You have one weird data and script to visualize but here is one way
clear all
warning off % you had references to F:/ folder in the mat file
format long
set(0,'DefaultAxesFontSize',20);
figure;
load('H_LC(2).mat');
dim=2; %number of variables of my system which are x and y
MMM=max(x(1:dim:end-2,:));
plot(x(end,:),MMM,'r', 'LineWidth',2); % RED
hold on
plot(x(end,[1 2]),MMM(1:2),'b', 'LineWidth',2); % BLUE LINE HERE
load('H_LC(2).mat');
M=min(x(1:dim:end-2,:)); % end-2 excludes the parameter and the period from the continuation variable x
plot(x(end,:),M,'r', 'LineWidth',2);
hold on
xlabel('$aa$','FontSize',20,'interpreter','latex','FontWeight','normal','Color','k');
ylabel('$bb$','FontSize',20,'interpreter','latex','FontWeight','normal','Color','k');
hold on
plot(x(end,[1 2]),M(1:2),'b', 'LineWidth',2); % BLUE LINE HERE
axis([.1142595 .1142604 .5295 .5297]);
