameter sensitivity and rich fractal patterns of SCNSF can be can be harnessed to develop more advanced encryption algorithms and more sensitive signal detection methods, thereby contributing to the advancement of information security and signal processing technologies. Overall, the chaotic and fractal properties of SCNSF make it a valuable asset in the pursuit of innovative solutions in multiple scientific and engineering disciplines.