       Re: Delay Differential Equations

• To: mathgroup at smc.vnet.net
• Subject: [mg105227] Re: [mg105198] Delay Differential Equations
• From: Yun Zhao <yun.m.zhao at gmail.com>
• Date: Wed, 25 Nov 2009 02:30:55 -0500 (EST)
• References: <200911241048.FAA00661@smc.vnet.net> <4B0C33E2.5070102@wolfram.com>

```Hi Daniel,

Thanks for your reply.  But my question is I was trying to solve an
equation, and the solution just doesnt make much sense, and I looked in the
help files, but they didn't really help me much.  The problem is this:

I have some cells of type A, and at some point in time, cells of type A are
going to slowly change into cells of type B.  So, population size of cell
type A will decrease over time due to two factors: (1) becoming cells of
type B and (2) dying over time.  So for a differential equation, i have two
rates, one is the transformation rate (0.0367), one is the death rate
(0.0123).  But I want to delay the transformation by 37 hours.  So from time
= 0 to time = 37, all that is changing in cells of type A is that they are
dying at the death rate, then after 37 hours, they are also disappearing at
the transformation rate.

So my differential equation is like this:

*solrandom1=NDSolve[{p'[t]**==0.0367*p[t-37]-0.0123*p[t],p[t/;t<0] 30000},p,{t,0,120}]*

What I expect when I plot p(t) over t is a gradual decrease from t=0 to
t=37.  Then more decrease from t=37 to t=120.  p(t) should never be less
than zero.  But when I ran that code in Mathematica, and plotted it using
this command

*Plot[Evaluate[p[t]/.solrandom1],{t,0,120},PlotRange**=EF=82=AEAutomatic]*

p(t) was actually less than zero.  I am not able to figure out why this is.

Please tell me what I did wrong.  Thanks.
On Tue, Nov 24, 2009 at 1:28 PM, Daniel Lichtblau <danl at wolfram.com> wrote:

>  Yun Zhao wrote:
>
>> Hi,
>>
>> Does anyone have experience working with delay differential equations in
>> Mathematica 7? I found some help files on wolfram and Mathematica help,
>> but
>> the information available there were very limited. If anyone can refer me
>> to
>> other online or textual sources, I would really appreciate it. Thank you
>> very much.
>>
>> Mike
>>
>
> Not sure what you saw in the Documentation Center. These are perhaps the
> most useful, worth checking if you have not encountered them already.
>
> howto/SolveDelayDifferentialEquations
> tutorial/NDSolveDelayDifferentialEquations
>
> Daniel Lichtblau
> Wolfram Research
>

```

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