function func = surfcdemo ( nu, nv );
% SurfCDemo
%
% This m-file is part of the material of the lecture
%   Scientific Computing and Software Tools
% at the Math Department of Halle University, Germany.
% Summer term 2004
%
% Author :      Prof. Dr. M. Arnold, arnold@mathematik.uni-halle.de
% Version of :  Apr 6, 2004
%
% Demonstration of Matlab command surfc, Remark 1.3
%
% Parameters
%   nu     (input)  : number of mesh points, u-direction
%   nv     (input)  : number of mesh points, v-direction
%
% Example
%   surfcdemo ( 80, 120 );

% -> problem parameters Lotka-Volterra, see lotkademo.m
alpha = 0.01;
beta  = 0.02;

umin =   5;
umax = 160;
vmin =   5;
vmax = 320;

% -> generate mesh data
u = linspace ( umin, umax, nu );
v = linspace ( vmin, vmax, nv );

[ U, V ] = meshgrid ( u, v );

% -> generate data of the invariant
C = - log ( U ) - log ( V ) + beta*U + alpha*V;

% -> plot
surfc ( U, V, C );
title ( 'Lotka-Volterra  \alpha = 0.01,  \beta = 0.02'  );
xlabel ( 'u' );   ylabel ( 'v' );   zlabel ( 'Invariante' );




