need help with ode45

so im trying to solve some diff eqs (xC, y, and w) and thus far i have:

% with xE=0 (no elites): egalitarian society
% xC(0) = 100 , xE(0) = 0 , y(0) = l , w(0) = 0

      d = 6.67e-6; %depletion rate
      am = .01; %normal (min) death rate
      aM = .07; %famine (max) death rate
      bC = .03; %commoner birth rate
      bE = .03; %elite brith rate
      s = .0005; %subsistence salary per capita
      p = .005; %threshold wealth per capita
      g = .01; %regeneration rate of nature
      l = 100; %nature carrying capacity
      k = 1; %inequality factor
      n = (aM-bC)/(aM-am);
      XM = (g*(l/2)^2)/(n*s); % max carry capacity

      options = odeset('RelTol',1e-4);
      [t, xC] = ode45('xC3',[0 1000],100,options);
      [t, y] = ode45('y3a',[0 1000],l,options);
      [t, w] = ode45('w3a',[0 1000],0,options);

      CC = min(1,w./wth)*s.*xC; % consumption rate commoners
      CE = min(1,w./wth)*k.*s.*xE; % consumption rate elite
      wth = p.*xC+k*p.*xE; % wealth threshold
      aC = am+max(0,1-CC/(s.*xC)).*(aM-am); % death rate commoners
      aE = am+max(0,1-CC/(s.*xE)).*(aM-am); % death rate elite

and my functions for the ode45 are:

function dxC = xC3(t,xC)
    dxC = bC.*xC-aC.*xC; % commoner population
end

function dy = y3a(t,y)
    dy = g.*y.*(l-y)-d.*xC.*y; % natural resources
end

function dw = w3a(t,w)
    dw = d.*xC.*y-CC-CE; % accumulated wealth
end

I'm getting these errors:

Undefined function or variable 'bC'.

Error in xC3 (line 2)
    dxC = bC.*xC-aC.*xC; % commoner
    population

Error in odearguments (line 88)
f0 = feval(ode,t0,y0,args{:});   % ODE15I
sets args{1} to yp0.

Error in ode45 (line 114)
[neq, tspan, ntspan, next, t0, tfinal, tdir,
y0, f0, odeArgs, odeFcn, ...

Error in fig3a (line 22)
    [t, xC] = ode45('xC3',[0
    1000],100,options);

I don't know why it says bC is undefined because I clearly define it, and I don't know what the other errors mean.

[Joey]

I know it's alot to look at, but ANY help is appreciated

Answer 1

[ragesh r menon]

The problem here is that the scope of variable "bC" is outside the definition of function. Either define them locally by defining within the function xC3 or make them global by declaring

global bC ..............

[Joey]

i globalized every variable but it still gave me the same errors

[Jan]

@joey: In the code you have posted, bC is not defined as a global inside e.g. the function xC3. So what does "I've globalized every variable" exactly mean?

Answer 2

[ragesh r menon]

See, you are not defining aC in the function xC3 and this aC is again dependent on the state xC

   aC = am+max(0,1-CC/(s.*xC)).*(aM-am); % death rate commoners

Instead of writing 3 separate function write them in one because dXc and dy are depedent on xC

function ... = xC3(t,x1,x2)
    CC = ....; % consumption rate commoners
    CE = ....; % consumption rate elite
    wth =....; % wealth threshold
    aC =.....  % death rate commoners
    aE = ....; % death rate elite

         dxC = bC.*x1-aC.*x1; % commoner population
         dy = g.*x2.*(l-x2)-d.*x1.*x2; % natural resources
         dw = d.*x1.*x2-CC-CE; % accumulated wealth
  end

I just copied and pasted your code..Modify accordingly.

[Joey]

so then how would i take the ode45 for those 3 diff eqs? would the output for the function be something like z where z = [dxC dy dw], and then i would do ode45('z',[0 1000], [100 l 0], options)?

[Jan]

@Joey: Exactly. Simply try it and read doc ode45.

[Joey]

heres what it says now:

Undefined function or variable 'p'.

Error in test (line 3)
wth = p.*z(1)+k*p.*xE; % wealth threshold

Error in odearguments (line 88)
f0 = feval(ode,t0,y0,args{:});   % ODE15I sets args{1} to yp0.

Error in ode45 (line 114)
[neq, tspan, ntspan, next, t0, tfinal, tdir, y0, f0, odeArgs, odeFcn, ...