Population Growth: Other Models: Harvesting: Example 1 Part 1 (DTub...

In this video I look at an example of a modification of the logistic equation by adding a negative constant to the differential population growth formula. This negative constant can be used to model the harvesting of fish, which is simply a constant rate of fishing. Adding this to the logistic equation will result in a case where there are two none-zero equilibrium solutions. When the initial fish population is below the lowest equilibrium solution value, in this example it is a population of 250 fish, than the given constant fishing rate of 15 per week is in fact a case of overfishing, and thus the population eventually goes to zero. This is the major difference that adding the harvesting constant adds to the logistic differential equation. I will solve this equation explicitly in the next video and compare the solution with that of the direction field graphed in this video, so stay tuned!

Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIhtVqJBMEixvPlKZi1g

View Video Notes on Steemit: https://steemit.com/mathematics/@mes/population-growth-other-models-harvesting-example-1-part-1