# Hindmarsh rose model with delay (dde)

• kaledh
In summary, the conversation discusses a problem with using the MATLAB dde23 solver to evaluate the delayed HR model. The model involves three differential equations and the question is how to set the history values for the delayed variable. The three suggested options are to use x(t) = x(0), x(t) = 0, or x(t-tau) = x(t) for t < 0. The conversation also mentions that the dde23 solver should work for this problem, and another potential solution is Simon Wood's solv95 program.

#### kaledh

hi all,

I have a problem using the MATLAB dde23 solver to evaluate the delayed HR model:

dx/dt = y(t) - a*x(t)^3 + b*x(t)^2 - z(t) + e (x(t-tau) - x(t))

dy/dt = c - d*x(t)^2 - y(t)

dz/dt = r [ s*(x(t) - xo) - z(t)]

how could I set the history values (-tau<t<0)?

it is possible use the dde23 solver or I must use some approximation? if so what's the best approximation method?

tnx

kaledh said:
hi all,

I have a problem using the MATLAB dde23 solver to evaluate the delayed HR model:

dx/dt = y(t) - a*x(t)^3 + b*x(t)^2 - z(t) + e (x(t-tau) - x(t))
dy/dt = c - d*x(t)^2 - y(t)
dz/dt = r [ s*(x(t) - xo) - z(t)]

how could I set the history values (-tau<t<0)?

it is possible use the dde23 solver or I must use some approximation? if so what's the best approximation method?

tnx

Hi,

I should have thought that the simplest thing to do would be just to put x(t) = x(0) for all t<0. An alternative would be x(t)=0 for t<0: this would imply that the delayed variable simply 'doesn't exist' before t=tau. Finally, you could put x(t-tau)=x(t)for t<0: this is tantamount to solving the undelayed ODE up to t-tau, and putting the delay in for t>tau. You could always experiment.

That said, most of the DDEs I have worked with have come out integrating a PDE w.r.t. its 'non-time' variable (e.g. Gurney WSC, Nisbet RM, Lawton, JH. 1983. The systematic formulation of tractable single-species population models incorporating age structure. Journal of Animal Ecology 52: 479-495.) and so the history of the delayed variable comes out naturally. Maybe just putting t-tau for t in the right-hand side of an ODE is not a good way of getting a DDE without extra thought.

The dde23 solve in Matlab should also work with this problem. There is also Simon Wood's solv95 programme (http://www.maths.bath.ac.uk/~sw283/simon/dde.html [Broken]).

Ashley

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