Re: Differntial Equations

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

```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,
10^10,
(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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