File:Lotka Volterra Phase plane 100.svg
![File:Lotka Volterra Phase plane 100.svg](https://upload.wikimedia.org/wikipedia/commons/thumb/1/18/Lotka_Volterra_Phase_plane_100.svg/512px-Lotka_Volterra_Phase_plane_100.svg.png?20101101212316)
Original file (SVG file, nominally 512 × 384 pixels, file size: 526 KB)
Captions
Captions
Summary
[edit]DescriptionLotka Volterra Phase plane 100.svg |
English: This figure shows the Prey-Predator dynamics
as described by the level curves of the conserved quantity H, α *x + y − log(x^α*y) = H α is a constant x represents the quantity of preys y represents the quantity of predator For more details, the reader can refer to Mathematical Biology: I. An Introduction, J.D. Murray |
Date | |
Source | Own work |
Author | Guillaume Jacquenot |
SVG development InfoField | |
Source code InfoField | MATLAB codefunction Lotka_Volterra_Phase_plane(alpha)
% This function shows the Prey-Predator dynamics
% as described by the level curves of the conserved quantity H,
% α *x + y − log(x^α*y) = H
% α is a constant
% x represents the quantity of preys
% y represents the quantity of predator
%
%
% For more details, the reader can refer to
% Mathematical Biology: I. An Introduction,
% J.D. Murray
%
if nargin == 0
alpha = 1;
end
%% Define step size and axis range
stepsize_c = 0.01;
stepsize_q = 0.5;
max_u_size = 8;
max_v_size = 8;
%% Generate the grid points and compute the Lotka Volterra function
[Xc,Yc]=meshgrid(0:stepsize_c:max_u_size,0:stepsize_c:max_v_size);
Zc = log(alpha*Xc+Yc-log(Xc.^alpha.*Yc));
%% Create graphic
figure;
box on
hold on
grid on
axis equal
axis([0 max_u_size 0 max_v_size]);
contour(Xc,Yc,Zc,0.5:0.1:4);
% [C,Hc] = contour(Xc,Yc,Zc,0.5:0.1:4);
% RR = get(Hc,'Children');
% for i=1:numel(RR)
% XD = get(RR(i),'XData');
% YD = get(RR(i),'YData');
% [XD,YD]
% end
% [PXc,PYc] = gradient(Zc,stepsize_c,stepsize_c);
%
% selectX = ismember(0:stepsize_c:max_u_size,...
% stepsize_q:stepsize_q:max_u_size-stepsize_q);
% selectY = ismember(0:stepsize_c:max_v_size,...
% stepsize_q:stepsize_q:max_v_size-stepsize_q);
% [Xq,Yq]=meshgrid(stepsize_q:stepsize_q:max_u_size-stepsize_q,...
% stepsize_q:stepsize_q:max_v_size-stepsize_q);
% quiver(Xq,Yq,PXc(selectX,selectY),PYc(selectX,selectY));
%% Create label and title
xlabel('x')
ylabel('y ','Rotation',0);
title(['\alpha = ' num2str(alpha)],'Interpreter','Tex');
filename = [mfilename '_' sprintf('%03d',floor(100*alpha))];
saveas(gcf,filename,'png');
plot2svg([filename '.svg']);
|
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Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled GNU Free Documentation License.http://www.gnu.org/copyleft/fdl.htmlGFDLGNU Free Documentation Licensetruetrue |
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Date/Time | Thumbnail | Dimensions | User | Comment | |
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current | 21:23, 1 November 2010 | ![]() | 512 × 384 (526 KB) | Gjacquenot (talk | contribs) | {{Information |Description={{en|1=This figure shows the Prey-Predator dynamics as described by the level curves of the conserved quantity H, α *x + y − log(x^α*y) = H α is a constant x represents the quantity of preys y represents the quantity of pr |
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Image title | Matlab Figure Converted by PLOT2SVG written by Juerg Schwizer -- Generated by Guillaume Jacquenot -- 2010-11-01 |
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