Chaos Identification Based On 0-1 Test Method And Its Application In Geology

The 0-1 test method is a new method which through the output value K(c)approaches to 1 or 0 to judge whether discrete time series are chaotic or not. In this paper, we first use the discrete time series generated by Verhulst population model as the research object, verified the validity of the 0-1 test method; Secondly, the influence of different data length N, amplitude a and normal white noise on the chaos recognition in 0-1 test algorithm is analyzed; Finally, the 0-1 test method and the traditional maximum Lyapunov exponent method are applied to the chaotic identification of metallogenic elements in Shangzhuang gold deposit, Shandong, the chaotic characteristics of polychromic chemical elements are identified. The main results of this paper are as follows:(1)0-1 test method validity test. The discrete sequences generated by the Verhulst population model are studied, respectively, we get the corresponding bifurcation diagram, ?-K(c) and 0-1 test chart. The results show that the bifurcation diagram is consistent with the state of the system reflected by the ?-K (c) graph, there are significant differences in p-q trajectories, n-Mc(n) and c-K(c) scatter plots for periodic, weakly chaotic and strong chaotic sequences , the K(c) value of the periodic sequence tends to 0, the strong chaotic sequence tends to 1, and the weak chaotic sequence K(c) is between 0 and 1. It is shown that 0-1 test method can effectively identify the chaotic state of the sequence.(2) Analysis of the effect of data length on 0-1 test method. Five sets of Verhulst sequences are selected as the study subjects, the influence of different data length N on 0-1 test method is analyzed. It is found that the K(c) value of the periodic sequence is close to zero as the data length N increases, and the K(c) value of the weak chaotic sequence is closer to 1 and the K(c) value of the strong chaotic sequence nearly 1. Therefore, the change trend and rate of K(c) values can be obtained by changing the data length to distinguish the degree of sequence chaos.(3) Analysis of noise in 0-1 test method. After adding three normal white noise with a noise level of 5% for three different types of Verhulst sequences, the corresponding K(c) value and 0-1 test chart changes little, it is shown that the 0-1 test method has a certain noise immunity for normal white noise with a noise level of 5%.(4) Analysis of the effect of amplitude a in 0-1 test method. The Verhulst sequences of three different properties (periodic, weak chaos, strong chaos) are selected to explore the effect of amplitude a on chaos recognition in 0-1 test algorithm.The Verhulst sequences of three different properties (periodic, weak chaos, strong chaos) are selected to explore the effect of amplitude a on chaos recognition in 0-1 test algorithm. As the amplitude a increases from 0 to 6, the K(c) value of the weak chaotic sequence is the most sensitive to the amplitude a, the K(c) value decreases fastest, followed by the strong chaotic sequence and the periodic sequence respectively, when the amplitude a is in the interval [0,6], the a-K(c) graph of the sequence can distinguish the degree of chaos from the sequence.(5) Application of 0-1 Test Method and Maximum Lyapunov Exponent Method in Geology. Taking the ore-forming elements of Shangzhuang gold deposit in Shandong as an example, Using the 0-1 test method, the chaotic characteristics of the mineral element content sequence is analyzed and compared with the maximum Lyapunov exponent method. The results show that the ore elements Au, Hg, Cu, Pb and Zn sequences have different degree of chaotic characteristics, while the As, Sb and Ag sequences do not have chaos, and the results of the two methods are basically the same, the Au element sequence has strong chaos and is favorable for its mineralization.