图片1代码
function dxdt = taihu(t, x, f_m,psi, c_prime, xi, pi, pi_prime, f_p1, f_prime)
dxdt = zeros(2, 1); % 初始化导数向量
% 计算状态变量的导数
dxdt(1) = x(1) * (1 – x(1)) * (((x(2)*(psi-1)-psi)*f_m)-c_prime+(1-x(2))*xi*(pi_prime-pi)); % 第一个状态变量的导数
dxdt(2) = x(2) * (1 – x(2)) * ((x(1)-1)*f_p1-x(1)*(1-xi)*(pi_prime-pi)+x(1)*psi*f_prime);
end
% 定义时间范围
tspan = [0, 20];
% 定义初始状态向量
x0_1 = [0.2, 0.8];
x0_2 = [0.4, 0.6];
x0_3 = [0.6, 0.4];
x0_4 = [0.8, 0.2];
% 定义参数
psi = 0.5;
f_p1 = 30;
c_prime = 100;
xi = 0.9;
f_m = 100;
f_prime = 40;
pi = 1189;
pi_prime = 1437;
% 求解微分方程
[t1, x1] = ode45(@(t, x) taihu(t, x, f_m,psi, c_prime, xi, pi, pi_prime, f_p1, f_prime), tspan, x0_1);
[t2, x2] = ode45(@(t, x) taihu(t, x, f_m,psi, c_prime, xi, pi, pi_prime, f_p1, f_prime), tspan, x0_2);
[t3, x3] = ode45(@(t, x) taihu(t, x, f_m,psi, c_prime, xi, pi, pi_prime, f_p1, f_prime), tspan, x0_3);
[t4, x4] = ode45(@(t, x) taihu(t, x, f_m,psi, c_prime, xi, pi, pi_prime, f_p1, f_prime), tspan, x0_4);
figure
plot(x1(:,1), x1(:,2), ‘ko-‘, ‘MarkerFaceColor’, ‘#D95319’, ‘MarkerSize’, 8, ‘MarkerEdgeColor’, ‘k’)
hold on;
plot(x2(:,1), x2(:,2), ‘kv-‘, ‘MarkerFaceColor’, ‘#FCA03D’, ‘MarkerSize’, 8, ‘MarkerEdgeColor’, ‘k’)
plot(x3(:,1), x3(:,2), ‘kd-‘, ‘MarkerFaceColor’, ‘#3DD2FC’, ‘MarkerSize’, 8, ‘MarkerEdgeColor’, ‘k’)
plot(x4(:,1), x4(:,2), ‘ks-‘, ‘MarkerFaceColor’, ‘#00552E’, ‘MarkerSize’, 8, ‘MarkerEdgeColor’, ‘k’);
xlabel(‘x’);
ylabel(‘y’);
title(‘演化’);
legend(‘x0=[0.2, 0.8]’, ‘x0=[0.4, 0.6]’, ‘x0=[0.6, 0.4]’, ‘x0=[0.8,0.2]’);
xlim([0, 1]);
ylim([0, 1]);
图片14
% 定义时间范围
tspan = [0, 1.2];
% 定义初始状态向量
x0_1 = [0.5, 0.5];
% 定义参数
f_p1 = 30;
c_prime = 100;
xi = 0.9;
f_m = 100;
f_prime = 50;
pi = 1189.86;
pi_prime = 1437.28;
% 定义 psi_vl 的值
psi_vl = [0.05, 0.35, 0.65, 0.95];
% 定义每个 psi 对应的标记类型和颜色
marker_types = {‘o’, ‘^’, ‘d’, ‘s’};
marker_colors = {‘#D95319’, ‘#FCA03D’, ‘#3DD2FC’, ‘#00552E’};
figure;
hold on;
% 循环迭代每个 psi 值
for i = 1:length(psi_vl)
% 当前的 psi 值
psi = psi_vl(i);
% 使用当前的 psi 值求解微分方程
[t1, x1] = ode45(@(t, x) taihu(t, x, f_m, psi, c_prime, xi, pi, pi_prime, f_p1, f_prime), tspan ,x0_1);
% 绘制结果，使用当前标记类型和颜色，并确保标记点是实心的
plot(x1(:,1), x1(:,2), [‘-‘, marker_types{i}], ‘Color’, ‘k’, ‘MarkerSize’, 7, ‘MarkerFaceColor’, marker_colors{i}, ‘MarkerEdgeColor’, ‘k’);
end
hold off;
xlabel(‘x’);
ylabel(‘y’);
title(‘演化’);
legend(‘psi = 0.05’, ‘psi = 0.35’, ‘psi = 0.65’, ‘psi = 0.95’);
xlim([0, 1]);
ylim([0, 1]);
图片16
% 定义时间范围
tspan = [0, 20];
% 定义初始状态向量
x0_1 = [0.5, 0.5];
% 定义参数
psi=0.5;
f_p1 = 30;
c_prime = 100;
xi = 0.9;
f_m = 100;
f_prime = 50;
% 定义 psi_vl 的值
pi_vl = [1039.859375,1189.86,1339.859375,1489.859375];
pi_prim = [1249.7802734375,1437.28,1624.7802734375,1812.2802734375];
% 定义每个 psi 对应的标记类型和颜色
marker_types = {‘o’, ‘^’, ‘d’, ‘s’};
marker_colors = {‘#D95319’, ‘#FCA03D’, ‘#3DD2FC’, ‘#00552E’};
figure;
hold on;
% 循环迭代每个 psi 值
for i = 1:length(pi_vl)
% 当前的 psi 值
pi = pi_vl(i);
pi_prime=pi_prim(i);
% 使用当前的 psi 值求解微分方程
[t1, x1] = ode45(@(t, x) taihu(t, x, f_m, psi, c_prime, xi, pi, pi_prime, f_p1, f_prime), tspan ,x0_1);
% 绘制结果，使用当前标记类型和颜色，并确保标记点是实心的
plot(x1(:,1), x1(:,2),[‘-‘, marker_types{i}], ‘Color’, ‘k’, ‘MarkerSize’, 6, ‘MarkerFaceColor’, marker_colors{i}, ‘MarkerEdgeColor’, ‘k’);
end
hold off;
xlabel(‘x’);
ylabel(‘y’);
title(‘演化’);
legend(‘{\beta=0}’, ‘{\beta=20}’, ‘{\beta=40}’, ‘{\beta=60}’,’latex’);
xlim([0, 1]);