determine_local_stability Function

public function determine_local_stability(a, ev) result(rst)

Determines the nature of stability/unstability near the point at which the dynamics matrix was computed.

For the linearized system $$\dot{\boldsymbol{x}} = A\boldsymbol{x},$$ a mode associated with eigenvalue $\lambda_i$ behaves as $e^{\lambda_i t}$. Therefore, the sign of $\operatorname{Re}(\lambda_i)$ determines exponential growth or decay. A fixed point is hyperbolic when no eigenvalue has zero real part.

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=real64),	intent(in),		dimension(:,:)	::	a	An N-by-N matrix containing the 'A' matrix, also known as the dynamics matrix.
complex(kind=real64),	intent(out),	optional,	dimension(:)	::	ev	An optional N-element array that, if supplied, will be filled with the eigenvalues of the matrix A.

Return Value integer(kind=int32)

One of the fixed-point classification constants defined above.

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