Figure 7 | Scientific Reports

Figure 7

From: Integer-dimensional fractals of nonlinear dynamics, control mechanisms, and physical implications

Figure 7

Long-dependence indicator in multi-dimensional spaces. The scatter diagram graphs pairs of sample ACFs \(({\rho }_{1x},{\rho }_{1y}),({\rho }_{2x},{\rho }_{2y}),\ldots ,({\rho }_{70x},{\rho }_{70y})\). Their components \({\rho }_{1y},\ldots ,{\rho }_{70y}\) (or \({\rho }_{1x},\ldots ,{\rho }_{70x}\)) placed above (or below) the diagonal line at larger lags become larger than 0.8 with rising η1y (or η1x) from 0.00075 to 0.00150; those lying on the diagonal line at larger lags become larger than 0.8 with rising η1y or η1x from 0.00017 to 0.00150; and all the ACF points placed above/below/on the diagonal line at larger lags decay more slowly and the distances between the sample ACF points and the point of one become smaller with rising slope indicator (η1x, η1y). These results indicates that the slope indicator is also a long-dependence indicator in multi-dimensional spaces.

Back to article page