A branching diagram is shown in Figure 1. We see a branch
of stationary solutions with two Hopf bifurcation points, for which
the parameter values and initial periods are
In Figures 2 and 3, simulations are performed with . The soft loss of stability in Figure 3 looks like a hard loss. The relatively steep transition is due to a slow reaction of the system. Note that the scaling that corresponds to in Figure 2 is the same as in Figure 1. The phase condition of the calculations in Figure 1 is , here fixing the maximum of y1(t). Hence there is an immediate correspondence between Figure 1 and Figure 2 in size, scaling, and dynamical behavior. This is similar in Figure 3, except for the reverse time; flip Figure 3 and it matches Figure 1 and 2.
``Continuous" refers to a continuous flow entering (and leaving) the reactor--that is, a CSTR is an open system. Human beings and other living organisms that have input of reactants (nutrients) and output of products (wastes) are complex examples of CSTRs. The exponential term in the equations reflects an infinite activation energy.
y1(t) simulation for , , with initial values y1(0)=0.1644, y2(0)=0.6658
y1(t) simulation for , , with initial values y1(0)=0.9279, y2(0)=3.76