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**THE UNIVERSITY OF ALBERTA**

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**Department of Mathematical and Statistical
Sciences**

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**Special Talk**

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**“Recent Development of Normal Form Theory**

**and
its Applications”**

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**Yuan
Yuan**

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**Department of Mathematics and Statistics**

**Memorial University of Newfoundland**

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**Monday, October 6, 2003**

**CAB 657 @ 3:00 p.m.**

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**Abstract:**

**Normal form theory is one of the most useful and
important tools in the study of nonlinear dynamical systems. Although some
theories and methodologies have been developed in this area, better approaches
are still needed in analyzing the complex behaviour such as instability and
bifurcations. Efficiently combining analytical and computational
(numerical/symbolic) methods is one of such approaches.**

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**The conventional normal form (CNF) can be further
simplified, leading to the simplest normal form (SNF), which is more powerful
in attacking higher dimensional and/or higher order nonlinear dynamical
systems. We have developed an efficient, recursive method for computing the SNF
of differential equations. In addition,
several specific techniques have been established for computing the SNF
associated with various singularities. Lie algebra is used for theoretical
proofs, while algorithms and Maple programs are developed to greatly facilitate
applications in solving real problems.**

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**This talk will also present some results of the
applications of normal form theory which we have been involved, including
epidemiology models in finite dimensional system, neuron network, high speed
aircraft and nonlinear oscillators in infinite dimensional systems with time
delay.**

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