Quadratic dynamical systems
Rabinovich, Y.; Sinclair, A.; Wigderson, A.
Foundations of Computer Science, 1992. Proceedings., 33rd Annual Symposium on
Volume , Issue , 24-27 Oct 1992 Page(s):304 - 313
Digital Object Identifier   10.1109/SFCS.1992.267761
Summary:The paper promotes the study of computational aspects, primarily the convergence rate, of nonlinear dynamical systems from a combinatorial perspective. The authors identify the class of symmetric quadratic systems. Such systems have been widely used to model phenomena in the natural sciences, and also provide an appropriate framework for the study of genetic algorithms in combinatorial optimisation. They prove several fundamental general properties of these systems, notably that every trajectory converges to a fixed point. They go on to give a detailed analysis of a quadratic system defined in a natural way on probability distributions over the set of matchings in a graph. In particular, they prove that convergence to the limit requires only polynomial time when the graph is a tree. This result demonstrates that such systems, though nonlinear, are amenable to quantitative analysis

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