Fixed Points of two differential equations

Thread starter msell2
Start date Nov 27, 2012
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Differential Differential equations Fixed points Points

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To find the fixed points of the given system of differential equations, set dx/dt and dy/dt to zero. This leads to the equations x(β-x-ay) = 0 and y(-1+ax-y) = 0. The fixed points occur when either x or y is zero, or when the expressions in parentheses equal zero. The discussion suggests using the method of dividing the equations to relate dx/dt and dy/dt, simplifying the analysis of the system. Understanding the fixed points is crucial for analyzing the behavior of the system over time.

Nov 27, 2012

msell2

Homework Statement

Determine all fixed points of:
dx/dt = x(β-x-ay)
dy/dt = y(-1+ax-y)

β and a are parameters.

I get what to do when there is just one differential equation, but not two.

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Nov 27, 2012

tadchem

Divide dx/dt = x(β-x-ay) by dy/dt = y(-1+ax-y) and you will get
(dx/dt)/(dy/dt) = [x(β-x-ay)]/[y(-1+ax-y)] = dx/dy

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