%однопараметрический анализ
%по параметру k2
k1=1;
k1m=0.04;
k2m=0.02;
k3=10;
j1=0;
j2=0;
j3=0;
y=[0.001:0.001:0.987];
n=max(size(y));
i=1;
x(i)=(k1*(1-y(i)))./(k1+k1m+k3.*y(i));
z(i)=(1-y(i)-x(i));
k2=(k2m.*y(i)^2.*(k1+k1m+k3.*y(i)).^2+(k1+k1m+k3.*y(i)).*k1.*k3.*y(i).*(1-y(i)))./((1-y(i)).^2.*(k1m+k3.*y(i)).^2);
a11=(-1).*k1+(-1).*k1m+(-1).*k3.*y(i);
a12=(-1).*k1+(-1).*k3.*x(i);
a21=(-2).*k2.*z(i)+(-1).*k3.*y(i);
a22=(-2).*k2.*z(i)+(-2).*k2.*y(i)+(-1).*k3.*x(i);
tr(i)=a11+a22;
Det(i)=a11.*a22-a12.*a21;
if Det(i)<=0
    k2i=-1;
end
D(i)=tr(i)^2-4.*Det(i);
xh=ones(n);
yh=ones(n);
k2h=ones(n);
xsn=ones(n);
ysn=ones(n);
k2sn=ones(n);
xD=ones(n);
yD=ones(n);
k2D=ones(n);
    for i=2:n
        x(i)=(k1*(1-y(i)))./(k1+k1m+k3.*y(i));
        z(i)=(1-y(i)-x(i));
        k2(i)=(k2m.*y(i)^2.*(k1+k1m+k3.*y(i)).^2+(k1+k1m+k3.*y(i)).*k1.*k3.*y(i).*(1-y(i)))./((1-y(i)).^2.*(k1m+k3.*y(i)).^2);
        a11=(-1).*k1+(-1).*k1m+(-1).*k3.*y(i);
        a12=(-1).*k1+(-1).*k3.*x(i);
        a21=(-2).*k2(i).*z(i)+(-1).*k3.*y(i);
        a22=(-2).*k2(i).*z(i)+(-2).*k2(i).*y(i)+(-1).*k3.*x(i);
        tr(i)=a11+a22;
        Det(i)=a11.*a22-a12.*a21;
        if Det(i)<=0
            k2i=-1;
        end
        D(i)=tr(i)^2-4.*Det(i);
        if tr(i)*tr(i-1)<=0
            j1=j1+1;
            xh(j1)=x(i);
            yh(j1)=y(i);
            k2h(j1)=k2(i);
        end
        if Det(i)*Det(i-1)<=0
            j2=j2+1;
            xsn(j2)=x(i);
            ysn(j2)=y(i);
            k2sn(j2)=k2(i);
        end
        if D(i)*D(i-1)<=0
            j3=j3+1;
            xD(j3)=x(i);
            yD(j3)=y(i);
            k2D(j3)=k2(i);
        end
    end
mh=j1;
msn=j2;
mD=j3;
figure;
plot(k2(1:n),x(1:n),'black','LineWidth',2);
hold on
plot(k2(1:n),y(1:n),'b--','LineWidth',2);
hold on
plot(k2h(1:mh),xh(1:mh),'s','MarkerFaceColor','k','MarkerEdgeColor','k','MarkerSize',6);
hold on
text(7,0.92,'$$sn2$$','interpreter','latex','FontSize',12,'FontName','Times New Roman');
text(1.15,0.33,'$$sn1$$','interpreter','latex','FontSize',12,'FontName','Times New Roman');
text(3.9 ,0.95,'$$x$$','interpreter','latex','FontSize',12,'FontName','Times New Roman');
text(4.5,0.68,'$$y$$','interpreter','latex','Color','blue','FontSize',12,'FontName','Times New Roman');
plot(k2h(1:mh),yh(1:mh),'s','MarkerFaceColor','k','MarkerEdgeColor','k','MarkerSize',6);
hold on
plot(k2sn(1:msn),xsn(1:msn),'*','MarkerFaceColor','k','MarkerEdgeColor','k','MarkerSize',10);
hold on
%plot(k2sn(1:msn),ysn(1:msn),'*','MarkerFaceColor','k','MarkerEdgeColor','k','MarkerSize',10);
%hold on
title(['Dependense on Parameter ','$$ k_2$$'],'interpreter','latex','FontSize',14,'FontName','Times New Roman');
text(0.5,0.80,['$$k_{1}=$$',num2str(k1)],'interpreter','latex','FontSize',12,'FontName','Times New Roman');
text(0.5,0.75,['$$k_{-1}=$$',num2str(k1m)],'interpreter','latex','FontSize',12,'FontName','Times New Roman');
text(0.5,0.70,['$$k_{-2}=$$',num2str(k2m)],'interpreter','latex','FontSize',12,'FontName','Times New Roman');
text(0.5,0.65,['$$k_{3}=$$',num2str(k3)],'interpreter','latex','FontSize',12,'FontName','Times New Roman');
ylabel('$$x,y $$','position',[-0.8 0.6],'interpreter','latex','fontsize',14,'rotation',0,'FontName','Times New Roman');
xlabel('$$k_2$$','interpreter','latex','fontsize',14,'rotation',0,'FontName','Times New Roman');
axis([0.0 8.0 -0.01 0.99]);
grid on
legend('x','y','saddle-node','saddle-node','Location','East','interpreter','latex','fontsize',14,'rotation',0,'FontName','Times New Roman');