plotting a periodic system of nonlinear differential equations

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Chinwendu Madubueze 2021-10-8

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https://ww2.mathworks.cn/matlabcentral/answers/1469686-plotting-a-periodic-system-of-nonlinear-differential-equations

I am ty to plot the solution of a system of differential equation that contains two periodic functions. I expect the plot to be periodic but is showing different plot that is the same when it is not periodic system.

These are my codes of the plot.

Thank you

function dS = lassaDFG(t, x)
        xdot = zeros(7,1);
       LambdH=10000;K=2000;beta1=0.221;beta4=0.052;beta3=0.206;beta2=0.0296;beta5=0.0637;omega=0.00578;d1=0.003;
       muH=0.00005;muR=0.003;sigma=0.528;deltaH=0.485;gamma=0.024;alpha1=0.04;alpha2=0.03;LambdR=0.172;muV=0.05;a=1;
       b=0.1;gamma1=0.31;p=365.5;
        
        N=x(1)+x(2)+x(3)+x(4); M=x(5)+x(6);K1=K*(1-gamma1*sin((2*pi*(t+b)/p)));LambdR1=LambdR*(a+cos((2*pi*(t+b)/p)));
        xdot(1)=LambdH + omega*x(4)-(beta1*x(3)+beta2*x(6))*x(1)/N -beta3*x(7)*x(1)- muH*x(1); 
        xdot(2)= x(1)*(beta1*x(3)+beta2*x(6))/N + beta3*x(7)*x(1)- sigma*x(2)-muH*x(2);
        xdot(3)=sigma*x(2)-(muH+deltaH+gamma)*x(3);
        xdot(4)=gamma*x(3)-(omega+muH)*x(4);
        xdot(5)=LambdR1*(1-M/K1)*M -beta4*x(5)*x(6)/M - beta5*x(5)*x(7)- (d1+muR)*x(5);
        xdot(6)=beta4*x(5)*x(6)/M+ beta5*x(5)*x(7)-(muR+d1)*x(6);
        xdot(7)=alpha1*x(6)+alpha2*x(3)- muV*x(7);
       dS = xdot;
       
       [t,v] = ode45 (@lassaDFG,[0 100],[2000 40 49 20 5000 100 150]);
        plot (t,v (:,3),'b','LineWidth',1.5);
        xlabel ('Time (Days)'); ylabel ('Miracidia') ;