Isocline and step function

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mks
mks on 1 Aug 2023
This question was flagged by Dyuman Joshi
% 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

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