In a hypothetical study of population dynamics, scientists have been tracking the number of rabbits and foxes on an island. The number of rabbits and foxes are determined once a year using high resolution infrared cameras and advanced computer vision methods. Each year, the number of rabbits and foxes are found to change by the following equations: $$ {\Delta}R = round( kr*R - krf*R*F ) $$ $$ {\Delta}F = round( -kf*F + kfr*R*F ) $$ where $ {\Delta}r $ and $ {\Delta} f $ are the changes in number of rabbits and foxes by the end of that year; and R and F are the population sizes at the end of the previous year. kr, krf, kf, kfr are coefficients that depend on the species of rabbits and foxes. With these dynamics, the scientists realize that one or both species can become extinct on the island. At the end of each year, if there are fewer than 2 animals of a kind, the scientists transfer rabbits and/or foxes to make sure there are at least 2 of each kind. Write a function rabbitsandfoxes_conservation(R,F, kr,krf,kfr,kf, T) that takes the number of rabbits and foxes at the end of the first year, and simulates the populations up to T years. Your function should return a matrix M that has T rows and 2 columns, with first column containing number of rabbits each year, and the second column containing number of foxes each year. First row of the matrix M should be same as [R,F]. In addition to returning the matrix M, your function should plot on a single figure, the population sizes of the rabbits and foxes over T years. Your figure should have axis labels and a legend indicating which plot is which species. >> rabbitsfoxes_conservation(200,100,0.3,0.01,0.001,0.2,4) ans = 200 100 60 100 18 86 8 70 >> rabbitsfoxes_conservation(200,100,0.3,0.1,0.001,0.2,4) ans = 200 100 2 100 2 80 2 64
In a hypothetical study of population dynamics, scientists have been tracking the number of rabbits and foxes on an island. The number of rabbits and foxes are determined once a year using high resolution infrared cameras and advanced computer vision methods.
Each year, the number of rabbits and foxes are found to change by the following equations:
where $ {\Delta}r $ and $ {\Delta} f $ are the changes in number of rabbits and foxes by the end of that year; and R and F are the population sizes at the end of the previous year. kr, krf, kf, kfr are coefficients that depend on the species of rabbits and foxes.
With these dynamics, the scientists realize that one or both species can become extinct on the island. At the end of each year, if there are fewer than 2 animals of a kind, the scientists transfer rabbits and/or foxes to make sure there are at least 2 of each kind.
Write a function rabbitsandfoxes_conservation(R,F, kr,krf,kfr,kf, T) that takes the number of rabbits and foxes at the end of the first year, and simulates the populations up to T years. Your function should return a matrix M that has T rows and 2 columns, with first column containing number of rabbits each year, and the second column containing number of foxes each year. First row of the matrix M should be same as [R,F].
In addition to returning the matrix M, your function should plot on a single figure, the population sizes of the rabbits and foxes over T years. Your figure should have axis labels and a legend indicating which plot is which species.
>> rabbitsfoxes_conservation(200,100,0.3,0.01,0.001,0.2,4) ans = 200 100 60 100 18 86 8 70 >> rabbitsfoxes_conservation(200,100,0.3,0.1,0.001,0.2,4) ans = 200 100 2 100 2 80 2 64
Trending now
This is a popular solution!
Step by step
Solved in 4 steps with 2 images
