New variable-order fractional chaotic systems for fast image encryption

Chaos - Tập 29 Số 8 - 2019
Guo–Cheng Wu1,2, Zhen-Guo Deng1,3, Dumitru Băleanu4,5,6, Deqiang Zeng1,2
15Institute of Space Sciences, P.O. Box, MG23, R 76900, Magurele Bucharest, Romania
2Data Recovery Key Laboratory of Sichuan Province, College of Mathematics and Information Science, Neijiang Normal University 1 , Neijiang 641100, People’s Republic of China
3School of Mathematics and Information Science, Guangxi University 2 , Nanning 530004, People’s Republic of China
4Department of Mathematics, Cankaya University 3 , 06530 Balgat, Ankara, Turkey
5Institute of Space Sciences 5 , P.O. Box, MG_23, R 76900, Magurele Bucharest, Romania
6State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering, Hohai University 4 , Nanjing 210098, Jiangsu, People’s Republic of China

Tóm tắt

New variable-order fractional chaotic systems are proposed in this paper. A concept of short memory is introduced where the initial point in the Caputo derivative is varied. The fractional order is defined by the use of a piecewise constant function which leads to rich chaotic dynamics. The predictor–corrector method is adopted, and numerical solutions of fractional delay equations are obtained. Then, this concept is extended to fractional difference equations, and generalized chaotic behaviors are discussed numerically. Finally, the new fractional chaotic models are applied to block image encryption and each block has a different fractional order. The new chaotic system improves security of the image encryption and saves the encryption time greatly.

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Chaos

Tập 29 Số 8

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