Solve Predator Prey Model Equilibrium Points

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Homework Help Overview

The discussion revolves around finding the equilibrium points of a predator-prey model described by a system of differential equations. The model includes parameters that influence the growth and interaction of predator and prey populations.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants are attempting to identify fixed points of the system, with some questioning the conditions under which equilibrium points can exist, particularly regarding the values of xa and ya.

Discussion Status

The discussion is ongoing, with participants exploring different equilibrium points and questioning the implications of certain values, such as whether xa or ya can be zero. There is acknowledgment of multiple equilibrium points, including (0,0), but no consensus on the complete set of points has been reached.

Contextual Notes

Participants note that the problem does not specify constraints on the values of xa and ya, leading to discussions about the implications of obtaining (0,0) as an equilibrium point.

sana2476
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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.
 

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