I want to plot Isocline i.e want plot (x,y) when system contains step function .

% Parameters
r =0.1; % Define the value of r
k = 50; % Define the value of k
a =0.01; % Define the value of a
e = 0.5; % Define the value of e
m = 0.05; % Define the value of m
F = 1; % Define the value of F
%s =0.1; % Define the value of s
w = 0.1; % Define the value of w
b = 0.001; % Define the value of b
M = 50; % Define the value of M
s =0.1; % Define the value of sx
% Initial conditions
x0 =2; % Define the initial value of x
y0 =1; % Define the initial value of y
initial_conditions = [x0; y0];
% Time span for simulation
tspan = [0, 100]; % Define the time span (e.g., [0, 10])
% Solve the system of differential equations
[t, y] = ode45(@(t, y) kkk(t, y, r, k, a, e, m, F, s, w, b, M, x), tspan, initial_conditions);

Unrecognized function or variable 'x'.

Error in solution>@(t,y)kkk(t,y,r,k,a,e,m,F,s,w,b,M,x) (line 20)
[t, y] = ode45(@(t, y) kkk(t, y, r, k, a, e, m, F, s, w, b, M, x), tspan, initial_conditions);

Error in odearguments (line 92)
f0 = ode(t0,y0,args{:}); % ODE15I sets args{1} to yp0.

Error in ode45 (line 107)
odearguments(odeIsFuncHandle,odeTreatAsMFile, solver_name, ode, tspan, y0, options, varargin);

% Extract the solution
x_sol = y(:, 1);
y_sol = y(:, 2);
function dydt = kkk(t,x,y, r, k, a, e, m, F, s, w, b, M)
x = y(1);
u = isocline_input(x, F, s, w, b, M);
dxdt = r * x * (1 - x / k) - a * x * y / (1 + q * u * M);
dydt = (e * a * x * y) / (1 + q * u * M) - m * y;
dydt = [dxdt; dydt];
end
function u = isocline_input(x, F,w, b, M, s)
pi0 = (w * F) / (s * (w + b * M));
pi1 = F * (w + b * M) / (s * w);
if x <= pi0
    u = 0;
elseif x >= pi1
    u = 1;
else
    u = (s*x) / (s*x + F) + w * (s*x - F) / (b * (s*x + F) * M);
end
end

I want to plot (x,y) where is my fault please help

[Walter Roberson]

What is the difference between this and https://www.mathworks.com/matlabcentral/answers/2002887-i-want-to-isocline-induced-step-function?s_tid=srchtitle ?

[Walter Roberson]

[t, y] = ode45(@(t, y) kkk(t, y, r, k, a, e, m, F, s, w, b, M, x), tspan, initial_conditions);
function dydt = kkk(t,x,y, r, k, a, e, m, F, s, w, b, M)

It is confusing that you are passing x as the last parameter in your call, but your function expects to receive x as the second parameter.

[mks]

sorry x is not parameter here x is prey population and y is predator population

step function split by the value of x

[mks]

There is few difference and code is not running and please help me

[Walter Roberson]

If you have equations that calculate the derivatives of the prey population and the derivatives of the predator population, then they must be combined into a single state vector instead of being separate variables

[t, y] = ode45(@(t, state) kkk(t, state, r, k, a, e, m, F, s, w, b, M), tspan, initial_conditions)
function dxydt = kkk(t, state, r, k, a, e, m, F, s, w, b, M)
   x = state(1);
   y = state(2);
   ....
   dxydt = zeros(size(state));
   dxydt(1) = ...
   dxdyt(2) = ...
end

[mks]

% Parameters
r =0.1; % Define the value of r
k = 50; % Define the value of k
a =0.01; % Define the value of a
e = 0.5; % Define the value of e
m = 0.05; % Define the value of m
F = 1; % Define the value of F
%s =0.1; % Define the value of s
w = 0.1; % Define the value of w
b = 0.001; % Define the value of b
M = 50; % Define the value of M
s =0.1; % Define the value of sx

% Initial conditions
x0 =2; % Define the initial value of x
y0 =1; % Define the initial value of y
initial_conditions = [x0; y0];

% Time span for simulation
tspan = [0, 100]; % Define the time span (e.g., [0, 10])

% Solve the system of differential equations
[t, y] = ode45(@(t, state) kkk(t,state,r, k, a, e, m, F, s, w, b, M), tspan, initial_conditions);
x = state(1); y = state(2); 

% [t, y] = ode45(@(t, state) kkk(t, state, r, k, a, e, m, F, s, w, b, M),
% Extract the solution
x_sol = y(:, 1);
y_sol = y(:, 2);


function dydt = kkk(t,x,y, r, k, a, e, m, F, s, w, b, M)
x = y(1);
u = isocline_input(x, F, s, w, b, M);

dxdt = r * x * (1 - x / k) - a * x * y / (1 + q * u * M);
dydt = (e * a * x * y) / (1 + q * u * M) - m * y;
dydt = [dxdt; dydt];
end

function u = isocline_input(x, F,w, b, M, s)
pi0 = (w * F) / (s * (w + b * M));
pi1 = F * (w + b * M) / (s * w);

if x <= pi0
    u = 0;
elseif x >= pi1
    u = 1;
else
    u = (s*x) / (s*x + F) + w * (s*x - F) / (b * (s*x + F) * M);
end
end

sir, please see and help . I have tired

[mks]

please solve my probelm .I can not understand the error.

Answer 1

[Walter Roberson]

Your code needs q but you did not define any q, so I had to pick SOME value for q in order to debug.

You need to change the definition of q to something appropriate for your situation.

% Parameters
r =0.1; % Define the value of r
k = 50; % Define the value of k
a =0.01; % Define the value of a
e = 0.5; % Define the value of e
m = 0.05; % Define the value of m
F = 1; % Define the value of F
%s =0.1; % Define the value of s
w = 0.1; % Define the value of w
b = 0.001; % Define the value of b
M = 50; % Define the value of M
s =0.1; % Define the value of sx

%user's code does not define any q, but we need a value of it to debug
rng(655321)
q = rand() * 10       %define the value of q

q = 3.1402

% Initial conditions
x0 =2; % Define the initial value of x
y0 =1; % Define the initial value of y
initial_conditions = [x0; y0];

% Time span for simulation
tspan = [0, 100]; % Define the time span (e.g., [0, 10])

% Solve the system of differential equations
[t, y] = ode45(@(t, state) kkk(t, state, r, k, a, e, m, F, s, w, b, M, q), tspan, initial_conditions);

% Extract the solution
x_sol = y(:, 1);
y_sol = y(:, 2);

subplot(2,1,1); plot(t, x_sol); title('x');
subplot(2,1,2); plot(t, y_sol); title('y');

function dydt = kkk(t, state, r, k, a, e, m, F, s, w, b, M, q)
    x = state(1);
    y = state(2);
    u = isocline_input(x, F, s, w, b, M);
    
    dxdt = r * x * (1 - x / k) - a * x * y / (1 + q * u * M);
    dydt = (e * a * x * y) / (1 + q * u * M) - m * y;
    dydt = [dxdt; dydt];
end

function u = isocline_input(x, F, s, w, b, M)
    pi0 = (w * F) / (s * (w + b * M));
    pi1 = F * (w + b * M) / (s * w);
    
    if x <= pi0
        u = 0;
    elseif x >= pi1
        u = 1;
    else
        u = (s*x) / (s*x + F) + w * (s*x - F) / (b * (s*x + F) * M);
    end
end

[mks]

why are you maintion 'u' as isclinefun

Here u is an adaptive step function .Which is contained in our system. My paper says that

1.when q=0.02,F=1

x=0:50;y=0:20,The system has an equilibrium point.

2.when q=0.03,F=1.714

x=0:50;y=0:20,The system has three equilibrium points

3.when q=0.02,F=1.8

x=0:50;y=0:20,The system has an equilibrium point.

4.when q=0.02,F=1.37

x=0:50;y=0:20,The system has an equilibrium point

5.

when q=0.03,F=1.613

x=0:50;y=0:20,The system have two equilibrium points

Give me suggetions how i can draw this plot(x,y)

I actually find the equilibrium points for choice of q and alternative resource F

[Sam Chak]

Hi @MD KAUSAR SK

What exactly do you mean by "u is an Adaptive Step Function"? I tried searching the keywords, but they seem unrelated. A closer look shows that depends on the parameter that is defined through 3 static (non-dynamic) If-Else statements, making it looks like the scheduling approach.