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please help with the following explanations b-h. variables are defined in the second image Let s(t) be the number of sardines and k(t) be the
please help with the following explanations b-h. variables are defined in the second image
Let s(t) be the number of sardines and k(t) be the number of sharks at time t and assume that the dynamics follow the differential equations ds S = 4s (1 6000 - 0.1sk, at dk -3k + 0.001sk. (1) at (a) Explain the biological meaning of all parts of the the differential equations. (b) Determine equations for all s- and k-nullclines and sketch them on the s-k-phase plane (choose appropriate dimensions for the axes). (c) Determine all equilibrium points of the system (mathematically, not graphically) and mark them on the phase plane. (d) Draw directional arrows in all (four) biologically relevant regions, divided by the nullclines. (e) Draw directional arrows on the different (biologically relevant) sections of all nullclines. (f) Determine the general Jacobian, corresponding to (the linearization of ) the system in (1). g) Classify (the stability of) the one equilibrium, where sardines and sharks coexist. (h) Assuming that the remaining equilibria are unstable, draw a plausible solution curve when starting with 2000 sardines and 10 sharks and explain its trajectory based on the results of the previous parts. In the long run, what do you predict for the evolution of the sardine and shark populations?SARdine CARRYing CAPAcity Rate Change -S of SARDines = 45 ( 1-S - 0. ISK 6000 SARDine growth RAte At which sharks RAfe Kill SARdines (Per SARDine RAfe change of sharks - 3 K + 0.0015K PER SHARK) decreasing conversion of many SHARK population SARdines into few sharks (shares reproduceStep by Step Solution
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