Analyzing Chaos Systems and Fine Spectrum Sensing Using Detrended Fluctuation Analysis Algorithm

Table 2

The scaling exponent average of the DFA curves and their respective relative standard deviation for multistable system time series generated with various parameter values. The behavior column abbreviations: P: persistent; AP: antipersistent; AP2: antipersistent oscillating between two values; LRC: long range correlation. The symbol “+” in the case of LRC and P refers to the set of the DFA curves contain time series that behaves as Brownian motion.

Parameter	Interval value	Scale	Variable		(%)	Behavior
	(1.0, 1.04)	[2^4, 2^6]		1.64	0.25	LRC
				1.64	0.20	LRC
				1.63	0.33	LRC
		[2^7, 2^12]		0.03	49.41	AP2
				0.00	4.7	AP2
				0.00	11.42	AP2
	[1.05, 1.53]	[2^4, 2^6]		1.69	1.20	LRC
				1.58	1.37	LRC
				1.49	3.23	P+
		(2^7, 2^12)		0.91	11.50	P
				0.21	12.88	AP
				0.01	25.57	AP2
	(1.0, 1.40]	[2^4, 2^6]		1.63	3.26	LRC
				1.51	1.76	LRC+
				1.43	0.80	P
		[2^7, 2^12]		0.90	9.20	P
				0.22	8.05	AP
				0.01	29.5	AP2
	[1.0, 1.47]	[2^4, 2^6]		1.70	1.20	LRC
				1.58	1.43	LRC
				1.49	3.39	P+
		[2^7, 2^12]		0.89	10.94	AP
				0.21	11.33	AP
				0.01	24.00	AP2