function lotka_test ( )

%*****************************************************************************80
%
%% lotka_test() tests ode_midpoint_system on the lotka problem.
%
%  Licensing:
%
%    This code is distributed under the MIT license.
%
%  Modified:
%
%    20 September 2019
%
%  Author:
%
%    John Burkardt
%
  fprintf ( 1, '\n' );
  fprintf ( 1, 'lotka_test:\n' );
  fprintf ( 1, '  Test ode_midpoint_system on the lotka problem.\n' );

  a = 0.0;
  b = 250;
  ya = [ 4.0, 2.0 ];
  n = 2000;
  [ xp, yp ] = ode_midpoint_system ( 'lotka(x,y)', a, b, ya, n );

  plot ( yp(1,:), yp(2,:), 'bo', 'markersize', 5 );
  grid ( 'on' );
  axis ( 'equal' );
  xlabel ( '<-- U -->' );
  ylabel ( '<-- V -->' );
  label = sprintf ( 'Lotka phase plot using %d steps', n );
  title ( label );
  filename = sprintf ( 'lotka.png', n );
  print ( '-dpng', filename );
  pause ( 5 );

  return
end

