Maxima and Minima for the Three-Variable Autocatalator
Maxima and Minima for the Three-Variable Autocatalator
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 . Such information is used to map the next maximum or minimum point. For particular values of the bifurcation parameter (for example, ), 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 ), a map of the next maximum/minimum displays only a small number of isolated points.
α(t)
μ
μ=0.154
μ=0.114