How to use the function lhsdesign in hypercube parameter search
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function Math462HW4Q3code
X=lhsdesign(7,5,xvector);
tspan=[1:1:100];
Cm=1;
Vm=1;
m=1;
n=1;
h=1;
gNa=100:130;
gK=12:50;
gl=;
VNa=;
VK=;
Vl=;
I0=;
vector=[Vm,m,n,h];
an=(1/100)*(Vm+10)/(exp((10+Vm)/10)-1);
am=(1/10)*(Vm+25)/(exp((25+Vm)/10)-1);
ah=(7/100)*exp(Vm/20);
bn=(1/8)*exp(Vm/80);
bm=4*exp(Vm/18);
bh=1/(exp((30+Vm)/10)+1);
%Apply the function ode45
[t,x]=ode45(@(t,vector)derivativefunc(gNa,gK,gl,VNa,VK,Vl,I0), tspan,vector);
plot(t,x,'bl'); %Plot solutions out.
xlabel('time');
ylabel('our solution');
title('Solution of logistic equation');
%We are trying to express xdot which is the given equation in the question.
function xdot=derivativefunc(~,paras,gNa,gK,gl,VNa,VK,Vl,I0)
Vm=paras(1);
m=paras(2);
n=paras(3);
h=paras(4);
CmVmdot=I0-gK*n^4*(Vm-VK)-gNa*m^3*h(Vm-VNa)-gl*(Vm-Vl);
ndot=an*(1-n)-bn*n;
mdot=am*(1-m)-bm*m;
hdot=ah(1-h)-bh*h;
xdot=[CmVmdot;ndot;mdot;hdot];
end
end
In this code, I am trying to use ODE45 to simulate the model but with tentative parameter values. I am wondering how to perform the hypercube parameter search by using lhsdesign. Here, my parameters are gNa,gK,gl,VNa,VK,Vl,I0 where gNa values can be between [100 130], gK can be between[12 50], gl can be between [0.1 2], VNa between [55 120], Vk between [-30 -5], Vl is between [5 20], I0 between [0 45]. I want to use lhsdesign to test how are values 7 parameters can lead to different result by setting them in values from these intervals and then simulate the system. How could I do that?
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