x = 0:0.01:1;
beta = 1;
y1 = (tanh(beta/2)+tanh(beta*(x-0.5)))/2/tanh(beta/2);
plot(x,y1);
hold on;
beta = 2;
y2 = (tanh(beta/2)+tanh(beta*(x-0.5)))/2/tanh(beta/2);
plot(x,y2);
hold on;
beta = 4;
y3 = (tanh(beta/2)+tanh(beta*(x-0.5)))/2/tanh(beta/2);
plot(x,y3);
hold on;
beta = 8;
y4 = (tanh(beta/2)+tanh(beta*(x-0.5)))/2/tanh(beta/2);
plot(x,y4);
hold on;
beta = 16;
y5 = (tanh(beta/2)+tanh(beta*(x-0.5)))/2/tanh(beta/2);
plot(x,y5);
hold on;
ylabel({'$\overline{\rho}_{e}$'},'Interpreter','latex');
xlabel({'$\widetilde{\rho}_{e}$'},'Interpreter','latex');