dx/dt = y + γ x + C z

dy/dt = ω x - δ2 y

ε dz/dt = (1 - x2) (S x - D z) - δ3 z

parameters: γ = 0.2, C = 2.2, δ2 = 0.001, δ3 = 0.0001, ε =0.3, ω = -10.0,
                      S = 1.667, D = 0.0
The step size of the fourth-order Runge-Kutta method: 0.001

Lyapunov exponents (log with base-e): 4.0784, 0.2011, -7.6791

Lyapunov dimension: 2.5573

Abarbanel先生は、下記の論文と本の中でδ3 = 0.001、ω=10.0、S=1667.0と書いておられますが、それらの値を使うと方程式の値を得ることが出来ません。Abarbanel先生は、誤ってそれらの値を書かれたのだと思います。上記の値を使うと問題なく計算が出来るので、これらの値が正しいと思います。

In the following paper and book, Professor Abarbanel wrote δ3 = 0.001, ω=10.0, S=1667.0 but we cannot obtain the value of the equation using those values.  I think Professor Abarbanel wrote those values incorrectly.  The calculation can be done without problems using the values mentioned above, so I think these values are correct.

Reference

Predicting physical variables in time-delay embedding

Henry Don Isaac Abarbanel, T. A. Carroll, Louis M. Pecora, John J. Sidorowich,
and Lev S. Tsimring

Physical Review E 49, 1840-1853 (1994)

DOI: 10.1103/PhysRevE.49.1840

Analysis of observed Chaotic Data (p. 33)

Henry Don Isaac Abarbanel

Springer-Verlag, New York (1996/Jan/15)

ISBN-10: 0387945237

ISBN-13: 978-0387945231

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