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Re: Differntial Equations

  • To: mathgroup at
  • Subject: [mg8052] Re: Differntial Equations
  • From: Mark James <mrj at>
  • Date: Mon, 4 Aug 1997 01:47:36 -0400
  • Organization: Basser Dept of Computer Science, University of Sydney, Australia
  • Sender: owner-wri-mathgroup at

Bernhard Petri wrote:
> I have a system of 2 Diff. Eqns. which describe an oscillating chemical
> reaction:
> x'[t]==z (d-(x[t] y[t]/(y[t] (1+x[t])+a)))
> y'[t]==(x[t] y[t]/(y[t] (1+x[t])+a))-b y[t]/(1+x[t])
> for a=30; b=0.1; d=0.03; z=1/6; and x[0]==1, y[0] == 15;
> I have tried to solve these with NDSolve. The system shows damped
> oscillations. A permanent oscillation will be obtained by the additional
> constraint that y[t] stays always above 0.00001. How can I include this
> constraint into my system? Has anybody a practical suggestion?

What about something like:

y'[t] == If[ y[t]<0.00001,
		(x[t] y[t]/(y[t] (1+x[t])+a))-b y[t]/(1+x[t])

or an equivalent softer threshold.

I tried it out, and y[t] only falls to about 0.01 anyway.

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