Complex dynamics in the segmented disc dynamo

Jianghong  Bao

doi:10.3934/dcdsb.2016098

Article Contents

2016, Volume 21, Issue 10: 3301-3314. Doi: 10.3934/dcdsb.2016098

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Complex dynamics in the segmented disc dynamo

Jianghong Bao^1,

1.
School of Mathematics, South China University of Technology, Guangzhou, Guangdong

Received: June 2015

Revised: July 2016

Published: December 2016

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Abstract

The present work is devoted to giving new insights into the segmented disc dynamo. The integrability of the system is studied. The paper provides its first integrals for the parameter $r=0$. For $r>0$, the system has neither polynomial first integrals nor exponential factors, and it is also further proved not to be Darboux integrable. In addition, by choosing an appropriate bifurcation parameter, the paper proves that Hopf bifurcations occur in the system and presents the formulae for determining the direction of the Hopf bifurcations and the stability of bifurcating periodic solutions.

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Mathematics Subject Classification: Primary: 37G10, 37J30; Secondary: 34C23.

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