## 55 Reputation

9 years, 195 days

## Set initial conditions for a dfieldplot...

Maple 17

Hi there,

I have an ODE system which apparently needs some initial conditions to have its vector field plotted.

I am giving Maple's dfieldplot function the following arguments:

dfieldplot([de1, de2], [A(t), G(t)], t = 0..1, [A(0) = 25, G(0) = 0], A = 0..900, G = 0..200)

But Maple yields an error that reads:

Error, (in DEtools%2Fdfieldplot) invalid use of initial points or option - see phaseportrait

I would say that the initial conditions are correctly stated, according to the documentation of the function.

This is the attempt: MaplePrimes_Malaria_infection_cont.mw

Any ideas on what's missing?

Thanks,

jon

## Loop over a set of lists...

Maple 17

Hi there,

I would like to have the Jacobian matrix of an ODE system evaluated, and their eigenvalues computed, at the steady states of the system.

I know how to get the Jacobian matrix evaluated and the eigenvalues computed on an individual basis, setting manually each steady state as the argument of the matrix.

However, I would like to have it in a loop, so that the loop manages all steady states, that is:

steadyStates:= solve(mySystem); # would yield a set of pairs/lists

m:=Jacobian(steadyStateN); # evaluate the Jacobian matrix

ev:= eigenvals(m); # compute the eigenvalues and save them to another variable/array and print them

end for:

First, I am not to find a way to loop over my steadyStates.

Attached is an example where the Jacobian matrix and eigenvalues are computed individually, where the steady states have been hard-coded once they have been computed: MaplePrimes_Predator_prey_model_Jacobian.mw

Any ideas on how to do this?

Thanks,

jon

## Compute and display isoclines (nullcline...

Maple 17

Hi there,

I would like to compute and display the nullclines of a set of ordinary differential equations.

AFAIK, I can compute the nullclines in Maple by defining the equations and solving the system

e.g.:

# Define the equations
eq1 := u(t)*(1-u(t)/kappa)-u(t)*v(t) = 0;
eq2 := g*(u(t)-1)*v(t) = 0;

# Solve the system (i.e. compute the nullclines)
sol := solve({eq1, eq2}, {u(t), v(t)});

However, I am not quite able to imagine how to display them over a dfieldplot or a phaseportrait.

Attached is an example with some differential equations, and their vector field and trajectories: MaplePrimes_Predator_prey_model_nullclines.mw.

It can be use to illustrate how to (compute and) display the nullclines.

Thank you,

jon

## Apply a math operator to an array/list o...

Maple 17

Hi there,

I would like to have an operator (in this case, the natural logarithm) applied to a list/array of points defined as:

ydata := [0.572594976618e-1, 0.327865007249e-1, 0.280821589546e-1, 0.114365745192e-1, 0.578537931608e-2, 0.139154661062e-2, 0.641467839994e-3, 0.18013801847e-3];

How can I apply Maple's ln() operator to the whole array (i.e. avoid to apply it to ydata [1], ydata [2], etc.)?

Thank you,

jon

## Solving differential equations...

Maple 17

Hi there,
I have the following set of equation which I want to solve using Maple's dsolve command:

d[V(t)*C(t)]/dt = G - K *C(t)
dV(t)/dt = alpha - beta

where V is the volume, C is the concentration, and t is the time variable. G, K, alpha and beta are constant parameters of the problem.

The solution for V(t) is easy to find operating the second equation:
V(t) = V_0 + (alpha - beta)*t

But solving for C(t) is a bit harder.

I would like Maple to solve the system, but the result I get does not really make sense to me. My attempt is this: Maple_artificial_kidney.mw

Any thoughts about how to introduce the equations successfully?

Thank you,
jon

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