Open AccessKOLMOGOROV CAPACITY AND LYAPUNOV DIMENSION OF STRANGE ATTRACTORS OF FORCED BRUSSELATOR
Author(s) -
Guangrui Wang,
Shigang Chen,
Bailin Hao
Publication year - 1984
Publication title -
wuli xuebao
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.199
H-Index - 47
ISSN - 1000-3290
DOI - 10.7498/aps.33.1246
Subject(s) - brusselator , attractor , lyapunov exponent , mathematics , dimension (graph theory) , lyapunov function , differential equation , mathematical analysis , pure mathematics , physics , nonlinear system , quantum mechanics
In this paper, by using stroboscopic sampling method which reduces the dimension of attractors, the Kolmogorov Capacity dC and Lyapunov dimension dL of some typical attractors of forced Brusselator are computed. The results show that the conjectures of ref. [6, 16] about the relations between dC and dL are correct. We spell out these conjectures as that if the maximal Lyapunov exponent λ1>0, then dC=dL; if λ1=0, then there exist examples that do not satisfy dC=dL. The reasons for noncon-vergence of dC for the forced Brusselator Caculated by using the Runge-Kutta difference equations and the way to improve it are pointed out and tested numerically. We conjecture further that by the same reason of using difference equations to approach differential equations, the capacity caculated from time series of a single observable may not be convergent.