Gaussian-Function-Driven Chaotic Memristive Dynamics with Application to Image Encryption
Qiya Guo, Jiale Chen, Yanbin Zhang, Weigang Sun
Abstract
This paper develops a Gaussian-function-driven chaotic memristive system in which the magnetic flux is characterized by a Gaussian function, distinguishing it from prevailing formulations that employ piecewise, polynomial, or weakly smooth nonlinearities. The proposed system exhibits the key fingerprints of memristive behavior, including pinched hysteresis loops, local activity and nonvolatility. Integrating the Gaussian function into Chua’s circuit produces a multiscroll chaotic Gaussian memristive system, where the attractors emerge in an organized and predictable pattern, with their numbers and spatial distribution determined by the Gaussian kernel parameters. To demonstrate the applicability of the proposed chaotic system, an image encryption scheme exploits the chaotic sequences generated by this system and integrates adaptive Zigzag scrambling, DNA encoding and bit-plane cross-diffusion. Experimental results show that the scheme achieves uniform histograms, negligible pixel correlation, strong key sensitivity and high resistance to noise and differential attacks. The incorporation of Gaussian function enriches the framework of chaotic memristive systems and establishes a flexible and robust foundation for secure image encryption.