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Perturbation Analysis Of The Limit Cycle Of The Free Van Der Pol Equation, Mohammad Dadfar, James Geer, Carl M. Andersen
Perturbation Analysis Of The Limit Cycle Of The Free Van Der Pol Equation, Mohammad Dadfar, James Geer, Carl M. Andersen
Computer Science Faculty Publications
. A power series expansion in the damping parameter E of the limit cycle U(t; E) of the free van der Pol equation Ul + E( U2 _1) U + U =0 is constructed and analyzed. Coefficients in the expansion are computed up to 0(E24) in exact rational arithmetic using the symbolic manipulation system MACSYMA and up to O(E163) using a FORTRAN program. The series is analyzed using Pade approximants. The convergence of the series for the maximum amplitude of the limit cycle is limited by two pairs of complex conjugate singularities in the complex e-plane. These singularities are the …