Consider the predator-prey model with all the same assumptions of the simple model explored in lab,...
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Consider the predator-prey model with all the same assumptions of the simple model explored in lab, except that the prey reproduction follows a logistic model instead of an exponential. The model equations can be written as follows: dx = ax - x-bx² - cxy dt dy = exy - fy dt As before, assume all model parameters are strictly positive (positive and not equal to zero). Problem 1: (4 pts) Check that the above system of equations as written does indeed reflect the assumption of logistic growth in prey (in the absence of predators). Do so by assuming that there are no predators and show that the resulting equation for dx/dt is equivalent to the logistic model as presented in lecture. In other words, find expressions for the parameters a and b from above in terms of the parameters Rmax and Pmax used for the logistic model in lecture. Problem 2: (6 pts) Find expressions for all fixed points of the model in terms of the model parameters. What does the fixed point with x > 0 and y>0 represent biologically (when it exists)? Consider the predator-prey model with all the same assumptions of the simple model explored in lab, except that the prey reproduction follows a logistic model instead of an exponential. The model equations can be written as follows: dx = ax - x-bx² - cxy dt dy = exy - fy dt As before, assume all model parameters are strictly positive (positive and not equal to zero). Problem 1: (4 pts) Check that the above system of equations as written does indeed reflect the assumption of logistic growth in prey (in the absence of predators). Do so by assuming that there are no predators and show that the resulting equation for dx/dt is equivalent to the logistic model as presented in lecture. In other words, find expressions for the parameters a and b from above in terms of the parameters Rmax and Pmax used for the logistic model in lecture. Problem 2: (6 pts) Find expressions for all fixed points of the model in terms of the model parameters. What does the fixed point with x > 0 and y>0 represent biologically (when it exists)?
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Given cie dre dt Note dy dt for finding fixed points of the given model da ... View the full answer
Related Book For
Applied Regression Analysis and Other Multivariable Methods
ISBN: 978-1285051086
5th edition
Authors: David G. Kleinbaum, Lawrence L. Kupper, Azhar Nizam, Eli S. Rosenberg
Posted Date:
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