I just need a push on this problem. Consider the following systems of rate of ch
ID: 2941802 • Letter: I
Question
I just need a push on this problem.Consider the following systems of rate of change equations:
system A System B
dx/dt=3x(1-x/10)-20xy dx/dt=0.3x-xy/100
dy/dt=-5y+xy/20 dy/dt= 15y(1-y/17)+25xy
In both of these systems, x and y refer to the number of two different species at time t. In particular, in one of these systems the prey are large animals and the predators are small animals, such as ants and a grasshopper. Therefore,it takes many predators to eat one prey, but each prey eaten is a tremendous benefit for the predator population. The other system has very large predators and very small prey.
* Figure out which system is which and explain the reasoning behind your decision. Try to develop more than one way to reach a conclusion .
Now, Ive already figured out who is the predator and who is the prey in both systems. But how do you approach figuring out which system is which?
Explanation / Answer
So you already know that in both systems y is the predator. Because those have a positive coefficient for the xy-term (predators benefit from meeting preys). In system A it is a tremendous loss for the population of the prey if they meat predators (-20) while it is only a small gain for the predators (+1/20). In system B it is a small loss for the population of the prey if they meat predators (-1/100) while it is a big gain for the predators (+25). That makes that system B is the one with the prey being the large animals.