TY - GEN
T1 - Numerical calculation of the lyapunov exponent for the logistic MAP
AU - Ibarra Olivares, E.
AU - Vázquez-Medina, R.
AU - Cruz-Irisson, M.
AU - Del-Río-Correa, J. L.
PY - 2008
Y1 - 2008
N2 - Chaotic maps can be used to describe the behavior of dynamical systems and they are characterized by a parameter. The logistic map (LM) is a chaotic map very used in different areas. In the analysis of the dynamical system an important feature is the system stability, which can be determined using the Lyapunov Exponent (LE). In this paper two ways to compute numerically the LE for the LM are shown. In the first alternative, the Birkhoff's Ergodic Theorem (BET) and the orbit produced by the LM are used. In the second alternative, the stationary distribution ρest of the LM is estimated using the first derived of the logistic function and the central values of each interval in the partition used in the estimation.
AB - Chaotic maps can be used to describe the behavior of dynamical systems and they are characterized by a parameter. The logistic map (LM) is a chaotic map very used in different areas. In the analysis of the dynamical system an important feature is the system stability, which can be determined using the Lyapunov Exponent (LE). In this paper two ways to compute numerically the LE for the LM are shown. In the first alternative, the Birkhoff's Ergodic Theorem (BET) and the orbit produced by the LM are used. In the second alternative, the stationary distribution ρest of the LM is estimated using the first derived of the logistic function and the central values of each interval in the partition used in the estimation.
UR - http://www.scopus.com/inward/record.url?scp=51749113538&partnerID=8YFLogxK
U2 - 10.1109/MMET.2008.4581011
DO - 10.1109/MMET.2008.4581011
M3 - Contribución a la conferencia
AN - SCOPUS:51749113538
SN - 9781424422845
T3 - Mathematical Methods in Electromagnetic Theory, MMET, Conference Proceedings
SP - 409
EP - 411
BT - Conference Proceedings - The 12th International Conference on Mathematical Methods in Electromagnetic Theory, MMET 08
T2 - 12th International Conference on Mathematical Methods in Electromagnetic Theory, MMET 08
Y2 - 29 June 2008 through 2 July 2008
ER -