American Institute of Mathematical Sciences

February  2020, 25(2): 749-760. doi: 10.3934/dcdsb.2019265

Bifurcation of relative equilibria generated by a circular vortex path in a circular domain

* Corresponding author: David Rojas (david.rojas@udg.edu)

Received  December 2018 Revised  March 2019 Published  November 2019

Fund Project: All the authors are partially supported by the MINECO/FEDER grant MTM2017-82348-C2-1-P. The first author is also partially supported by the MINECO/FEDER grant MTM2017-86795-C3-1-P.

We study the passive particle transport generated by a circular vortex path in a 2D ideal flow confined in a circular domain. Taking the strength and angular velocity of the vortex path as main parameters, the bifurcation scheme of relative equilibria is identified. For a perturbed path, an infinite number of orbits around the centers are persistent, giving rise to periodic solutions with zero winding number.

Citation: David Rojas, Pedro J. Torres. Bifurcation of relative equilibria generated by a circular vortex path in a circular domain. Discrete & Continuous Dynamical Systems - B, 2020, 25 (2) : 749-760. doi: 10.3934/dcdsb.2019265
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References:
Phase portrait of system (3) depending on the parameters according to Theorem 2.1
Bifurcation diagram of the phase-portrait of system (3) on $D_R$. The bold curve corresponds to bifurcation parameters $\mathcal B$, whereas the remaining ones correspond to regular parameters. In Theorem 2.1 the phase portrait at each region is given
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