How can I treat the final time of the ode solver a variable? Please read the question for detail.

Below is the main file in which I solve an ode. I have attached the parameter (mu, K, d1) files and the file (para_1d.m) in which ode is defined as well. My parameters are available as seasonal averages. So I have 4 average values per year (for spring, summer, fall and winter). I assume that each season is of equal length i.e., 91.25 days. But I have to incorporate the fact that the length of the seasons can vary. For example, there may be some years in which winter is longer but spring/fall is shorter. If suppose my year starts with spring and ends in winter, and if winter is short the length of my year will also be shorter. So I cannot use a fixed length (i.e., 365 days) of each year as well. I am not able to include this flexibility in my code. Any suggestions/comments will be helpful. Thanks!

clear all
  p = 20;%  indicates the number of years the simulation will run

    yearlength = 365;

    finaltime = p*yearlength;
    t = 0:finaltime;
    % calling parameters
    mugen;
    Kgen;
    d1gen;

    n = 2;
    y0 = 20000; % initial conditions

    deltat = 1;
    tspan = 0:deltat:finaltime;

    options = odeset('RelTol',1e-10,'AbsTol',1e-10);

    sol = ode23s(@(t,y)para_1d(t,y,n, mug,Kg,d1g),tspan,y0,options);

    X = sol.x;
    Y = (sol.y)';

    plot(X,Y(:,1),'r-')

Answer 1

[Jeremy D'Silva]

Try using Latin Hypercube sampling from a reasonable range for each season length. In pseudocode:

springRange = [some ball around 91.25] e.g. [81.25,101.25]
summerRange = [some ball around 91.25] e.g. [81.25,101.25]
fallRange = [some ball around 91.25] e.g. [81.25,101.25]
winterRange = [some ball around 91.25] e.g. [81.25,101.25]
ranges = [springRange(1),  summerRange(1),fallRange(1), winterRange(1); ...
    springRange(2), summerRange(2), fallRange(2), winterRange(2)];
ourHyperCube = lhsdesign(number_of_runs,4); %Makes a Latin Hypercube

for i = 1:number of runs
    SeasonLengths_run = ourHyperCube(i,:) * (ranges(2,:) - ranges(1,:)) + ranges(1,:);
% SeasonLengths_run = something of the form [springLength, summerLength, fallLength, winterLength];      
    sum season lengths to get t_final
    simulate ODE over [t_0 t_final]
         pass season values to ODE
    save run
end
%%%%%%%%%%%%%%
Then, in your ODE file, incorporate time-varying parameters. You can do this in a trivial way by telling it (

if t<startOfSummer
     use SpringParams
end

and likewise for the other seasons.

This is a really rough sketch, obviously, but the concept might work. And I'd be interested to see your solution, so let us know if it works!