Formalizing the Notion of Stability
Suppose a train proceeds down a track toward its destination. Suppose the remaining distance to its destination is always decreasing by at least 100 km/hr so long as the train is at least 10 km from its destination. Suppose the initial distance from the train to the destination is 510 km. The reader can no doubt appreciate that the train can take at most five hours before lying within 10 km of its destination. This simple idea could readily be extended to other dimensions, say the three-dimensional rendezvous of a spacecraft with a manned satellite. The details of motion are unknown and unneeded; yet the conclusion is obvious.
KeywordsPositive Orthant Lyapunov Theorem Nonnegative Orthant Attractor Trajectory Finite Boundary
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- [May]R. M. May, Stability and Complexity in Model Ecosystems, Princeton U. Press, 1973.Google Scholar