# differential equation equilibria!??

• Mar 10th 2008, 02:24 PM
calcusucks
differential equation equilibria!??

consider an interaction between two mutually inhibiting proteins with concentrations x and y, given by the differential equations:

dx/dt = f(y)-x
and
dy/dt = g(x)-y

where both f(y) and g(x) are decreasing functions.

*show that equilibria occur when f[g(x)]=x

how do i do the asterick part? any help would be very much appreciated..
• Mar 31st 2008, 07:11 PM
mr fantastic
Quote:

Originally Posted by calcusucks

consider an interaction between two mutually inhibiting proteins with concentrations x and y, given by the differential equations:

dx/dt = f(y)-x
and
dy/dt = g(x)-y

where both f(y) and g(x) are decreasing functions.

*show that equilibria occur when f[g(x)]=x

how do i do the asterick part? any help would be very much appreciated..

Require that both rates of change equal zero:

f(y) - x = 0 => x = f(y) ..... (1)
g(x) - y = 0 => y = g(x) .... (2)

Solve equations (1) and (2) simultaneously:

Substitute (2) into (1) ......