Using the Monte Carlo Simulation to test the Hurst exponent
of a random series to which it could be compared, we then produced 10,000 Gaussian random series, each with a period of 1246 values, the equivalent of five years of trading.
Next, we begin with calculating the MLE and plotting the Lyapunov exponent
spectrum for two typical one-dimensional maps, Tent Map and Logistic Map.
The authors developed a combination of DFA with the dependence of scale and time, which they designated by time and scale Hurst exponent
The existence of the linear trend may be a reason why the value of scaling exponent
in the FA curve is higher than in the DFA1-3 curves.
Figure 5 shows that the Lyapunov exponent
of the pitch angle in the condition of [a.sub.d] = sina is much larger than that of [a.sub.d] = 0, which indicates that the dynamic stability gets worse when the manipulator movements exist and the manipulator movements will affect the quadrotor pitching motion, and even may lead to the instability.
where H is the Hurst exponent
. H depends on the underlying distribution of the step size of the random walker.
For each parameter combination, the Largest Lyapunov exponent
is computed with the equation 8 and the contour plots that show how changes this exponent
in function of the three parameters are showed in figures 9,11 and 13.
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The Lyapunov exponents
of the nonlinear system are evaluated by Wolf's algorithm  to determine whether the chaotic phenomenon of the nonlinear system actually occurs.
The results show that the average population size and area take on exponent
decay patterns (Figure 4).
Recently, Tan and Liu  gave some boundedness of [T.sub.[OMEGA],[sigma]] on function spaces with variable exponent
. For the applications of fractional integral operator in fractional order system, we choose to refer to .
The takeover of Immediate Media - which has been owned by Exponent
Private Equity since 2011 - is expected to be confirmed this week, according to Sky News which cited sources.