In Problems 3–6, find the critical point set for the given system.
The critical points are
Consider the system as:
For finding the critical points put the system equal to 0.
Put the value of y in another equation and solve, then;
Thus, the critical points are .
This is the required result.
Feedback System with Pooling Delay. Many physical and biological systems involve time delays. A pure time delay has its output the same as its input but shifted in time. A more common type of delay is pooling delay. An example of such a feedback system is shown in Figure 5.3 on page 251. Here the level of fluid in tank B determines the rate at which fluid enters tank A. Suppose this rate is given by where and V are positive constants and is the volume of fluid in tank B at time t.
b. Find a general solution for the system in part (a) when and .
c. Using the general solution obtained in part (b), what can be said about the volume of fluid in each of the tanks as ?
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