A conservative system based on a triangular wave memristor and its application in image encryption

Reconstruction techniques can capture the attractor data of dissipative chaotic systems, which will lead to a threat to the security of the cryptosystem. Since conservative chaotic systems do not form chaotic attractors, they can avoid the defects of the dissipative system and resist attacks. This paper aims to construct a new type of active charge-controlled memristor based on a triangular wave and apply it to build a non-Hamiltonian globally conservative circuit, the characteristic roots of which are all on the imaginary axis. The system is critically stable and presents extremely high sensitivity to the initial values, exhibiting heterogeneous multistability and homogeneous multistability with local amplitude modulation. This special multistability is of great significance to engineering applications. In addition, as the hardware accuracy is limited and only a few conservative systems have been implemented digitally, the DSP platform is employed herein for the physical implementation of the proposed system. In the end, we applied the novel system to a plaintext-related image encryption algorithm. The results show that the system not only merely can resist the risk of data reconstruction, but also has excellent random characteristics, and is suitable for encryption. Therefore, this research makes major contributions to enriching the types of charge-controlled memristors and providing a conservative chaotic system in engineering.