Dynamical analysis and circuit realization of a high complexity fourth-order double-wing chaotic system with transient chaos and its application in image encryption

Abstract

Abstract This paper proposes a fourth-order double-wing chaotic system with high complexity. After conducting a dynamic analysis, it is found that the system exhibits transient chaos and a rare inverse period-doubling bifurcation phenomenon in the bifurcation diagram. The system also exhibits attractor coexistence, with periodic, quasi-periodic, indicating high sensitivity to initial values. These phenomena sufficiently demonstrate the rich dynamical characteristics of chaotic systems. By introducing an impulse function with a cosine function in the foundation of the proposed system, it is found that controllable wing number and staircase burst oscillations occur. Furthermore, the number of wings and oscillation periods vary with changes in parameters, which has significant implications in engineering applications. The circuit design and construction are carried out using the Multisim simulation software, and the digital circuit is realized by using a Field-Programmable Gate Array (FPGA). It is found that the simulation results and the actual implementation results are highly consistent with the phase portrait of the system, thus demonstrating the feasibility of the circuit. Finally, by combining the proposed system with a DNA encryption algorithm, a novel image encryption algorithm with multiple layers of encryption is designed, greatly enhancing the security of encrypted images. The security of this encryption algorithm is analyzed in terms of information entropy, key space, correlation, and resistance to attacks. It is found that the proposed encryption algorithm exhibits high confidentiality and resistance to attacks. The proposed system has significant reference value in secure communication when applied to image encryption.