Open AccessON THE NONCONVERGENCE PROBLEM IN COMPUTING THE CAPACITY OF STRANGE ATTRACTORS
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.33.437
Subject(s) - discretization , ode , convergence (economics) , attractor , mathematics , brusselator , interval (graph theory) , computer science , scheme (mathematics) , mathematical optimization , mathematical analysis , nonlinear system , physics , quantum mechanics , combinatorics , economics , economic growth
The convergence of box-counting algorithm for computing the capacity of strange attrac-tors is affected by the discretization procedure, because the period of the difference equations differs from that of the original ODE'S and, in addition, a damping factor appears. Simply decreasing the time-steps in the integration scheme not only costs more computer time, but also may deprive the convergence at all. The nonconvergence problem can be overcome by choosing at first a correct sampling interval. We give numerical evidence for what said above on the example of the periodically forced Brusselator.