Check stability of fixed points of 2D vectorfield

function stability = check_stability(rho,psi,gamma,lambda,epsilon,f)

This function evaluates the eigenvalues of the Jacobian of the flow that induces a 2D vectorfield, to establish their stability. It assumes the fixed points to be hyperbolic (Jain and Haller, 2021).

nRho = length(rho);
stability = zeros(size(rho));
for j = 1:nRho

The stability is assesed by the eigenvalues of the Jacobian

$J(\rho)=\left[\begin{array}{cc}\partial_{\rho}a(\rho) & -\rho\left[b(\rho)-m\Omega\right]\\\partial_{\rho}b(\rho)+\frac{\left[b(\rho)-m\Omega\right]}{\rho} & \frac{a(\rho)}{\rho}\end{array}\right]$

    J = frc_Jacobian(rho(j),psi(j),gamma,lambda,epsilon,f);
    trJ = trace(J);
    detJ = det(J);

Routh Stability criterion

    if detJ>0 && trJ<0 % asymptotically stable
        stability(j) = 1;
    else % not asymptotically stable
        stability(j) = 0;
    end

end
stability = logical(stability);

end