Solve Predator Prey Model Equilibrium Points

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Homework Statement


x'=x(1+2x-x2-y)
y'=y(x-a)



I need help finding the equilibrium points of this system.
 
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What part are you confused about?
 
well let me state the entire problem:

Consider the predator prey type of system that's given above with a>0. The population x is prey. By itself, its rate of growth increases for small populations and then decreases for x>1. The predator is given by y, and it dies out when no prey is present. The parameter is given by a. You are asked to show that this system has a Hopf bifurcation.
i) Find the fixed point (xa,ya) with both xa,ya positive.
 
Can xa or ya be 0?
 
It doesn't say anything about that. And as a matter of fact, I was getting (0,0) as one of my equilibrium points.
 
(0,0) is an equilibrium point. Another one occures when x = 0, a 3rd one occurs when y = 0. To find the 4th equilibrium point, solve 1+2x-x2-y and x - a simultaneously.
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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