dx/dt = y

dy/dt = -x3 - K y + B cos z

dz/dt = 1

parameters: B = 7.5, K =0.05
The step size of the fourth-order Runge-Kutta method: 0.001

Lyapunov exponents (log with base-e): 0.0999,  0.0000, -0.1499

Lyapunov dimension: 2.6664

#----------------------------------------------

sum of the Lyapunov exponents: -0.0500000000

trace of the Jacobian matrix: -0.0500000000

#----------------------------------------------

The trace of the Jacobian matrix of the Lorenz system is -K.  Therefore, the sum of the Lyapunov exponents is theoretically equal to -K.

Reference

Randomly transitional phenomena in the system governed by Duffing's equation

Yoshisuke Ueda

Journal of Statistical Physics 20, pages181–196 (1979)

DOI: 10.1007/BF01011512

Chaos and Time-Series Analysis (pp. 182, 183 and 429)

Julien Clinton Sprott

Oxford University Press (2001/Sep/27)

ISBN-10: 0198508409

ISBN-13: 978-0198508403

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