Global asymptotic stability in a model of networks |
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Authors: | Hassan M. Fathallah-Shaykh Abraham Freiji |
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Affiliation: | Departments of Mathematics and Neurology, The University of Alabama, Birmingham, AL, United States of America |
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Abstract: | Global asymptotic stability is of importance from a theoretical as well as an application point of view in several fields. We study a system of cubic polynomials that models biological networks. We classify the equilibria and show that the property that the interconnection matrix is Lyapunov diagonally stable is a key feature that determines convergence to a single equilibrium. The results are applied to chains of negative edges, cycles, and to interconnected graphs. We give numerical examples and study network graphs obtained from a model of the Drosophila circadian clock. |
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Keywords: | Global asymptotic stability Lyapunov function Lyapunov diagonal stability networks dynamics |
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