SYMBOLIC MANIPULATION FOR SOME NON-ALGEBRAIC OBJECTS AND ITS APPLICATION IN COMPUTING THE LCE OF VAN DER POL EQUATION

The applications of symbolic manipulation methods based on algebraic e quation solving theory are extended to a class of non-algebraic object s, called analytic equalities, for finding algorithmic solutions to so me mathematical problems related to nonlinear dynamics. A symbolic man ipulation method for analytic equalities is established, based on whic h an algorithm for constructing necessary conditions for analytic equa lity sets is developed to mechanically derive some unknown relations. As an example, the method is used to compute the Lyapunov Characterist ic Exponent (LCE) of the chaotic attractor of Van der Pol equation. In stead of numerically computing the LCE, we try to find its dependence on the system parameters by symbolic manipulation. Combining our resul t on the LCE with related qualitative results on the system, we get so me conclusions on the system behavior.