Coexistence analysis and image encryption of chaos-like attractors in conservative systems

Abstract

Abstract: It is very important to construct new conservative chaotic systems in engineering applications. On the basis of Hamilton’s generalized system theory, a chaotic system that is conservative in both energy and volume is proposed. After further analysis, it is found that the system has hidden chaotic attractors with strong characteristics and a large range of chaotic states. In addition, when the conservative chaotic system has sine function, cosine function or tangent function in the Hamiltonian energy function, it can produce an infinite number of coexisting chaotic attractors. Since the system exhibits good chaotic dynamics characteristics, it is suitable for engineering applications such as communication security and image encryption. Finally, the system is applied to image encryption, and the good security performance of the encryption algorithm based on this system is verified through qualitative analysis and quantitative analysis.

Key words: conservative system, large-scale chaos, infinite coexistence, image encryption

CLC Number:

YAN Min-xiu, ZHANG Ping. Coexistence analysis and image encryption of chaos-like attractors in conservative systems[J]. Journal of Lanzhou University of Technology, 2023, 49(5): 102-111.

References

[1] LORENZ E N.Deterministic non-periodic flow [J].Journal of the Atmospheric Sciences,1963,20(2):130-141.
[2] DONG E Z,WANG Z,YU X,et al.Topological horseshoe analysis and field-programmable gate array implementation of a fractional-order four-wing chaotic attractor [J].Chinese Physics B,2018,27(1):010503.
[3] WANG J Y,MOU J,YAN H Z,et al.A three-port switch NMR laser chaotic system with memristor and its circuit implementation [J].The European Physical Journal Plus,2021,136(11):1112.
[4] CXA B,RZA B,Yl C.New chaotic memristive cellular neural network and its application in secure communication system-science direct [J].Chaos,Solitons & Fractals,2020,141:110316.
[5] 颜闽秀,徐辉.新分数阶混沌系统的电路设计和同步控制 [J].兰州理工大学学报,2021,47(1):105-112.
[6] YAN M X,XU H.The multi-scroll hyper-chaotic coexistence attractors and its application [J].Signal Processing Image Communication,2021,95:116210.
[7] 张泽峰,黄丽莲,项建弘,等.新的具有宽参数范围的五维保守超混沌系统的动力学研究 [J].物理学报,2021,11(10):1-22.
[8] DONG E Z,LI R H,DU S Z.A multi-directional controllable multi-scroll conservative chaos generator:modelling,analysis and FPGA implementation [J].Chinese Physics B,2021,30(2):020505.
[9] 薛薇,张永超.保守超混沌在数字图像加密中的应用 [J].计算物理,2020,37(4):497-504.
[10] WANG N,ZHANG G S,KUZNETSOV N V,et al.Hidden attractors and multistability in a modified Chua’s circuit [J].Communications in Nonlinear Science and Numerical Simulation,2021,92:105494.
[11] DONG E Z,YUAN M F,DU S Z,et al.A new class of Hamiltonian conservative chaotic systems with multistability and design of pseudo-random number generator [J].Applied Mathematical Modelling,2019,73:40-71.
[12] WANG Z,QI G Y.Modeling and analysis of a three-terminal-memristor-based conservativechaotic system [J].Entropy,2021,23(1):71.
[13] JAFARI S,SPROTT J C,DEHGHAN S.Categories of conservative flows [J].International Journal of Bifurcation and Chaos,2019,29(2):1950021.
[14] QI G Y,HU J B,WANG Z.Modeling of a Hamiltonian conservative chaotic system and its mechanism routes from periodic to quasiperiodic,chaos and strong chaos [J].Applied Mathematical Modelling,2020,78:350-365.
[15] POURASAD Y,RANJBARZADEH R,MARDANI A.A new algorithm for digital image encryption based on chaos theory [J].Entropy,2021,23(3):341.
[16] CHEN L,HAO Y,HUANG T,et al.Chaos in fractional-order discrete neural networks with application to image encryption [J].Neural Networks,2020,125:174-184.
[17] HU G,LI B.A uniform chaotic system with extended parameter range for image encryption [J].Nonlinear Dynamics,2021(1):1-22.
[18] LIU J Y,YANG D D,ZHOU H B,et al.A digital image encryption algorithm based on bit-planes and an improved logistic map [J].Multimedia Tools and Applications,2018,77(8):10217-10233.
[19] YILDIRIM M,KACAR F.Chaotic circuit with OTA based memristor on image cryptology [J].AEU-International Journal of Electronics and Communications,2020,127:153490.
[20] FENG W,HE Y G,LI H M,et al.Image encryption algorithm based on discrete logarithm and memristive chaotic system [J].The European Physical Journal Special Topics,2019,228(10):1951-1967.
[21] XIU C,ZHOU R,ZHAO S,et al.Memristive hyperchaos secure communication based on sliding mode control [J].Nonlinear Dynamics,2021(4):1-17.
[22] WANG Y,LI C,CHENG D.New approaches to generalized Hamiltonian realization of autonomous nonlinear systems [J].Science in China (Series F),2003,46(6):431-444.