Solved: 2931 Consumer resource models often have the following general form R9 fsRd 2

Chapter 10, Problem 30

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2931 Consumer resource models often have the following general form R9 fsRd 2 tsR, Cd C9 tsR, Cd 2 hsCd where R is the number of individuals of the resource and C is the number of consumers. The function fsRd gives the rate of replenishment of the resource, tsR, Cd describes the rate of consumption of the resource, and hsCd is the rate of loss of the consumer. The constant , where 0 , , 1, is the conversion efficiency of resources into consumers. Find all equilibria of the following examples and determine their stability properties. A model for self-reproducing resources is obtained by choosing fsRd rR, tsR, Cd bRC, and hsCd C. Suppose r 2, b 1, 1, and 1.