Design of a dissipative chaotic system based on Hamiltonian energy function and its application

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Abstract The construction and enhancement of chaotic systems are the research hotspot, especially in the secure communication applications fields. By applying Hamiltonian energy function to differential dynamical system, a dissipative nonlinear system is constructed based on generalized Hamiltonian system and Hamiltonian energy function, which enlarge the range of chaos system construction. The dynamical behavior of the new system is analyzed using bifurcation diagrams, maximum Lyapunov exponent diagrams and phase diagrams. It is shown that the system can produce an extensive range of continuous chaos by modulating the input parameters of external energy. At the same time, various attractors are found with the evolution of different initial values, that is the phenomenon known as ‘multi stability’, which has more advantage in image encryption. Due to high spectral entropy complexity of the chaotic sequences generated from the dissipative system, the practical application in image encryption is investigated. Considering the demand of efficient image transmission, a multi-image encryption algorithm is proposed based on DNA encoding operation. The algorithm is mainly composed of the following parts: image reconstruction, cross-plane scrambling and DNA diffusion. Eventually, the security analysis results reveal that the encryption algorithm can encrypt numrous color images of different sizes at once, and better security performance can be verified. By combining energy transfer and dissipation with the folding and contraction of trajectories in chaotic motion, a new chaotic system is constructed through energy distribution. This construction method has a deep physical background and is easy to understand the chaotic phenomenon, which has great potential engineering application value.

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