##
**Chemical Reaction with Autocatalytic Step**

exd6

Variables and parameters:
*y*_{i}(*t*): concentrations of chemicals
:
flow )
:
velocity coefficient of autocatalytic step (bifurcation parameter)

Model equations:

Hopf Bifurcation at
with initial period
*T*_{0}=6.03555

Figure 1

Stable solutions,
for
;
the time is normalized to unity. Stationary and periodic orbits meet in a Hopf bifurcation.

Figure 2

,
projection to the (*y*_{1},*y*_{2}) plane. Initial values: *y*_{1}=2, *y*_{2}=*y*_{3}=1. Dynamics of a stable focus.

Figure 3

,
projection to the (*y*_{1},*y*_{2}) plane. Initial values: *y*_{1}=2, *y*_{2}=*y*_{3}=1. Dynamics of a stable limit cycle.

Figure 4

Bifurcation diagram *y*_{1}(0) versus ;
Hopf bifurcation at
.

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Postscript-Files for better printing results:

This Example

Figure 1

Figure 2

Figure 3

Figure 4