ダフィング方程式
Duffing equations
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
The sum of the Lyapunov exponents is theoretically the same as -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
programme
duffing_lyap.c contains the main function.