How to use the function lhsdesign in hypercube parameter search

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Zhukun Wang 2021-3-29

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/787164-how-to-use-the-function-lhsdesign-in-hypercube-parameter-search

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

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?