| Form now on,we used to use crowding index,poly mass index,dispersion index,information entropy and variance / mean and so on to study the Uniformity of the point set as traditional methods,but all of the methods study are essence on to describe the data distribution using the variance of uniformity outside of the information entropy methods, generally speaking, while the variance of the data or sample points is small, the degree of dispersion is small, then the uniformity is small as well. However, through a number of specific research, there is existence of such a situation:when the the variance is small, but the uniformity is large (for the very uniform distribution of the data, had a great degree, but the variance is small.),Although the information entropy method can measure accurately, but the calculation is too complex, as divide of the point set space, the scale choice also is a big problem.with respect to the above method, the uniformity not only can overcome the problem of variance can not Characterization the uniform point set, and its calculation depends entirely on the track, and system-independent, less computation.In this paper,we use the key of the uniformity thesis:Chaos Instantaneous chaometry (ICM) and the K-step Chaos Instantaneous chaometry(SCM) as research tool,to study the sequence of ICM of the rules orbit, quasi-periodic orbits, periodic orbits and random orbit;try to measure the information with uniformity,by numerical simulation, we find that the two Characteristic quantity had synchronization perfectly;we also gives two methods to help determine parameters of the ICM;try to resolve the previous stock market turmoil with Uniformity,and established the multi-objective decision model of stock market based on uniformity. the main results obtained are as follows:(1) characteristics of the track's ICM sequence1 if the track X = { x1 , x2 ,..., xN}is from the random system F, then for any space with a number of steps K2, ICM are random sequences.2 for periodic orbits X = { x1 , x2 ,..., xN}, when the K1 is meet with K1 < T and track is long enough, where T is the period of orbital, for any number of K2, We have the following conclusions:the ICM sequence is a periodic orbit and its period T0 < T. 3 for alignment of periodic orbits X = { x1 , x2 ,..., xN},,ICM is quasi-periodic sequences.4 Guess: for the addition to the above rules t and chaos track, with the number of K2 is large enough, ICM sequence is random sequence.5 for the random ICM sequence, they are independent and identically distributed relevant with K2, only when the K2 is greater than some constant K0, to demonstrate that ICM is independent and identically distributed.6 the distribution function is normal distribution while ICM sequence is random,and the distribution function curve more and more fat with random Increased.(2) ICM synchronization the information entropy1 Through the information entropy measure of information and analytical of the nature of ICM measure uniform, found that there are significant similarities between them, by numerical simulation of kent map and Lorenz attractor, proved the synchronization of information entropy and ICM is very good.2 established multi-objective decision making model based on uniformity: is the securities transaction rates, is the rate of securities return on investment, is expected return.(3) two standard of determine the parameters K1 and K21 for the select of K2, There are many ways,just as the selection of time delay,such as: autocorrelation function,the average displacement method and the average mutual information function,and so on,while you determined specifically,can be based on the following two criteria:on the one hand,the expansion of phase space, makes the phase space trajectories expansion from the main diagonal line of the phase space as possible as we can, but do not overlap;on the other hand,reduce the correlation of each fragment,but maintaining each fragment contains the system information;2 for K1,we define: E ( k ) =ΔS CM = ( k +Δk )SCM - kSCM, called the kSCM's change rate,define: E *( k ) = E ( k ) /Δk , called the kSCM's average change rate,actually,it is the average instantaneous change rate of the k-step ICM, When E*( k ) is not change, K is the number of steps which we need, a large number of measured data simulation shows that the algorithm is convergence. |
