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Using this information: (a) Clearly identify your dependent and independent variables, in- cluding their units (b) Derive a differential equation for the rabbit population that takes all factors listed above into account, using the trick with h small and calculating the change

Using this information: (a) Clearly identify your dependent and independent variables, in- cluding their units (b) Derive a differential equation for the rabbit population that takes all factors listed above into account, using the trick with h small and calculating the change

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Our goal in this problem is to develop a model for the bunny population by taking the following factors into account: • The initial population on Jan 1 was 50 rabbits On average, every rabbit has 0.1 offspring per month On average, 30% of the existing rabbit population dies per month 30 rabbits migrate into the Using this information: area per month. (a) Clearly identify your dependent and independent variables, in- cluding their units (b) Derive a differential equation for the rabbit population that takes all factors listed above into account, using the trick with h small and calculating the change (c) Perform a qualitative analysis: and the equilibrium solutions, draw the bifurcation diagram, plot the equilibrium solution and at least two other solutions, and determine if the equilibrium solution is stable/unstable/bistable (d) Solve the ODE, including the initial condition (e) Use your solution to figure out what happens to the population of bunnies as t→∞. 1
Transcribed Image Text:Our goal in this problem is to develop a model for the bunny population by taking the following factors into account: • The initial population on Jan 1 was 50 rabbits On average, every rabbit has 0.1 offspring per month On average, 30% of the existing rabbit population dies per month 30 rabbits migrate into the Using this information: area per month. (a) Clearly identify your dependent and independent variables, in- cluding their units (b) Derive a differential equation for the rabbit population that takes all factors listed above into account, using the trick with h small and calculating the change (c) Perform a qualitative analysis: and the equilibrium solutions, draw the bifurcation diagram, plot the equilibrium solution and at least two other solutions, and determine if the equilibrium solution is stable/unstable/bistable (d) Solve the ODE, including the initial condition (e) Use your solution to figure out what happens to the population of bunnies as t→∞. 1
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