An Introduction to Dynamical Systems

Science Signaling  20 Sep 2011:
Vol. 4, Issue 191, pp. tr6
DOI: 10.1126/scisignal.2001982

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This Teaching Resource provides lecture notes, slides, and a problem set that can assist in teaching concepts related to dynamical systems tools for the analysis of ordinary differential equation (ODE)–based models. The concepts are applied to familiar biological problems, and the material is appropriate for graduate students or advanced undergraduates. The lecture explains how equations describing biochemical signaling networks can be derived from diagrams that illustrate the reactions in graphical form. Because such reactions are most frequently described using systems of ODEs, the lecture discusses and illustrates the principles underlying the numerical solution of ODEs. Methods for determining the stability of steady-state solutions of one or two-dimensional ODE systems are covered and illustrated using standard graphical methods. The concept of a bifurcation, a condition at which a system’s behavior changes qualitatively, is also introduced. A problem set is included that (i) requires students to implement an ODE model of biochemical reactions using MATLAB and (ii) allows them to explore dynamical systems concepts.

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