Each system of DE is a model for 2 species that either compete for the same resources or cooperate for mutual benefit.
$$\frac{dx}{dt}=0.12x-0.0006x^2+0.00001xy$$

Question

Each system of DE is a model for 2 species that either compete for the same resources or cooperate for mutual benefit. 
$$\frac{dx}{dt}=0.12x-0.0006x^2+0.00001xy$$

anonymous · Answer

I think you are missing some info

anonymous · Answer

$$\frac{dy}{dt}=0.08x+0.00004xy$$

anonymous · Answer

I have to equations, one with dx/dt and the other with dy/dt. What's the main idea behind that?

anonymous · Answer

this would be totally okay for me if it were linear, but...

anonymous · Answer

It's only calc II

anonymous · Answer

really?

anonymous · Answer

Yes.  I think I'm supposed to only decide whether each system describes a competition or cooperation.

anonymous · Answer

hm... this is seeming strange to me
all this terminology is new, though I should know it if it's calc II

anonymous · Answer

The chapter is differential equations and the section is "predator-prey systems"
$$\frac{dR}{dt}=kR$$ k is a positive constant
$$\frac{dW}{dt}=-rW$$ r is a positive constant
$$\frac{dR}{dt}=kR-aRW$$
$$\frac{dW}{dt}=-rW=bRW$$

anonymous · Answer

the last 2 equation are the predaor-prey equations

fwizbang · Answer

Look at the xy term in both of the equations. If both coefficients are positive, then rate of change of x and y both increase, which means that each species benefits from the other's presence...... a cooperation. If both terms were negative, then each would increase its prospects by driving the other out of existence, which would be competition.