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Location

Integrated Science Center (ISC), Room 3020
540 Landrum Dr
Williamsburg, VA 23185Map this location

Abstract: Many large-scale dynamical systems arising from different fields of science and engineering can be regarded as coupled systems on networks. Examples include biological and artificial neural networks, nonlinear oscillators on lattices, complex ecosystems and the transmission models of infectious diseases in heterogeneous populations. A new systematic approach, based on Kirchhoff's Matrix Tree Theorem from graph theory, is developed to guide the constructions of Lyapunov functions for coupled systems on networks. This graph-theoretic approach is applied to investigate global stability problems for several coupled systems in engineering, mathematical ecology, and mathematical epidemiology. The approach allows improvement of existing results in the literature and, particularly, resolution of a 30-year open problem in mathematical epidemiology.

Contact

[[jxshix, Junping Shi]]