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Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain


Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email:

Delay-Coupled Mathieu Equations in Synchrotron Dynamics

Journal of Applied Nonlinear Dynamics 5(3) (2016) 337--348 | DOI:10.5890/JAND.2016.09.006

Alexander Bernstein; Richard Rand

$^{1}$ Center for Applied Mathematics, Cornell University

$^{2}$ Dept. of Mathematics and Dept. of Mechanical and Aerospace Engineering, Cornell University

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This paper investigates the dynamics of two coupled Mathieu equations. The coupling functions involve both delayed and nondelayed terms. We use a perturbation method to obtain a slow flow which is then studied using Routh-Hurwitz stability criterion. Analytic results are shown to compare favorably with numerical integration. The numerical integrator, DDE23, is shown to inadvertently add damping. It is found that the nondelayed coupling parameter plays a significant role in the system dynamics. We note that our interest in this problem comes from an application to the design of nuclear accelerators.


The authors wish to thank their colleagues J. Sethna, D. Rubin, D. Sagan and R. Meller for introducing us to the dynamics of the Synchrotron.


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