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Averaging using elliptic functions: Approximation of limit cycles. (English) Zbl 0699.34032
Summary: We apply the method of averaging to first order in the small parameter $$\epsilon$$ to the autonomous system $$x''+\alpha x+\beta x^ 3+\epsilon g(x,x')=0$$ where we do not consider $$\beta$$ as small. This involves perturbing off of Jacobian elliptic functions, rather than off of trigonometric functions as is usually done. The resulting equations involve integrals of elliptic functions which are evaluated using a program written in the computer algebra system MACSYMA. The results are applied to the problem of approximating limit cycles in the above differential equation.

##### MSC:
 34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations 34C29 Averaging method for ordinary differential equations 34-04 Software, source code, etc. for problems pertaining to ordinary differential equations
MACSYMA
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