ISSN:
1572-9265
Keywords:
computational dynamics
;
global bifurcations
;
invariant manifolds
;
34
;
65
Source:
Springer Online Journal Archives 1860-2000
Topics:
Computer Science
,
Mathematics
Notes:
Abstract We illustrate and discuss the computer-assisted study (approximation and visualization) of two-dimensional (un)stable manifolds of steady states and saddle-type limit cycles for flows in R n . Our investigation highlights a number of computational issues arising in this task, along with our solutions and “quick-fixes” for some of these problems. Two examples illustrative of both successes and shortcomings of our current approach are presented. Representative “snapshots” demonstrate the dependence of two-dimensional invariant manifolds on a bifurcation parameter as well as their interactions. Such approximation and visualization studies are a necessary component of the computer-assisted study and understanding of global bifurcations.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1023/A:1019104828180
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