Neural Networks and Biological Modeling
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چکیده
is the jacobian matrix of F . If this matix has n distinct eigenvalues λk (real or complex), the system can be diagonalized, and the solutions can be expressed as combinations of exponentials of the form ek. Therefore, x − x∗ → 0 if all the eigenvalues have a negative real part. If one or more eigenvalues have positive real part, |x− x∗| → ∞. Therefore, • The fixed point x∗ is stable if all the eigenvalues of F ′(x∗) have negative real part. • The fixed point x∗ is unstable if one or more eigenvalues of F ′(x∗) have positive real part. • If some eigenvalues have a vanishing real part (which occurs for pairs of eigenvalues since they are complex conjugates), the linear stability analysis is not sufficient to determine the stability of the fixed point.
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