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2012•International Journal of Bifurcation and ChaosRequires access

BIFURCATION OF QUASI-PERIODIC OSCILLATIONS IN MUTUALLY COUPLED HARD-TYPE OSCILLATORS: DEMONSTRATION OF UNSTABLE QUASI-PERIODIC ORBITS

Kyohei Kamiyama, Motomasa Komuro, Tetsuro Endo

Open publisher page 16 citations

Abstract

In this paper, we obtain bifurcations of quasi-periodic orbits occuring in mutually coupled hard-type oscillators by using our recently developed computer algorithm to directly determine the unstable quasi-periodic orbits. So far, there is no computer algorithm to draw unstable invariant closed curves on a Poincare map representing quasi-periodic orbits. Recently, we developed a new algorithm to draw unstable invariant closed curves by using the bisection method. The results of this new algorithm are compared with the previously obtained averaging method results. Several new results are found, which could not be clarified by the averaging method.

About this research paper

What this paper is about

In this paper, we obtain bifurcations of quasi-periodic orbits occuring in mutually coupled hard-type oscillators by using our recently developed computer algorithm to directly determine the unstable quasi-periodic orbits. So far, there is no computer algorithm to draw unstable invariant closed curves on a Poincare map representing quasi-periodic orbits. Recently, we developed a new algorithm to draw unstable invariant closed curves by using the bisection method. The results of this new algorithm are compared with the previously obtained averaging method results. Several new results are found, which could not be clarified by the averaging method.

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OpenAlex reports 16 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

In this paper, we obtain bifurcations of quasi-periodic orbits occuring in mutually coupled hard-type oscillators by using our recently developed computer algorithm to directly determine the unstable quasi-periodic orbits. So far, there is no computer algorithm to draw unstable invariant closed curves on a Poincare map representing quasi-periodic orbits. Recently, we developed a new algorithm to draw unstable invariant closed curves by using the bisection method. The results of this new algorithm are compared with the previously obtained averaging method results. Several new results are found, which could not be clarified by the averaging method.

Key concepts: Periodic orbits, Quasi periodic, Bifurcation, Invariant (physics), Mathematics, Poincaré map, Periodic function, Type (biology)

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