basin for attraction of multiple attractor

Question

Ajay 2023-9-2

0
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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2016001-basin-for-attraction-of-multiple-attractor

评论： Kalyanashis 2024-2-9

how can basin of attraction of multiple attractor for a three dim system can plot as i am just able to plot only for one attractor and don't have an idea how to plotbasin of attraction for multiple attractor.

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Ajay 2023-9-2

编辑：Walter Roberson 2023-10-23

在 MATLAB Online 中打开

% Lorenz system parameters

clear all;

clc;

alpha = 10;

row= 28;

beta = 8/3;

% Define the Lorenz system equations

lorenz = @(t, xyz) [alpha * (xyz(2) - xyz(1));

xyz(1) * (row - xyz(3)) - xyz(2);

xyz(1) * xyz(2) - beta * xyz(3)];

% Define the attractor coordinates (you can adjust )

attractor = [0, 0, 0];

% Define the time span for simulation

tspan = [0, 5];

% Number of points for the grid

num_points = 20;

% Create a grid of initial conditions for x, y, and z

x_range = linspace(-30, 30, num_points);

y_range = linspace(-30, 30, num_points);

z_range = linspace(0, 50, num_points);

[X, Y, Z] = meshgrid(x_range, y_range, z_range);

% Create a colormap for plotting

colormap([1 0 0; 0 0 1]); % Red and blue

% Initialize a matrix to store basin of attraction information

basin = zeros(size(X));

% Loop through all initial conditions

for i = 1:numel(X)

x0 = X(i);

y0 = Y(i);

z0 = Z(i);

% Simulate the Lorenz system from (x0, y0, z0)

[~, sol] = ode45(lorenz, tspan, [x0, y0, z0]);

% Check if the trajectory converges to the attractor

if norm(sol(end, :) - attractor) < 1.0

% Mark this point as part of the basin of attraction

basin(i) = 1;

end

% Plot the basin of attraction

figure;

slice(X, Y, Z, basin, [], [], []);

xlabel('X');

ylabel('Y');

zlabel('Z');

title('Basin of Attraction for Lorenz Attractor');

colorbar;

axis tight;

Kalyanashis 2023-10-18

This program will give a blank figure

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Answer 1

Varun 2023-9-11

1
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2016001-basin-for-attraction-of-multiple-attractor#answer_1306996

编辑：Varun 2023-9-11

在 MATLAB Online 中打开

Hi Ajay,

I understand that you are currently able to plot basin of attraction for one attractor, but you want to plot basin of attraction for multiple attractions.

To achieve this, you can modify the existing code by introducing an array of attractor coordinates. You define an array “attractor” that holds the coordinates of all the attractors you want to consider. .

Then, during the loop that checks if the trajectory converges to an attractor, you iterate over each attractor in the attractors array and break the loop as soon as a match is found. The value assigned to “basin(i)” represents the index of the attractor that the point converges to.

Please refer the updated code:

% Lorenz system parameters
clear all;
clc;
alpha = 10;
row= 28;
beta = 8/3;
% Define the Lorenz system equations
lorenz = @(t, xyz) [alpha * (xyz(2) - xyz(1));
                   xyz(1) * (row - xyz(3)) - xyz(2);
                   xyz(1) * xyz(2) - beta * xyz(3)];
% Define the attractor coordinates
attractors = [  % Add the coordinates of your attractors here
    0, 0, 0;
    10, -10, 20;
    -10, 10, 30
];
% Define the time span for simulation
tspan = [0, 5];
% Number of points for the grid
num_points = 20;
% Create a grid of initial conditions for x, y, and z
x_range = linspace(-30, 30, num_points);
y_range = linspace(-30, 30, num_points);
z_range = linspace(0, 50, num_points);
[X, Y, Z] = meshgrid(x_range, y_range, z_range);
% Create a colormap for plotting
colormap([1 0 0; 0 0 1]);  % Red and blue
% Initialize a matrix to store basin of attraction information
basin = zeros(size(X));
% Loop through all initial conditions
for i = 1:numel(X)
    x0 = X(i);
    y0 = Y(i);
    z0 = Z(i);
    
    % Simulate the Lorenz system from (x0, y0, z0)
    [~, sol] = ode45(lorenz, tspan, [x0, y0, z0]);
    
    % Check if the trajectory converges to any of the attractors
    for j = 1:size(attractors, 1)
        if norm(sol(end, :) - attractors(j, :)) < 1.0
            % Mark this point as part of the basin of attraction
            basin(i) = j;  % Use the index of the attractor as the value
            break;  % Break the loop if a match is found
        end
    end
end
% Plot the basin of attraction
figure;
slice(X, Y, Z, basin, [], [], []);
xlabel('X');
ylabel('Y');
zlabel('Z');
title('Basin of Attraction for Lorenz Attractors');
colorbar;
axis tight;