Analysis and application of conditionally symmetric memristive chaotic systems with attractor growth phenomena

To further explore chaotic systems more suitable for practical engineering applications, a flux-controlled memristor was introduced into a three-dimensional chaotic system, resulting in the construction of a new four-dimensional conditionally symmetric memristor chaotic system. The dynamical behavior of the system was analyzed using conventional methods, including bifurcation diagrams, Lyapunov exponent spectra, and phase trajectory plots. The analysis revealed that the new system exhibits constant Lyapunov exponents and transient chaotic phenomena, as well as hidden homogeneous extreme multistability phenomena dependent on initial conditions. Additionally, the system exhibits attractor growth phenomena that vary with changes in parameters and initial conditions. Furthermore, the phase diagrams captured on the hardware platform are consistent with the numerical simulation results, confirming the existence of the system. Finally, this study designed a medical image encryption scheme based on the conditionally symmetric memristive chaotic system and DNA encoding technology. It explored the impact of growing and non-growing attractors on encryption performance through methods such as information entropy and correlation analysis.