error in ode45. I have declared the vector to be 3x1 but it only reads it as 2x1.

for kpm=27:1:30

tspan = 0:30;

yo=[0.01 0.05 0.179];

[t,y]=ode45(@newwaykumar2004,tspan,yo);

end

function dydt=newwaykumar2004(t,y)

kp=3;

global kpm;

kmp = 25;

klm = 15;

kl = 1;

theta=1;

w=0.5;

function qz=f(m)

qz=1+tanh((m-theta)/w);

end

dpdt=kp*y(1)*(1-y(1))-kpm*y(1)*y(2);

dmdt=(kmp*y(1)+y(3))*y(2)*(1-y(2))-y(2);

dIdt=klm*f(y(2))-kl*y(3);

dydt=[dpdt;dmdt;dIdt];

end

Answer 1

[Dyuman Joshi]

You get the error because dpdt is empty, and thus dydt is 2x1.

Instead of defining kpm as global, it is better to define it as an input to the ode function. MathWorks recommends to avoid the use of global as well

Note that in your code t and y are being overwritten in each iteration of the loop. I have modified t and y to store the result of each iteration

%Defining constant value variables outside the loop
kpm = 27:1:30;
tspan = 0:30;
yo=[0.01 0.05 0.179];

n = numel(kpm);
nt = numel(tspan);
nyo = numel(yo);

%Pre-allocation
t = zeros(nt,n);
y = zeros(nt,nyo,n);

%Ode Loop
for k = 1:n
[t(:,k),y(:,:,k)]=ode45(@(t,y) newwaykumar2004(t,y,kpm(k)), tspan, yo);
end

%t(:,k) represents a solution corresponding to kpm(k)
t

t = 31×4

0 0 0 0 1 1 1 1 2 2 2 2 3 3 3 3 4 4 4 4 5 5 5 5 6 6 6 6 7 7 7 7 8 8 8 8 9 9 9 9

%y(:,:,k) represents a solution corresponding to kpm(k)
y

y = 
y(:,:,1) =

    0.0100    0.0500    0.1790
    0.0561    0.0489    0.4715
    0.0591    0.1776    0.7081
    0.0044    0.2052    1.0206
    0.0005    0.1854    1.0996
    0.0001    0.1686    1.0806
    0.0000    0.1508    1.0303
    0.0000    0.1309    0.9670
    0.0000    0.1094    0.8979
    0.0000    0.0876    0.8284
    0.0000    0.0672    0.7634
    0.0001    0.0494    0.7067
    0.0007    0.0352    0.6604
    0.0062    0.0256    0.6254
    0.0580    0.0305    0.6074
    0.0759    0.2007    0.7492
    0.0023    0.2373    1.1380
    0.0001    0.2241    1.2470
    0.0000    0.2198    1.2647
    0.0000    0.2172    1.2619
   -0.0000    0.2142    1.2526
   -0.0000    0.2103    1.2386
    0.0000    0.2049    1.2194
   -0.0000    0.1976    1.1938
    0.0000    0.1881    1.1602
    0.0000    0.1757    1.1176
    0.0000    0.1603    1.0652
    0.0000    0.1420    1.0041
    0.0000    0.1214    0.9359
    0.0000    0.0995    0.8667
    0.0000    0.0781    0.7985


y(:,:,2) =

    0.0100    0.0500    0.1790
    0.0540    0.0481    0.4711
    0.0586    0.1675    0.6959
    0.0048    0.1943    0.9850
    0.0006    0.1727    1.0543
    0.0001    0.1533    1.0280
    0.0000    0.1331    0.9714
    0.0000    0.1116    0.9043
    0.0000    0.0898    0.8350
    0.0001    0.0692    0.7696
    0.0003    0.0512    0.7121
    0.0016    0.0370    0.6651
    0.0131    0.0291    0.6308
    0.0879    0.0538    0.6258
    0.0291    0.2158    0.8615
    0.0013    0.2077    1.1050
    0.0001    0.1911    1.1424
    0.0000    0.1772    1.1161
    0.0000    0.1616    1.0681
    0.0000    0.1434    1.0083
    0.0000    0.1228    0.9411
    0.0000    0.1010    0.8711
    0.0000    0.0795    0.8027
    0.0000    0.0600    0.7402
    0.0000    0.0434    0.6877
    0.0000    0.0303    0.6451
    0.0004    0.0206    0.6127
    0.0048    0.0143    0.5895
    0.0617    0.0163    0.5771
    0.0989    0.2203    0.7202
    0.0012    0.2602    1.2164


y(:,:,3) =

    0.0100    0.0500    0.1790
    0.0521    0.0474    0.4707
    0.0589    0.1581    0.6842
    0.0053    0.1853    0.9552
    0.0007    0.1627    1.0185
    0.0002    0.1416    0.9882
    0.0001    0.1202    0.9288
    0.0001    0.0983    0.8610
    0.0001    0.0770    0.7941
    0.0003    0.0580    0.7335
    0.0013    0.0424    0.6825
    0.0092    0.0325    0.6439
    0.0625    0.0441    0.6286
    0.0493    0.1828    0.7753
    0.0029    0.1959    1.0286
    0.0003    0.1750    1.0753
    0.0000    0.1566    1.0430
    0.0000    0.1370    0.9854
    0.0000    0.1158    0.9181
    0.0000    0.0939    0.8483
    0.0000    0.0729    0.7816
    0.0000    0.0542    0.7222
    0.0002    0.0388    0.6726
    0.0014    0.0272    0.6338
    0.0144    0.0210    0.6064
    0.1126    0.0487    0.6057
    0.0208    0.2327    0.8997
    0.0006    0.2146    1.1448
    0.0000    0.2005    1.1806
    0.0000    0.1896    1.1607
    0.0000    0.1773    1.1218


y(:,:,4) =

    0.0100    0.0500    0.1790
    0.0502    0.0467    0.4704
    0.0591    0.1494    0.6738
    0.0057    0.1771    0.9284
    0.0008    0.1537    0.9870
    0.0002    0.1316    0.9542
    0.0001    0.1096    0.8938
    0.0001    0.0878    0.8271
    0.0002    0.0675    0.7633
    0.0008    0.0501    0.7074
    0.0046    0.0373    0.6627
    0.0312    0.0359    0.6347
    0.0848    0.1121    0.6774
    0.0094    0.1901    0.9267
    0.0008    0.1688    1.0242
    0.0001    0.1477    1.0048
    0.0000    0.1266    0.9487
    0.0000    0.1047    0.8816
    0.0000    0.0831    0.8134
    0.0001    0.0631    0.7502
    0.0003    0.0461    0.6958
    0.0020    0.0331    0.6522
    0.0163    0.0266    0.6213
    0.0999    0.0596    0.6232
    0.0202    0.2071    0.8726
    0.0010    0.1896    1.0614
    0.0001    0.1696    1.0720
    0.0000    0.1511    1.0285
    0.0000    0.1311    0.9668
    0.0000    0.1095    0.8980
    0.0000    0.0877    0.8286

function dydt=newwaykumar2004(t,y,kpm)
kp=3;
kmp = 25;
klm = 15;
kl = 1;
theta=1;
w=0.5;
%function handle
f = @(m) 1+tanh((m-theta)/w);
dpdt=kp*y(1)*(1-y(1))-kpm*y(1)*y(2);
dmdt=(kmp*y(1)+y(3))*y(2)*(1-y(2))-y(2);
dIdt=klm*f(y(2))-kl*y(3);
dydt=[dpdt;dmdt;dIdt];
end

[Stephen23]

Ayush Ranjan: you should follow Dyuman Joshi's excellent advice to make KPM an input argument (and avoid GLOBAL variables). Note that the ODE45 documentation includes an example showing how to pass extra parameters to the ODE function:

https://www.mathworks.com/help/matlab/ref/ode45.html#bu3uhuk

which links in turn to this page:

https://www.mathworks.com/help/matlab/math/parameterizing-functions.html