摘要
为了改善经典Logistic、Sine和Tent等映射仅在小范围内具有混沌行为且复杂性低等不足,提出了基于正弦变换混沌映射的构造方法。该方法对现有混沌映射的输出进行线性加权组合,再对组合结果进行正弦函数变换并产生新的映射。通过分叉图和Lyapunov指数法检验该类映射具有混沌特性,并对该类映射产生序列所对应的样本熵和Kolmogorov熵测试与分析,结果表明,基于正弦变换混沌映射的构造方法产生的混沌映射相较于经典Logistic、Sine和Tent映射其混沌范围所占比例分别提高了89.25%、85%、40%,最大的Lyapunov指数提高了0.5个单位,样本熵和Kolmogorov熵也均有所提高。提出方法所产生的新混沌映射有较大的混沌范围、鲁棒性以及更好的复杂性和不可预测性。
In order to improve the disadvantages that classical Logistic map,Sine map,and Tent map all have only chaotic behaviors in a small range and their low complexities,a constructive sine-transform-based chaotic system is proposed.In this system,firstly,the output of the existing chaotic maps is linearly weighted and combined,then the transformation of sine function is performed on this combination results,therefore a new chaotic map is generated.Finally,the bifurcation graph and Lyapunov exponent method are used to test the chaos characteristics of this map,and the sample entropy and Kolmogorov entropy corresponding to the sequence generated by the maps are tested and analyzed.Experimental results show that the chaotic maps generated by this new system can increase the chaos ranges by 87.5%,85%,and 60% respectively compared to the classical Logistic,Sine,and Tent chaotic maps,and the maximum Lyapunov exponent can be increased by around 0.5unit.Sample entropy and Kolmogorov entropy also can be increased. Therefore,the new system have greater chaos range,better complexity,robustness,and unpredictability than other traditional chaotic maps.
引文
[1]LUO S,SONG Y.Chaos analysis-based adaptive backstepping control of the microelectromechanical resonators with constrained output and uncertain time delay[J/OL].IEEE Transactions on Industrial Electronics,2016,63(10):6217-6225[2018-05-12].http://ieeexplore.ieee.org/document/7470459/.DOI:10.1109/TIE.2016.2569462.
[2]吴成茂,景党伟,王辉.基于动态分组和扩散置乱的混沌加密方法[J/OL].西安邮电大学学报,2014,19(4):15-20[2018-05-16].http://kns.cnki.net/KCMS/detail/detail.aspx?filename=xayd201404003&dbname=CJFD&dbcode=CJFQ.DOI:10.13682/j.issn.2095-6533.2014.04.003.
[3]WU Y,ZHOU Y,BAO L.Discrete wheel-switching chaotic system and applications[J/OL].IEEE Transactions on Circuits and Systems I:Regular Papers,2014,61(12):3469-3477[2018-05-11].http://ieeexplore.ieee.org/document/6876011/.DOI:10.1109/TC SI.2014.2336512.
[4]ZHOU Y,HUA Z,PUN C M,et al.Cascade chaotic system with applications[J/OL].IEEE Transactions on Cybernetics,2014,45(9):2001-2012[2018-05-21].http://ieeexplore.ieee.org/document/6940279/.DOI:10.1109/TCYB.2014.2363168.
[5]HUA Z,ZHOU Y.Dynamic parameter-control chaotic system[J/OL].IEEE Transactionson Cybernetics,2016,46(12):3340-3341[2018-04-17].https://ieeexplore.ieee.org/document/7360152/htm.DOI:10.1109/TCYB.2015.2504180.
[6]LI H,LIU Y,LüJ,et al.Suppressing EMI in power converters via chaotic SPWM control based on spectrum analysis approach[J/OL].IEEE Transactions on Industrial Electronics,2014,61(11):6128-6137[2018-05-10].http://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=6748951.DOI:10.1109/TIE.2014.2308131.
[7]ZHOU Y,BAO L,CHEN C L P.A new 1Dchaotic system for image encryption[J/OL].Signal processing.2014(97):172-182[2018-05-12].http://dl.acm.org/citation.cfm?id=2565801.DOI:10.1016/j.sigpro.2013.10.034.
[8]CHOU H G,CHUANG C F,WANG W G,et al.Afuzzy model-based chaotic synchronization and its implementation on a secure communication system[J/OL].IEEE Transactions on Information Forensics and Security,2013,8(12):2177-2185[2018-04-29].https://ieeexplore.ieee.org/document/6637014/htm.DOI:10.1109/TIFS.2013.2286268.
[9]BERGAMO P,D’ARCO P,DE SANTIS A,et al.Security of public-key cryptosystems based on Chebyshev polynomials[J/OL].IEEE Transactions on Circuits and Systems I:Regular Papers,2005,52(7):1382-1393[2018-05-25].https://ieeexplore.ieee.org/document/1487666/htm.DOI:10.1109/TCSI.2005.851701.
[10]CHO K,MIYANO T.Chaotic cryptography using augmented Lorenz equations aided by quantum key distribution[J/OL].IEEE Transactions on Circuits and Systems I:Regular Papers,2015,62(2):478-487[2018-05-04].http://ieeexplore.ieee.org/document/6975253/.DOI:10.1109/TCSI.2014.2365767.
[11]LI C Y,CHEN Y H,CHANG T Y,et al.Period extension and randomness enhancement using highthrough putreseeding-mixing PRNG[J/OL].IEEETransactions on Very Large Scale Integration(VLSI)Systems,2012,20(2):385-389[2018-05-09].https://ieeexplore.ieee.org/document/5711011/htm.DOI:10.1109/TVLSI.2010.2103332.
[12]ELHADJ Z,SPORRT J C.Robustification of Chaos in2D Maps[J/OL].Advances in Complex Systems,2011,14(6):817-827[2018-05-13].https://www.researchgate.net/publication/227651628_Robustification_of_Chaos_in_2D_Maps.DOI:10.1142/S0219525911003402.
[13]WU Y,ZHOU Y,BAO L.Discrete wheel-switching chaotic system and applications[J/OL].IEEE Transactions on Circuits and Systems I:Regular Papers,2014,61(12):3469-3477[2018-04-29].https://ieeexplore.ieee.Org/document/6876011/htm.DOI:10.1109/TCSI.2014.2336512.
[14]TLELO-CUAUTLE E,RANGLE-MAGDALENO JJ,PANO-AZUCENA A D,et al.FPGA realization of multi-scroll chaotic oscillators[J/OL].Communications in Nonlinear Science and Numerical Simulation,2015,27(1-3):66-80[2018-05-25].http://www.sciencedirect.com/science/article/pii/s1007570415000878.DOI:10.1016/j.cnsns.2015.03.003.
[15]LIN L,SHEN M,SO H C,et al.Convergence analysis for initial condition estimation in coupled map lattice systems[J/OL].IEEE Transactions on Signal Processing,2012,60(8):4426-4432[2018-04-25].http://ieeexplore.ieee.org/document/6188537/.DOI:10.1109/TSP.2012.2195659.
[16]DENG Y,HU H,XIONG W,et al.Analysis and design of digital chaotic systems with desirable performance via feedback control[J/OL].IEEE Transactions on Systems,Man,and Cybernetics:Systems,2015,45(8):1187-1200[2018-05-16].http://ieeexplore.ieee.org/document/7042746/.DOI:10.1109/TSMC.2015.2398836.
