Question: I need help with these questions, especially MATLAB! 3.2 The Logistic Predator-Prey Recall that an underlying assumption of (4) is that both species will exhibit

 I need help with these questions, especially MATLAB! 3.2 The LogisticPredator-Prey Recall that an underlying assumption of (4) is that both species

I need help with these questions, especially MATLAB!

3.2 The Logistic Predator-Prey Recall that an underlying assumption of (4) is that both species will exhibit exponential behavior if there are no inter-species interactions (1.e if the interaction terms x1x2 are excluded from the model). This assumption ignores the natural limits imposed on a prey population by its environment, such as finite food A slightly more complicated but realistic way to model predator-prey interactions is to adjust the prey equation to include these constraints, which gives rise to the Logistic Predator-Prey system da dt dr dt Now the underlying assumption of this model is, in the absence of predation, the prey population will obey a logistic growth model instead of an exponential growth model. This means that If the prey population is small, the rate of growth is proportional to its size If the prey population is too large to be supported by its environment, the population will decrease As in (), if the species do not interact the predator population will exhibit exponentially decaying solutions. Section 3.2: Questions . Analytically find the nullclines and equilibrium solutions of the Logisic Predator-Prey system (5). 2. Assign the parameters in (5) the values a = 1.5, b = 1.1, c = 2.5, d = 1.4. and k = 0.5. Modify the provided script flow.m in Matlab so it computes the phase portrait of the system (5). Use ode45 in Matlab to simulate solutions to (5) starting from the initial condition ai(0)-0.5, 2(0)-1.0 over the time intervalte [0, 50) and then plot the following together: . Use flow. m to plot the phase portrait ofon the domain-1

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