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Chemical Reaction with Autocatalytic Step

Original source of the model: H.-J. Krug, L. Kuhnert: Ein oszillierendes Modellsystem mit autokatalytischem Teilschritt. Z. Phys. Chemie 266 (1985) 65-73.

The flow $\gamma$ describes the input of y1; y1,y2,y3 are dimensionless variables. For large values of $\lambda$, a relaxation oscillation develops.

Figure 1
Stable solutions, $y_1(t;\lambda)$ for $0.2\le \lambda\le 3$; the time is normalized to unity. Stationary and periodic orbits meet in a Hopf bifurcation.

Figure 2
$\lambda=1$, projection to the (y1,y2) plane. Initial values: y1=2, y2=y3=1. Dynamics of a stable focus.

Figure 3
$\lambda=1.5$, projection to the (y1,y2) plane. Initial values: y1=2, y2=y3=1. Dynamics of a stable limit cycle.

Figure 4
Bifurcation diagram y1(0) versus $\lambda$; Hopf bifurcation at $\lambda_0=1.30176$.

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