ON PERIODIC ORBITS OF RELAXATION OSCILLATIONS

Shagi-Di Shih

doi:10.11650/twjm/1500407430

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Home > Journals > Taiwanese J. Math. > Volume 6 > Issue 2 > Article

2002 ON PERIODIC ORBITS OF RELAXATION OSCILLATIONS

Shagi-Di Shih

Taiwanese J. Math. 6(2): 205-234 (2002). DOI: 10.11650/twjm/1500407430

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Abstract

Two nonlinear oscillators of relaxation type are studied for representing periodic orbits in terms of two inverse functions of x exp(x). The limit of the limit cycle of singularly perturbed van der Pol differential equation is approximated analytically; while the periodic orbit of singularly perturbed Lotka-Volterra system is represented in exact manner. These results are in an excellent agreement with numerical results computed via a stiff/nonstiff Maple ODE solver “NODES package” authored by Lawrence F. Shampine and Robert M. Corless. Some remarks are provided for the relaxation period.