Bifurcation and Equilibria points...

Hello,

One again, I have a problem to solve some bifurcation problem using maple.

Discuss the existance of Equilibria and determine any possible bifurcation.

x'=r*x-ln(x+1);

where \$r\$ is a parameter.

many thinks for your help and suggestion.

Wrapper for plot() etc....

I am considering to write a wrapper for plot and related commands (could redefine the commands or introduce a new name) which facilitates export of Maple plots to postscript. The command should interpret some of the options and remove them from the options sequence before submitting the remaining ones to the original plot().
E.g. it should recognize a title="TITLE" parameter and process TITLE (e.g. write it to a specific file). Similarly I would want to be able to pass additional parameters, e.g. filename="FILE" in order to specify how the output file name should be set. Is this a sensible approach. How can I realize this detailed option 'parsing' in Maple?

solving a symbolic inequality...

Hi, those who are in mapleprimes.

i have a problem in solving inequality with symbolic notated parameters.

I wrote the following code to solve for n(SPH), but couldn't obtain any result but an error message.

solve(-s*(-n(SPF)*tau+n(SPH))/(tau-1) <= n(SPH),n(SPH)) assuming (tau<1,s>0,s<1,tau>0);

The error was

Error, (in assuming) when calling 'unknown'. Received: 'invalid input: Utilities:-SetSolutions expects its 2nd argument, solutions, to be of type ({list, set})({piecewise, ({list, set})({name, relation})}), but received [s = -tau~+1, [SPF = SPF, s = s, tau~ <= 0]]'

Please tell me how I should do to solve the inequality.

taro

Pde system with initial condition...

Dear Maple Users,

I'm beginner in Maple.

I have this system of Pde:

with lambda experimental parameter and n,c,v dependent variables. I write this on Maple but I read on internet that the solution "float(undefined)" is an error.

I will insert this initial condition: c(x,0)=0,n(x,0)=0.4

Thanks everybody

Formal parameters understanding...

Hi everyone.

i want to undestand how to use the passing by reference in Maple i do this:

generate_x := proc (x)

x := (rand(1 .. 10))()

end proc;

generate_y := proc (y)

y := (rand(1 .. 5))();

print(y)

end proc;

print_xy := proc ()

local x, y;

generate_x(x);

print(x);

generate_y(y) end proc;

print_xy();

#print(x)  works but generate_y(y) doesn't print the value of y.

Can you help me to understand WHY i dont get the print of y.

Thanks and happy christmas to you!

plot ODE parameter against the time ...

Hello experts..

The following is the IVP:

restart:Digits:=14:t0:=0.0:tN:=5000.0: N1:=5000;th:=evalf((tN-t0)/N1):

dsys1 :=diff(y(t),t)=y(t)*((1-y(t)/3-epsilon)-0.8*y(t)/(y(t)^2+0.5^2));

var:={y(t)}:ini1:=y(0)=0.5:

dsol1 :=dsolve({dsys1,ini1},var,numeric, output=listprocedure, abserr=1e-9, relerr=1e-8,range=0..1);

dsolu:=subs(dsol1,y(t)):

t1:=array(0..N1,[]):u1:=array(0..N1,[]):pt1:=array(0..N1,[]):

for i from 0 to N1 do t1[i]:=evalf(th*i):u1[i]:=evalf(dsolu(t1[i]));pt1[i]:=[t1[i],u1[i]]:

od:

mytab1:=eval([seq(pt1[i],i=0..N1)]):

the above code is to plot y(t) against the time t for fixed epsilon

Now the question is how to plot epsilon against the time???

Statistics question ...

I have a statistics task that is very complicated to me, and I would really appretiate some help!

I believe that I have completed task a, but task b and c seems to be too hard for me to grasp.

Here is a presentation of the task text:

xi 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
yi 12.3 12.8 16.8 17.9 20.5 22.7 24.9 27.5 26.9 29.4 30.3 34.2 36.4 36.7 41.1

Assume that the data represents independent realizations of a "linearlnormal" model.

Yi = α + β xi + ei i = 1..15,

where ei˜N(0,σ), where sigma is unknown.

(a) create a scatterplot of the data {f(xi,yi)}15 ; i=1
Then calculate the empiric correlation coefficient.

(b) Find the minimum least square estimate for α & β.

(c) Create a 95% confidence interval for the parameter β. What does this confidence interval express?

Is there anyone out there who are able to help me with some maplecode?

Soeta

What symbol can't be used as a parameter?...

Here's a Maple trivia question: There is a Maple symbol that cannot be used as a procedure parameter. As far as I can tell it is the only one. What is it?

Curve fitting on multiple data series...

Hello,

I have two sets of data representing two function that depends on x with a parameter A.

I need to do a fit on both data series at the same time so to fit with the best parameter A.

Here is how I do a fit on one function

`> f(x):=A*cos(x-B)^(2);               `
`> g(x):=A*(cos(x-C)^(2)+ sin(x-C)^(2))^2; `
`> fit1 := Fit(f(x), r, x, parameternames = [A, B, C...`

How do i print to PDF the parameters of a model in...

I have a model with 3 parameter blocks containing a lot of constants. I would like to know how can i print those lists to papper, .pdf, word or something like that.

Thanks

problem with function solve...

Hi,

I am trying to solve the following system using the function "solve", but the message "warning solutions may have been lost" appears.

This is my script (a,b,c,d,e,f, Resp, Malcyt,Pyrcyt are parameters). The unknown variables are Citcyt, Citmt,Malmt,Pyrmt:

`e1 := 0 = a.Pyrcyt-a.Pyrmt+(b-c).Malmt; e2 := 0 = d.Malcyt+e.Citmt-(d+b+c).Malmt; e3 := 0 = f.Citcyt+c.Malmt-(e+f).Citmt;`
` e4 := 0 = 2.*e.Citmt+(b+c).Malmt-Resp;`

Procedure inputs??...

Hi all,

I read the help on using parameters, then I tried to modify the example

f := proc(a, b, c)

if _params['b','c'] = NULL then
a
elif _params['c'] = NULL then
a + b
else
a + b + c

end if

end proc:

I can't really spot where it went wrong, but it just wouldnt execute as I would expect...

Graphing parametric sweep results of a MapleSim mo...

Hi,

I'm running a 2D parameter sweep from Maple 15 on a MapleSim 5 model. The output is stored in a 2D matrix.  I've encountered two problems:

1) when I graph it with matrixplot the z-axis values are fine but I can't figure out how to change the x-axis and y-axis values from the matrix indices to the actual values of the swept parameters.

2) When the parameter sweep begins I get a warning about storing the values in a matrix.  Maple...

Can I make variables appear in DSolve numeric outp...

numeric_de.mw

hello boffins

if my de was soluble analytically, I would get an expression of time in terms of the other variables (V,theta,x) easily, but because it is only numerically solvable, i get an expression x(t)=proc(t)...,- the variables V and theta are mixed up in it-. Is there anyway they can appear?

I know I can put numerical values on V and Theta (and x) and solve for time (using parameters...

Graphing and parameter sensitivity analysis in map...

`eq1 := diff(E[X(t)], t) = lambda-delta*E[X(t)]-beta*E[X(t)*V(t)];`
` eq2 := diff(E[Y(t)], t) = -delta*E[Y(t)]+beta*exp(-rho*tau)*E[X(t)*V(t)];                                                    eq3 := diff(E[V(t)], t) = gamma+N*kappa*E[Y(t)]-mu*E[V(t)]-beta*E[X(t)*V(t)]`
`NB:- E[X(t)]= the expected value of variable X at time t. `
`Please help me know how to input this...`