Solve Predator Prey Model Equilibrium Points

[sana2476]

Homework Statement

x'=x(1+2x-x²-y)
y'=y(x-a)



I need help finding the equilibrium points of this system.

 

[cse63146]

What part are you confused about?

 

[sana2476]

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 (x_a,y_a) with both x_a,y_a positive.

 

[cse63146]

Can x_a or y_a be 0?

 

[sana2476]

It doesn't say anything about that. And as a matter of fact, I was getting (0,0) as one of my equilibrium points.

 

[cse63146]

(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.