One of the more enduring topics of methodological interest at IIASA has been the problem of ascertaining and describing stability characteristics for large-scale systems. These points have been of particular applied interest in the ecology and energy areas where the terms "resilience" and "hypotheticality" have been used to intuitively characterize the type of stability of greatest practical interest.
Our primary purpose in this note is to present some new results in stability theory which have great relevance to the aforementioned studies. These results deal with the problem of "connective" stability, in which the basic question is how large a perturbation in structure the system can withstand and still remain asymptotically stable. In many ways, these results are similar in spirit to structural stability questions in which the invariance of the topological features of the system trajectory is the central issue. However, the two theories are not the same as connective stability deals with the stability of a point under structural perturbation, while structural stability is concerned with trajectories. In addition, connective stability is a quantitative theory as precise numerical estimates can be given for the magnitude of the allowed perturbation, while structural stability is primarily qualitative. Therefore, we feel justified in presenting these results in order to provide systems analysts with another tool to probe the stability characteristics of applied systems.
A secondary objective of this note is to point out the connections between the notion of connective stability and the idea of a system's connectivity pattern. All of these results will be illustrated with examples from energy and ecology
