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| bgcolor="#DDDDDD" align="center"| | | bgcolor="#DDDDDD" align="center"| Mathematical results arising from systems biology | ||
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We describe new sufficient conditions for global injectivity of general nonlinear functions, necessary and sufficient conditions for global injectivity of polynomial functions, and related criteria for uniqueness of equilibria in nonlinear dynamical systems. Some of these criteria are graph-theoretical, others are checked using symbolic computation. We also mention some applications of these methods in the study of Bezier curves and patches, and other types of manifolds used in geometric modeling. Also, we discuss some criteria for persistence and boundedness of trajectories in polynomial or power-law dynamical systems. All these seemingly unrelated results have been inspired by the study of mathematical models in systems biology. | |||
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Revision as of 00:04, 10 September 2010
Gheorghe Craciun, UW-Mathematics
| Mathematical results arising from systems biology |
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We describe new sufficient conditions for global injectivity of general nonlinear functions, necessary and sufficient conditions for global injectivity of polynomial functions, and related criteria for uniqueness of equilibria in nonlinear dynamical systems. Some of these criteria are graph-theoretical, others are checked using symbolic computation. We also mention some applications of these methods in the study of Bezier curves and patches, and other types of manifolds used in geometric modeling. Also, we discuss some criteria for persistence and boundedness of trajectories in polynomial or power-law dynamical systems. All these seemingly unrelated results have been inspired by the study of mathematical models in systems biology. |
Jean-Marc Vanden-Broeck, UW-Mathematics
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Thierry Goudon, INRIA-Lille, France
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Vageli Coutsias, University of New Mexico
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Anne Gelb, Arizona State University
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