Points and Dynamics in the Linear Regime

Assume that a chemical reaction system of N interacting chemicals is described by the differential equations 

In the neighborhood of the critical point, the dynamics can be studied by computing the linear part of Eq. (3), which is given by 

The eigenvalues of A, pi, p2. Pn, which are found by solving the characteristic equation 

Several workers have recently been developing methods to analyze the local stability of a critical point on the basis of the signs of the elements of A.(17 5-40) been shown that all the eigenvalues of a matrix have 

If these five conditions apply, the matrix A is called qualitatively stable. 

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