% IDE Integrodifference Equation Simulator
%
%	This program numerically solves a scalar
%	integrodifference equation and plots the
%	result.
%
%	Author: Michael Neubert
%		2/8/2000

% r = growth parameter
% alpha = dispersal parameter
% iterations = number of iterations to perform
% lowval = truncation threshold
% diameter = length of the domain
% nodes = number of nodes in domain (should be 2^m + 1)
% x = vector of node locations
% x2 = vector of node locations for extended domain
% dx = internode distance
% n = matrix of population densities
% k = dispersal kernel
% f = growth function
% xmin, xmax, ymin, ymax: graphics scales
% irad = radius of initial condition
% idens = initial density

  iterations = 50;
  r = 1;
  alpha = 7;
  lowval = 1e-14;
  diameter = 250;  
  nodes = (2^13)+1;
  irad = 0.1;
  idens = 1;
  xmin = -60; xmax = 60;
  ymin = 0; ymax = 1.2;

  radius = diameter/2;
  x = linspace(-radius,radius,nodes);
  x2 = linspace(-diameter,diameter,2*nodes-1);
  dx = diameter/(nodes-1);
  n = zeros(1,length(x));

  k = (alpha/2)*exp(-alpha*abs(x2));


%SET THE INITIAL CONDITIONS

  n = zeros(size(n));
 
  temp = find(abs(x) <= irad);
  n(temp) = idens*ones(size(n(temp)));

%PLOT INITIAL CONDITIONS AND WAIT FOR KEYSTRIKE

  plot(x,n);
  xlabel('location (x)'); ylabel('population density [ n_{t} (x) ]');
  title('t = 0'); 
  axis([xmin xmax ymin ymax]);
  drawnow;
  disp('Strike any key when ready...');
  pause;

%DO THE SIMULATION ITERATIONS
  
  n1 = zeros(1,length(x2)+length(x)-1);
  for j = 1:iterations

     n1 = zeros(size(n1));
  
     % Ricker Growth
     f = n.*exp(r*(1-n));

     % Convolution
     n1 = fft_conv(k,f);
     n = dx*n1(nodes:length(x2));
     n(1) = n(1)/2; n(nodes) = n(nodes)/2;
     temp = find(n < lowval);
     n(temp) = zeros(size(n(temp)));
    
     % Graphics
     plot(x,n);
     xlabel('location (x)'); ylabel('population density [ n_{t} (x) ]'); 
     title(['t = ',num2str(j)]); 
     axis([xmin xmax ymin ymax]);
     drawnow;

  end