In recent years,fractional-order chaotic maps have been paid more attention in publications because of the memory effect.This paper presents a novel variable-order fractional sine map(VFSM)based on the discrete fracti...In recent years,fractional-order chaotic maps have been paid more attention in publications because of the memory effect.This paper presents a novel variable-order fractional sine map(VFSM)based on the discrete fractional calculus.Specially,the order is defined as an iterative function that incorporates the current state of the system.By analyzing phase diagrams,time sequences,bifurcations,Lyapunov exponents and fuzzy entropy complexity,the dynamics of the proposed map are investigated comparing with the constant-order fractional sine map.The results reveal that the variable order has a good effect on improving the chaotic performance,and it enlarges the range of available parameter values as well as reduces non-chaotic windows.Multiple coexisting attractors also enrich the dynamics of VFSM and prove its sensitivity to initial values.Moreover,the sequence generated by the proposed map passes the statistical test for pseudorandom number and shows strong robustness to parameter estimation,which proves the potential applications in the field of information security.展开更多
电子回旋共振离子推力器(electron cyclotron resonance ion thruster,ECRIT)外部联结磁场是影响羽流中和过程以及中和器耦合电压的因素之一。联结磁场随离子源和中和器安装方位及其内部磁极方向的不同而不同,计算联结磁场分布规律、实...电子回旋共振离子推力器(electron cyclotron resonance ion thruster,ECRIT)外部联结磁场是影响羽流中和过程以及中和器耦合电压的因素之一。联结磁场随离子源和中和器安装方位及其内部磁极方向的不同而不同,计算联结磁场分布规律、实验研究磁场对羽流中和的影响是非常重要的工作。针对离子源的2个功率和2个流量,加速电压350~1450 V内,开展中和实验,研究离子源与中和器磁极方向和位置关系的变化对离子束流引出和最高耦合电压大小的影响规律。结果表明,离子束流引出不受磁极方向和离子源与中和器安装方位的影响。离子源与中和器相对垂直安装时能降低中和器耦合电压,同时通过改变中和器磁极方向使其与离子源磁极方向相反也能降低中和器耦合电压。当离子源与中和器磁极方向相反且垂直安装时,中和器耦合电压最低。展开更多
基金Project supported by the National Natural Science Foundation of China(Grant Nos.62071496,61901530,and 62061008)the Natural Science Foundation of Hunan Province of China(Grant No.2020JJ5767).
文摘In recent years,fractional-order chaotic maps have been paid more attention in publications because of the memory effect.This paper presents a novel variable-order fractional sine map(VFSM)based on the discrete fractional calculus.Specially,the order is defined as an iterative function that incorporates the current state of the system.By analyzing phase diagrams,time sequences,bifurcations,Lyapunov exponents and fuzzy entropy complexity,the dynamics of the proposed map are investigated comparing with the constant-order fractional sine map.The results reveal that the variable order has a good effect on improving the chaotic performance,and it enlarges the range of available parameter values as well as reduces non-chaotic windows.Multiple coexisting attractors also enrich the dynamics of VFSM and prove its sensitivity to initial values.Moreover,the sequence generated by the proposed map passes the statistical test for pseudorandom number and shows strong robustness to parameter estimation,which proves the potential applications in the field of information security.
