Maxima and Minima for the Three-Variable Autocatalator

time series

next maxima map

next minima map

bifurcation parameter μ

0.145

Peng et al. [1] derived three coupled nonlinear ODEs to describe the behavior of the three-variable autocatalator. This Demonstration plots the loci of the maxima and minima of the time series

α(t)

. Such information is used to map the next maximum or minimum point. For particular values of the bifurcation parameter

μ

(for example,

μ=0.154

), the result is chemical chaos, and a map of the next maximum/minimum shows the typical behavior of a chaotic attractor. On the other hand, when periodic behavior is observed (e.g., for

μ=0.114

), a map of the next maximum/minimum displays only a small number of isolated points.