Question

"Predator - Prey"Consider the following systems of rate of change equations:System A(dx/dt)= 3x(1-(x/10))- 20xy(dy/dt)= -5y+(xy/20)System B(dx/dt)= 0.3x-(xy/100)(dy/dt)= 15y(1-(y/17))+25xyIn 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 piranhas and humans. Thus 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.

Answer 1

Answer:

The responses to this questin can be defined as follows:

Step-by-step explanation:

Take system A. The predator must be there. If we feel the attacker is x, that drop in y (a further prey eaten) must raise by x. Growing x could render y falling much quicker because more predators become available. See the equation of $\frac{dx}{dt}$.

$\frac{dx}{dt} = 3x(1- \frac{x}{10})-20xy$

It will see that dx/dt is an x both y function. It is indeed difficult to tell something about the dependence among $\frac{dx}{dt}$ and x, but it is quite easy: the higher to y, its higher the 20xy (since x and y are positive numbers). And therefore -20xy is much more negative, but $\frac{dx}{dt}$ is much worse. Going to find: the larger y, the less or even more negative $\frac{dx}{dt}$, the less x.

Test: It implies that higher y means less x (more prey) (fewer predators). Then, does the assumption which x is a predator confirmed? No, because more prey, and thus more predators, would mean better lunch for both the predators, People could see that x is now a prey as well as y a predator, even though more predators(y) exist.

They use the second equation to check this:

$\frac{dy}{dt} = -\frac{5y+xy}{20}$

Perhaps, now we're just talking about basic dependency as of now: one is from dy/dt to x. A larger x means that the y (predator) is growing faster. For System B we are using the same rationale.Thus, x is a predator and y a predator (as high x indicates higher 25 x but this results in increased y population increase (EQ.2), as higher x means lower $\frac{XY}{100}$ and reduces x) Afterwards, we would like to learn which system has big and small predators. To conclusion, they must realize that this piranha does not impact that population of humans in the case of piranhas. However in cases where y = I and y = i+1 would not significantly differ from $\frac{dx}{dt}$ (alter in the number of individuals) (i is an arbitrary number of piranhas)

This function of system B can be seen: $\frac{dx}{dt} = 0.3x - \frac{xy}{100}$. And what's the reason? Given the fact that the element beside y is $\frac{1}{100}$, another tiger shark is no worse than $\frac{dx}{dt}$ and therefore not willing to make a significant contribution to the elimination of global life. Through system A, they could see that the predator is huge because one predator implies a major shift in $\frac{dx}{dt}$ almost. I belive that, this message has been observed by you. But I also hope that throughout the end I have created no error:) This should try to not learn with your heart, since it is helpful when you grasp the task. Another way to approach the problem might be to try to consider $\frac{dy}{dt}$ instead of $\frac{dx}{dt}$ for both systems and then to see that what prey is tiny or large. This big predator should not imply many hunters with one location or each other and will eat a meal (System A seems to have this feature: $(\frac{dy}{dy} = -5y)$