Mismatched Stability check.

16 Ansichten (letzte 30 Tage)
Sabrina Garland
Sabrina Garland am 6 Jun. 2024
Kommentiert: Sabrina Garland am 7 Jun. 2024
Ran in:
I have system of two equations. I solved the model - variable k and t for each value of parameter m, between 0 and 1, and checked for stability of solution. I got all solution as stable
% Define the equations as anonymous functions
eq1 = @(vars, m) (sqrt(vars(1))/sqrt(1-vars(1))) + ((vars(2)*(2*(m^3) + vars(2)^3 - 3*vars(2)*((m+1)^2))^2)/(6*vars(2) - 3*((m-vars(2))^2)) + ((m-vars(2))^2)*(m+2*vars(2))*(m/(3*vars(2)) + 2/3)) / ((m^3 - (vars(2)^2)*(3*m+3) + 2*(vars(2)^3))*(m/(3*vars(2)) - (2*m+vars(2))/(3*(2*vars(2)-((m-vars(2))^2))) + 2/3) - vars(2)*((m-vars(2))^2)*(2*m+vars(2))*((2*m/3) + vars(2)/3));
eq2 = @(vars, m) vars(2) - ((sqrt(vars(1))/sqrt(1-vars(1)))*(((m/vars(2))+2)/3) - (1/3)*(2 + (m/vars(2)) + ((2*m+vars(2))/(((m-vars(2))^2)-2*vars(2))))) / ((sqrt(vars(1))/sqrt(1-vars(1)))*(2*(m^3) - 3*((1+m)^2)*vars(2) + vars(2)^3)/(3*(((m-vars(2))^2)-2*vars(2))) - ((2*m+vars(2))/3));
% Range of m values
m_values = linspace(0, 1, 100); % 100 values of m between 0 and 1
% Preallocate arrays to store solutions
k_solutions = zeros(size(m_values));
t_solutions = zeros(size(m_values));
stabilities = cell(size(m_values));
% Loop over m values and solve the system of equations for each m
for i = 1:length(m_values)
m = m_values(i);
% System of equations for current m
system_of_equations = @(vars) [eq1(vars, m); eq2(vars, m)];
% Initial guess for [k, t]
initial_guess = [0.75, 1.5];
% Solve the system of equations using fsolve
options = optimoptions('fsolve', 'Display', 'off');
solution = fsolve(system_of_equations, initial_guess, options);
% Store solutions if they meet the criteria
k_solution = solution(1);
t_solution = solution(2);
if k_solution > 0.5 && k_solution < 1 && t_solution > 0
k_solutions(i) = k_solution;
t_solutions(i) = t_solution;
% Compute the Jacobian matrix
J = [diff(eq1([k_solution, t_solution], m), 1, 1), diff(eq1([k_solution, t_solution], m), 1, 2);
diff(eq2([k_solution, t_solution], m), 1, 1), diff(eq2([k_solution, t_solution], m), 1, 2)]
% Calculate eigenvalues of the Jacobian matrix
eigenvalues = eig(J);
% Analyze stability
if all(real(eigenvalues) < 0)
stabilities{i} = 'Stable';
elseif all(real(eigenvalues) == 0)
% Use center manifold method for stability analysis
% Modify this part with your center manifold method implementation
stabilities{i} = 'Center manifold method';
elseif any(real(eigenvalues) > 0)
stabilities{i} = 'Unstable';
end
else
k_solutions(i) = NaN;
t_solutions(i) = NaN;
stabilities{i} = 'NaN';
end
end
J = [] J = [] J = [] J = [] J = [] J = [] J = [] J = [] J = [] J = [] J = [] J = [] J = [] J = [] J = [] J = [] J = [] J = [] J = [] J = [] J = [] J = [] J = [] J = [] J = [] J = [] J = [] J = [] J = [] J = [] J = [] J = [] J = [] J = [] J = [] J = [] J = [] J = [] J = [] J = [] J = [] J = [] J = [] J = [] J = [] J = [] J = [] J = [] J = [] J = [] J = [] J = [] J = [] J = [] J = [] J = [] J = [] J = [] J = [] J = [] J = [] J = [] J = [] J = [] J = [] J = [] J = [] J = [] J = [] J = [] J = [] J = [] J = [] J = [] J = [] J = [] J = [] J = [] J = [] J = [] J = [] J = [] J = [] J = [] J = [] J = [] J = [] J = [] J = [] J = [] J = [] J = [] J = [] J = [] J = [] J = [] J = [] J = [] J = [] J = []
% Display solutions and stabilities
disp('Solutions for each m:');
Solutions for each m:
for i = 1:length(m_values)
fprintf('m = %.2f, k = %.4f, t = %.4f, Stability = %s\n', m_values(i), k_solutions(i), t_solutions(i), stabilities{i});
end
m = 0.00, k = 0.8968, t = 1.3405, Stability = Stable m = 0.01, k = 0.8900, t = 1.3562, Stability = Stable m = 0.02, k = 0.8831, t = 1.3715, Stability = Stable m = 0.03, k = 0.8762, t = 1.3864, Stability = Stable m = 0.04, k = 0.8693, t = 1.4010, Stability = Stable m = 0.05, k = 0.8624, t = 1.4154, Stability = Stable m = 0.06, k = 0.8556, t = 1.4294, Stability = Stable m = 0.07, k = 0.8488, t = 1.4432, Stability = Stable m = 0.08, k = 0.8420, t = 1.4569, Stability = Stable m = 0.09, k = 0.8354, t = 1.4703, Stability = Stable m = 0.10, k = 0.8288, t = 1.4836, Stability = Stable m = 0.11, k = 0.8223, t = 1.4967, Stability = Stable m = 0.12, k = 0.8159, t = 1.5096, Stability = Stable m = 0.13, k = 0.8097, t = 1.5225, Stability = Stable m = 0.14, k = 0.8035, t = 1.5352, Stability = Stable m = 0.15, k = 0.7975, t = 1.5479, Stability = Stable m = 0.16, k = 0.7916, t = 1.5604, Stability = Stable m = 0.17, k = 0.7858, t = 1.5729, Stability = Stable m = 0.18, k = 0.7802, t = 1.5853, Stability = Stable m = 0.19, k = 0.7747, t = 1.5976, Stability = Stable m = 0.20, k = 0.7693, t = 1.6099, Stability = Stable m = 0.21, k = 0.7641, t = 1.6221, Stability = Stable m = 0.22, k = 0.7590, t = 1.6343, Stability = Stable m = 0.23, k = 0.7540, t = 1.6464, Stability = Stable m = 0.24, k = 0.7492, t = 1.6585, Stability = Stable m = 0.25, k = 0.7445, t = 1.6706, Stability = Stable m = 0.26, k = 0.7399, t = 1.6826, Stability = Stable m = 0.27, k = 0.7355, t = 1.6946, Stability = Stable m = 0.28, k = 0.7312, t = 1.7067, Stability = Stable m = 0.29, k = 0.7270, t = 1.7187, Stability = Stable m = 0.30, k = 0.7229, t = 1.7306, Stability = Stable m = 0.31, k = 0.7190, t = 1.7426, Stability = Stable m = 0.32, k = 0.7151, t = 1.7546, Stability = Stable m = 0.33, k = 0.7114, t = 1.7666, Stability = Stable m = 0.34, k = 0.7078, t = 1.7786, Stability = Stable m = 0.35, k = 0.7043, t = 1.7905, Stability = Stable m = 0.36, k = 0.7009, t = 1.8025, Stability = Stable m = 0.37, k = 0.6977, t = 1.8145, Stability = Stable m = 0.38, k = 0.6945, t = 1.8265, Stability = Stable m = 0.39, k = 0.6914, t = 1.8385, Stability = Stable m = 0.40, k = 0.6884, t = 1.8505, Stability = Stable m = 0.41, k = 0.6855, t = 1.8625, Stability = Stable m = 0.42, k = 0.6827, t = 1.8745, Stability = Stable m = 0.43, k = 0.6799, t = 1.8866, Stability = Stable m = 0.44, k = 0.6773, t = 1.8986, Stability = Stable m = 0.45, k = 0.6747, t = 1.9107, Stability = Stable m = 0.46, k = 0.6722, t = 1.9228, Stability = Stable m = 0.47, k = 0.6698, t = 1.9349, Stability = Stable m = 0.48, k = 0.6675, t = 1.9470, Stability = Stable m = 0.49, k = 0.6652, t = 1.9591, Stability = Stable m = 0.51, k = 0.6630, t = 1.9712, Stability = Stable m = 0.52, k = 0.6608, t = 1.9834, Stability = Stable m = 0.53, k = 0.6587, t = 1.9955, Stability = Stable m = 0.54, k = 0.6567, t = 2.0077, Stability = Stable m = 0.55, k = 0.9565, t = 0.8397, Stability = Stable m = 0.56, k = 0.9575, t = 0.8376, Stability = Stable m = 0.57, k = 0.9586, t = 0.8355, Stability = Stable m = 0.58, k = 0.9596, t = 0.8334, Stability = Stable m = 0.59, k = 0.9606, t = 0.8313, Stability = Stable m = 0.60, k = 0.9616, t = 0.8292, Stability = Stable m = 0.61, k = 0.9626, t = 0.8272, Stability = Stable m = 0.62, k = 0.9636, t = 0.8251, Stability = Stable m = 0.63, k = 0.9646, t = 0.8230, Stability = Stable m = 0.64, k = 0.9655, t = 0.8210, Stability = Stable m = 0.65, k = 0.9665, t = 0.8189, Stability = Stable m = 0.66, k = 0.9674, t = 0.8168, Stability = Stable m = 0.67, k = 0.9683, t = 0.8148, Stability = Stable m = 0.68, k = 0.9692, t = 0.8127, Stability = Stable m = 0.69, k = 0.9701, t = 0.8107, Stability = Stable m = 0.70, k = 0.9709, t = 0.8086, Stability = Stable m = 0.71, k = 0.9718, t = 0.8066, Stability = Stable m = 0.72, k = 0.9726, t = 0.8045, Stability = Stable m = 0.73, k = 0.9734, t = 0.8025, Stability = Stable m = 0.74, k = 0.9742, t = 0.8004, Stability = Stable m = 0.75, k = 0.9749, t = 0.7984, Stability = Stable m = 0.76, k = 0.9757, t = 0.7963, Stability = Stable m = 0.77, k = 0.9764, t = 0.7943, Stability = Stable m = 0.78, k = 0.9771, t = 0.7922, Stability = Stable m = 0.79, k = 0.9778, t = 0.7901, Stability = Stable m = 0.80, k = 0.9785, t = 0.7881, Stability = Stable m = 0.81, k = 0.9791, t = 0.7860, Stability = Stable m = 0.82, k = 0.9797, t = 0.7839, Stability = Stable m = 0.83, k = 0.9804, t = 0.7819, Stability = Stable m = 0.84, k = 0.9810, t = 0.7798, Stability = Stable m = 0.85, k = 0.9815, t = 0.7777, Stability = Stable m = 0.86, k = 0.9821, t = 0.7756, Stability = Stable m = 0.87, k = 0.9826, t = 0.7735, Stability = Stable m = 0.88, k = 0.9832, t = 0.7713, Stability = Stable m = 0.89, k = 0.9837, t = 0.7692, Stability = Stable m = 0.90, k = 0.9842, t = 0.7671, Stability = Stable m = 0.91, k = 0.9846, t = 0.7649, Stability = Stable m = 0.92, k = 0.9851, t = 0.7627, Stability = Stable m = 0.93, k = 0.9856, t = 0.7606, Stability = Stable m = 0.94, k = 0.9860, t = 0.7584, Stability = Stable m = 0.95, k = 0.9864, t = 0.7562, Stability = Stable m = 0.96, k = 0.9868, t = 0.7539, Stability = Stable m = 0.97, k = 0.9872, t = 0.7517, Stability = Stable m = 0.98, k = 0.9875, t = 0.7494, Stability = Stable m = 0.99, k = 0.9879, t = 0.7471, Stability = Stable m = 1.00, k = 0.9882, t = 0.7448, Stability = Stable
Now, the problem arose when I took k as an exogenous variable. When I input the value of k say 0.6945 (In above code, I got one of the solution as for m=0.38 I had k=0.6945 and t =1.82 and it was stable), I got value of t as 1.82 against m=0.38, as should be. But now this solution is unstable. Why? Can anyone help me why I am getting it stable in above code. While it is unstable in below. Please help
% Define the range of m values
m_values = linspace(0, 1, 100); % Adjust the number of points for higher accuracy
% Define the value of k
k = 0.6945;
% Initialize cell arrays to store fixed points and their stability
fixed_points = cell(length(m_values), 1);
stability_info = cell(length(m_values), 1);
% Define the function f(t, m)
f = @(t, m) real(((((k).^(1/2)).*(((m./t)+2)/3) - ((1-k).^(1/2)).*(1/3)*(2 + (m./t) + ((2*m + t)./(((m - t)^2) - 2*t)))))./((((k).^(1/2)).*(2*m^3 - 3*((1+m)^2)*t + t^3)/(3*(((m - t)^2) - 2*t)) - ((1-k).^(1/2)).*((2*m + t)/3))) - t);
% Define initial guesses for fsolve
initial_guesses = [0.1, 0.5, 1.7];
% Loop over the range of m values
for i = 1:length(m_values)
m_val = m_values(i);
% Initialize temporary storage for current m
current_fixed_points = [];
current_stability_info = [];
% Find fixed points using fsolve with multiple initial guesses
for guess = initial_guesses
options = optimset('Display', 'off', 'TolFun', 1e-10, 'TolX', 1e-10);
try
[t_val, fval, exitflag] = fsolve(@(t) f(t, m_val), guess, options);
% Check if the solution is valid and positive
if exitflag > 0 && t_val > 0 && isreal(t_val) && ~isnan(t_val) && ~isinf(t_val)
% Check if the solution is already found (to avoid duplicates)
if isempty(current_fixed_points) || all(abs(current_fixed_points - t_val) > 1e-6)
% Calculate the partial derivative (Jacobian) at the fixed point to check stability
df_dt = (f(t_val + 1e-6, m_val) - f(t_val, m_val)) / 1e-6;
% The eigenvalue in this 1D case is just df_dt
eigenvalue = df_dt;
% Check stability based on the real part of the eigenvalue
is_stable = real(eigenvalue) < 0;
% Store the fixed point and its stability
current_fixed_points = [current_fixed_points, t_val];
current_stability_info = [current_stability_info, is_stable];
end
end
catch
% Skip this initial guess if it causes an error
continue;
end
end
% Store results for current m
fixed_points{i} = current_fixed_points;
stability_info{i} = current_stability_info;
end
% Display results
for i = 1:length(m_values)
m_val = m_values(i);
t_vals = fixed_points{i};
stability_vals = stability_info{i};
for j = 1:length(t_vals)
fprintf('For m = %.2f, t = %.6f: stable = %d\n', m_val, t_vals(j), stability_vals(j));
end
end
For m = 0.00, t = 1.000000: stable = 1 For m = 0.00, t = 0.999999: stable = 1 For m = 0.00, t = 1.004399: stable = 0 For m = 0.01, t = 0.972720: stable = 1 For m = 0.02, t = 0.964445: stable = 1 For m = 0.03, t = 0.958973: stable = 1 For m = 0.04, t = 0.954766: stable = 1 For m = 0.05, t = 0.951274: stable = 1 For m = 0.05, t = 1.162613: stable = 0 For m = 0.06, t = 0.948240: stable = 1 For m = 0.07, t = 0.945521: stable = 1 For m = 0.07, t = 1.209997: stable = 0 For m = 0.08, t = 0.943032: stable = 1 For m = 0.08, t = 1.232926: stable = 0 For m = 0.09, t = 0.940716: stable = 1 For m = 0.09, t = 1.255454: stable = 0 For m = 0.10, t = 0.938538: stable = 1 For m = 0.10, t = 1.277632: stable = 0 For m = 0.11, t = 0.936469: stable = 1 For m = 0.11, t = 1.299500: stable = 0 For m = 0.12, t = 0.934492: stable = 1 For m = 0.12, t = 1.321089: stable = 0 For m = 0.13, t = 0.932590: stable = 1 For m = 0.13, t = 1.342424: stable = 0 For m = 0.14, t = 0.930754: stable = 1 For m = 0.14, t = 1.363528: stable = 0 For m = 0.15, t = 0.928975: stable = 1 For m = 0.15, t = 1.384416: stable = 0 For m = 0.16, t = 0.927246: stable = 1 For m = 0.16, t = 1.405106: stable = 0 For m = 0.17, t = 0.925560: stable = 1 For m = 0.17, t = 1.425609: stable = 0 For m = 0.18, t = 0.923915: stable = 1 For m = 0.18, t = 1.445937: stable = 0 For m = 0.19, t = 0.922306: stable = 1 For m = 0.19, t = 1.466101: stable = 0 For m = 0.20, t = 0.920729: stable = 1 For m = 0.20, t = 1.486111: stable = 0 For m = 0.21, t = 0.919183: stable = 1 For m = 0.21, t = 1.505973: stable = 0 For m = 0.22, t = 0.917665: stable = 1 For m = 0.22, t = 1.525695: stable = 0 For m = 0.23, t = 0.916173: stable = 1 For m = 0.23, t = 1.545286: stable = 0 For m = 0.24, t = 0.914706: stable = 1 For m = 0.24, t = 1.564749: stable = 0 For m = 0.25, t = 0.913262: stable = 1 For m = 0.25, t = 1.584092: stable = 0 For m = 0.26, t = 0.911839: stable = 1 For m = 0.26, t = 1.603320: stable = 0 For m = 0.27, t = 0.910437: stable = 1 For m = 0.27, t = 1.622437: stable = 0 For m = 0.28, t = 0.909055: stable = 1 For m = 0.28, t = 1.641448: stable = 0 For m = 0.29, t = 0.907691: stable = 1 For m = 0.29, t = 1.660357: stable = 0 For m = 0.30, t = 0.906345: stable = 1 For m = 0.30, t = 1.679169: stable = 0 For m = 0.31, t = 0.905017: stable = 1 For m = 0.31, t = 1.697886: stable = 0 For m = 0.32, t = 0.903705: stable = 1 For m = 0.32, t = 1.716512: stable = 0 For m = 0.33, t = 0.902409: stable = 1 For m = 0.33, t = 1.735050: stable = 0 For m = 0.34, t = 0.901128: stable = 1 For m = 0.34, t = 1.753504: stable = 0 For m = 0.35, t = 0.899862: stable = 1 For m = 0.35, t = 1.771876: stable = 0 For m = 0.36, t = 0.898611: stable = 1 For m = 0.36, t = 1.790169: stable = 0 For m = 0.37, t = 0.897373: stable = 1 For m = 0.37, t = 1.808385: stable = 0 For m = 0.38, t = 0.896149: stable = 1 For m = 0.38, t = 1.826527: stable = 0 For m = 0.39, t = 0.894938: stable = 1 For m = 0.39, t = 1.844597: stable = 0 For m = 0.40, t = 0.893739: stable = 1 For m = 0.40, t = 1.862598: stable = 0 For m = 0.41, t = 0.892553: stable = 1 For m = 0.41, t = 1.880530: stable = 0 For m = 0.42, t = 0.891380: stable = 1 For m = 0.42, t = 1.898397: stable = 0 For m = 0.43, t = 0.890218: stable = 1 For m = 0.43, t = 1.916201: stable = 0 For m = 0.44, t = 0.889067: stable = 1 For m = 0.44, t = 1.933942: stable = 0 For m = 0.45, t = 0.887928: stable = 1 For m = 0.45, t = 1.951622: stable = 0 For m = 0.46, t = 0.886799: stable = 1 For m = 0.46, t = 1.969244: stable = 0 For m = 0.47, t = 0.885682: stable = 1 For m = 0.47, t = 1.986808: stable = 0 For m = 0.48, t = 0.884575: stable = 1 For m = 0.48, t = 2.004317: stable = 0 For m = 0.49, t = 0.883478: stable = 1 For m = 0.49, t = 2.021771: stable = 0 For m = 0.51, t = 0.882391: stable = 1 For m = 0.51, t = 2.039172: stable = 0 For m = 0.52, t = 0.881314: stable = 1 For m = 0.52, t = 2.056522: stable = 0 For m = 0.53, t = 0.880246: stable = 1 For m = 0.53, t = 2.073821: stable = 0 For m = 0.54, t = 0.879188: stable = 1 For m = 0.55, t = 0.878139: stable = 1 For m = 0.56, t = 0.877099: stable = 1 For m = 0.57, t = 0.876068: stable = 1 For m = 0.58, t = 0.875046: stable = 1 For m = 0.59, t = 0.874032: stable = 1 For m = 0.60, t = 0.873027: stable = 1 For m = 0.61, t = 0.872029: stable = 1 For m = 0.62, t = 0.871040: stable = 1 For m = 0.63, t = 0.870059: stable = 1 For m = 0.64, t = 0.869085: stable = 1 For m = 0.65, t = 0.868119: stable = 1 For m = 0.66, t = 0.867161: stable = 1 For m = 0.67, t = 0.066626: stable = 0 For m = 0.67, t = 0.866210: stable = 1 For m = 0.68, t = 0.068546: stable = 0 For m = 0.68, t = 0.865266: stable = 1 For m = 0.69, t = 0.070490: stable = 0 For m = 0.69, t = 0.864329: stable = 1 For m = 0.70, t = 0.072458: stable = 0 For m = 0.70, t = 0.863399: stable = 1 For m = 0.71, t = 0.074450: stable = 0 For m = 0.71, t = 0.862475: stable = 1 For m = 0.72, t = 0.076466: stable = 0 For m = 0.72, t = 0.861559: stable = 1 For m = 0.73, t = 0.078506: stable = 0 For m = 0.73, t = 0.860649: stable = 1 For m = 0.74, t = 0.080570: stable = 0 For m = 0.74, t = 0.859745: stable = 1 For m = 0.75, t = 0.082657: stable = 0 For m = 0.75, t = 0.858848: stable = 1 For m = 0.76, t = 0.084768: stable = 0 For m = 0.76, t = 0.857957: stable = 1 For m = 0.77, t = 0.086902: stable = 0 For m = 0.77, t = 0.857072: stable = 1 For m = 0.78, t = 0.089060: stable = 0 For m = 0.78, t = 0.856193: stable = 1 For m = 0.79, t = 0.091241: stable = 0 For m = 0.79, t = 0.855319: stable = 1 For m = 0.80, t = 0.093446: stable = 0 For m = 0.80, t = 0.854452: stable = 1 For m = 0.81, t = 0.095673: stable = 0 For m = 0.81, t = 0.853590: stable = 1 For m = 0.82, t = 0.097923: stable = 0 For m = 0.82, t = 0.852734: stable = 1 For m = 0.83, t = 0.100197: stable = 0 For m = 0.83, t = 0.851883: stable = 1 For m = 0.84, t = 0.102493: stable = 0 For m = 0.84, t = 0.851037: stable = 1 For m = 0.85, t = 0.104812: stable = 0 For m = 0.85, t = 0.850197: stable = 1 For m = 0.86, t = 0.107153: stable = 0 For m = 0.86, t = 0.849361: stable = 1 For m = 0.87, t = 0.109517: stable = 0 For m = 0.87, t = 0.848531: stable = 1 For m = 0.88, t = 0.111904: stable = 0 For m = 0.88, t = 0.847706: stable = 1 For m = 0.89, t = 0.114313: stable = 0 For m = 0.89, t = 0.846885: stable = 1 For m = 0.90, t = 0.116745: stable = 0 For m = 0.90, t = 0.846069: stable = 1 For m = 0.91, t = 0.119199: stable = 0 For m = 0.91, t = 0.845258: stable = 1 For m = 0.92, t = 0.121675: stable = 0 For m = 0.92, t = 0.844451: stable = 1 For m = 0.93, t = 0.124173: stable = 0 For m = 0.93, t = 0.843649: stable = 1 For m = 0.94, t = 0.126693: stable = 0 For m = 0.94, t = 0.842851: stable = 1 For m = 0.95, t = 0.129236: stable = 0 For m = 0.95, t = 0.842057: stable = 1 For m = 0.96, t = 0.131800: stable = 0 For m = 0.96, t = 0.841268: stable = 1 For m = 0.97, t = 0.134386: stable = 0 For m = 0.97, t = 0.840482: stable = 1 For m = 0.98, t = 0.136994: stable = 0 For m = 0.98, t = 0.839700: stable = 1 For m = 0.99, t = 0.139624: stable = 0 For m = 0.99, t = 0.838922: stable = 1 For m = 1.00, t = 0.142275: stable = 0 For m = 1.00, t = 0.838148: stable = 1
% Plot fixed points as a function of m with stability info
figure;
hold on;
for i = 1:length(m_values)
t_vals = fixed_points{i};
stability_vals = stability_info{i};
for j = 1:length(t_vals)
if stability_vals(j)
plot(m_values(i), t_vals(j), 'go'); % Stable points in green
else
plot(m_values(i), t_vals(j), 'ro'); % Unstable points in red
end
end
end
xlabel('m');
ylabel('Fixed Point t');
title('Fixed Points and Stability as a Function of m');
legend('Stable', 'Unstable');
hold off;
  21 Kommentare
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Torsten
Torsten am 7 Jun. 2024
As I could see, eigenvalues for t are near zero but eigenvalues for k are quite large.
The equations are not separable - there are no eigenvalues for t and eigenvalues for k. So you cannot say that the system is stable with respect to t and unstable with respect to k or something similar.
Sabrina Garland
Sabrina Garland am 7 Jun. 2024
Okay... Thanks @Torsten

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