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==1, y == 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.