Re: nullcine?

From: Robert Israel (israel_at_math.ubc.ca)
Date: 01/09/05 

Date: 9 Jan 2005 03:29:26 GMT

In article <1105146362.113074.123800@f14g2000cwb.googlegroups.com>,
ames_kin@yahoo.com <ames_kin@yahoo.com> wrote:
>how would you describe the benefit of studying the nullcline or a
>system.

>I ask because while reading a powerpoint presentation of well known
>adam arkin, he pointed out that with certain system, it is possible to
>get cubic nullcline with addition of noise.
>what exactly are nullclines and how do you study them?

For a differential equation dy/dt = f(t,y) the nullclines are the
curves f(t,y) = 0. For an autonomous two-dimensional system

dx/dt = f(x,y)
dy/dt = g(x,y)

the nullclines are f(x,y) = 0 and g(x,y) = 0.
Studying the nullclines often gives qualitative information about
the behaviour of the differential equation or system, especially as
t -> infinity or -infinity.

Robert Israel israel@math.ubc.ca
Department of Mathematics http://www.math.ubc.ca/~israel
University of British Columbia Vancouver, BC, Canada