7. A simple model that describes the nutrients in a food chain is given in the diagram below. The three compartments are

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7 A Simple Model That Describes The Nutrients In A Food Chain Is Given In The Diagram Below The Three Compartments Are 1 (55.51 KiB) Viewed 59 times

7. A simple model that describes the nutrients in a food chain is given in the diagram below. The three compartments are phytoplankton, water and zooplankton with amount of nutrients yı(t), y(t), y(t) at time t respectively. The constant alongside the arrow connecting one compartment to another indicates the rate the nutrients from that compartment pass to the other. (i) Find the system of differential equations that describe the amount of nutrients in each compartment at time t. (ii) Write down the general solution of this system by finding the eigenvalue and eigenvectors of the underlying matrix of the system in (i). (iii) (MATLAB) Compare your answer in (ii) using MATLAB command given in Question 2. (You need to add a third component y3 to the first second and fourth command lines.) Phytoplankton 0.05/hr (respiration) 0.05/hr (grazing) 0.10/hr 0.02/hr Water Zooplankton 0.05/hr (excretion)