Main Points: Differential equations can be used to consider growth of two interacting populations, such as species competing for food, predator/prey, and symbiosis. This action requires a system of differential equations. This system is found by using the Lotka-Volterra equations. It states that the number of "encounters" between the two species is proportional to the product of the populations. Phase planes are used to graph the two populations against time. The point of the two populations versus eachother moves, and this path is called the phase trajectory. Slope fields are also used to see what the solution will look like. Setting the equations equal to zero helps find the equilibrium points. The shape of the trajectory tells how the populations vary with time, and a closed curve means that both populations oscillate periodically.
Challenges: I was confused on how the book came to the equations for the worm/robin example. I don't quite follow the part about the different constants either.
Reflections: The Lotka-Volterra equation is really helpful in finding how different populations depend on eachother. I'm sure that ecologists use this alot to see how different species are changing in number and how the food chain works.
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