The circuit realization of a fifth‐order multi‐wing chaotic system and its application in image encryption

Summary In this paper, a new fifth‐order eight‐wing chaotic system is proposed on the basis of a five‐dimensional four‐wing chaotic system. The resulting new system is used as a basis for introducing a method that can control both the number of wings of the system and the direction of the change in the number of wings. Add a rounding function with a cosine function or a sine function to the system equation. The number of wings of the control system is controlled by changing the parameter values of the rounding function. This method can significantly increase the complexity of the system when applied in multiple directions of the system equations. And this method can achieve the purpose of controlling the wing number of the whole system by changing only one parameter. By observing the phase diagram and bifurcation diagram of the system, it is found that it has more complex chaotic properties and rich dynamical behavior and there are coexisting attractors. The chaotic properties of the system are confirmed by observing the Poincaré cross section and the 0–1 test results of the system. Afterward, the simulation circuit of the fifth‐order system is built in the simulation software Multisim. And the obtained phase diagram is consistent with the results obtained in MATLAB which confirmed the realizability of the system. An FPGA hardware implementation of this fifth‐order eight‐wing system has also been completed at the end of the paper to demonstrate the implementability of the system. And the results are highly consistent with those obtained in the MATLAB software. The fifth‐order chaotic system is combined with the dislocation algorithm and diffusion algorithm to apply to the image encryption system. The encryption system contains a variety of encryption algorithms for secondary encryption of images including Arnold dislocation and repeat‐free scrambling algorithm. The diffusion algorithm includes the addition of the modulus length diffusion and multiplicative operation diffusion based on the GF(257) domain. After a series of performance analysis, the encryption system is proved to have good secrecy effect and great application value in the image encryption neighborhood.