Before revision:  An analytic method is then described in which a variable acting on the self-regulating terms of a community matrix enables one, depending on the field of the maximal eigenvalue, to either determine the size of the key feedback that leads to the system's tipping point, or narrows down the search space .
After revision:  This leads to quite rich combinatorial structure among the destabilising cycle sets as set size grows within the coefficients of the characteristic polynomial .