An improved high performance Lorenz system and its application

Abstract

Lorenz system is one of the most typical chaotic system models, and it has been well studied and widely applied. In order to obtain more complex structure and dynamic behavior of chaotic attractor for Lorenz system, improving the Lorenz system has become one of the important tasks in chaotic dynamical system. Therefore, an improved Lorenz system with complex dynamic behavior is proposed and used to protect image information security. Based on the existing various improvement Lorenz systems, firstly, a new Lorenz chaotic system is constructed by increasing the control parameters and modifying nonlinear expression in the existing Lorenz chaotic system; secondly, the mathematical properties of dissipation, symmetry, and stability in the proposed Lorenz system, which are similar to those in the existing Lorenz system, Bao system, Tee system and Y system, are investigated by modern differential dynamical system, and the experimental results of Lyapunov index and random sequence correlation of five different Lorenz systems show that the proposed Lorenz system has a more complex structure and chaotic dynamic behavior; finally, the discrete pseudo random sequences generated by five different Lorenz chaotic systems are used for scrambling the pixel position and diffusing the pixel value to protect image information security. The analyses of correlation and statistic histogram entropy of adjacent pixels, anti-differential attack and key sensitivity of the encrypted image, indicate that the improved Lorenz system proposed in this paper has much better potential advantages than other existing improved Lorenz system in image encryption application.