Numerical Computation of Grazing Bifurcation for Periodic Orbit

Qing Wan Hu; Yong Cai Liu

doi:10.4028/www.scientific.net/AMM.63-64.651

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HomeApplied Mechanics and MaterialsApplied Mechanics and Materials Vols. 63-64Numerical Computation of Grazing Bifurcation for...

Numerical Computation of Grazing Bifurcation for Periodic Orbit

Abstract:

In this paper, a numerical algorithm for computing grazing bifurcation of periodic orbit in autonomous planar systems is derived and analyzed. We propose an analytical condition which to ensure the orbit quadratically intersects the switching manifold. Based upon this, we take into a new phase condition which ensure there is a branch of periodic orbits. The nondegenerate condition with respect to its bifurcation parameter is presented to ensure the defining equation well posed. A numerical simulation is carried out for the bifurcation diagram of the van der pol system, which agrees with analytical results very well.

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Periodical:

Applied Mechanics and Materials (Volumes 63-64)

Pages:

651-654

DOI:

https://doi.org/10.4028/www.scientific.net/AMM.63-64.651

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Online since:

June 2011

Authors:

Qing Wan Hu, Yong Cai Liu

Keywords:

Grazing Bifurcation, Hyperbolic Periodic Solution, Nondegenerate

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References

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