Negative Feedback Loops. Suppose some quantities -*1 (0 , x2(t), ...,*(/) can be modeled
Chapter 9, Problem 14(choose chapter or problem)
Negative Feedback Loops. Suppose some quantities -*1 (0 , x2(t), ...,*(/) can be modeled by differential equations of the formdx i * = -* 1' 1bxndx2 ~dtdxn dt= X\ - k2X2xn 1 ~ ' knXnwhere b is positive and the kt are positive. (The matrix of this system has negative numbers on the diagonal, 1 s directly below the diagonal, and a negative number in the top right comer.) We say that the quantities x\.......xn describe a (linear) negative feedback loop. a. Describe the significance of the entries in this system, in practical terms. b. Is a negative feedback loop with two components (n = 2) necessarily stable? c. Is a negative feedback loop with three components necessarily stable?
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