Analysis of Chaotic Behavior in Non-linear Dynamical Systems by Michał Piórek

Author:Michał Piórek
Language: eng
Format: epub, pdf
ISBN: 9783319948874
Publisher: Springer International Publishing

(5.36)

From the definition of in Eq. (4.​9) the jth pair of points being initially nearest neighbors diverge with approximately the rate of the largest Lyapunov exponent:

(5.37)

and the same is fulfilled in quaternion domain:

(5.38)

where is the initial distance between jth pair of points.

By taking the logarithm of both sides Eq. (5.38) we may estimate the largest Lyapunov exponent in quaternion domain as:

(5.39)

Equation (5.39) as in original version of Rosenstein’s algorithm represents a set of approximately parallel lines (for j 1,2,..., M), each with a slope roughly proportional to . Hence that the largest Lyapunov exponent in quaternion domain is calculated then by linear regression

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