A Simple Model for Photosynthesis of Individual Leaves Photosynthesis is a complex

Chapter 8, Problem 4

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A Simple Model for Photosynthesis of Individual Leaves Photosynthesis is a complex mechanism; the following model is a very simplified caricature: Suppose that a leaf contains a number of traps that can capture light. If a trap captures light, the trap becomes energized. The energy in the trap can then be used to produce sugar, which causes the energized trap to become unenergized. The number of traps that can become energized is proportional to the number of unenergized traps and the intensity of the light. Denote by T the total number of traps (unenergized and energized) in a leaf, by I the light intensity, and by x the number of energized traps. Then the following differential equation describes how the number of energized traps changes over time: dx dt = k1(T x)I k2x Here, k1 and k2 are positive constants. Find all equilibria, and use the eigenvalue approach to study their stability.