Generating Multiwing Hidden Chaotic Attractors With Only Stable Node-Foci: Analysis, Implementation, and Application

Abstract

Based on Shil'nikov criterion, i.e., extending the number of unstable saddle-focus -type equilibria of chaotic system, a rich and varied multiwing chaos with complicated topology and remarkable pseudorandomness has been coined. However, it is a challenging task to construct multiwing chaos with only stable node-focus -type equilibria as the Shil'nikov criterion is not applicable in the circumstances. To eliminate this difficulty and enrich the multiwing chaos, we construct a simple three-dimensional autonomous system with only two symmetric stable equilibria, and further introduce a sawtooth wave modulation function to configure more equilibria. The highlight is that multiwing chaotic attractors can be generated from system with two or multiple stable node-foci. This characteristic indicates that the attractors can be hidden oscillating and are difficult to be located in the small neighborhoods of equilibria, which makes the system has good concealment performance for security applications. The design mechanism and system properties are theoretically analyzed and numerically investigated using phase portraits, finite-time Lyapunov exponents, and basins of attraction. Hardware experiments based on field-programmable gate array verify the feasibility of the system. Finally, based on the generated multiwing hidden chaotic attractors, an image encryption scheme with high security performance is designed to enhance its application.