Delay-Coupled Mathieu Equations in Synchrotron Dynamics
نویسندگان
چکیده
This paper investigates the dynamics of two couplecd Mathieu equations. The coupling functions involve both delayed and nondelay 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.
منابع مشابه
Delay-Coupled Mathieu Equations in Synchrotron Dynamics Revisited: Delay Terms in the Slow Flow
In a previous work, we applied perturbation methods to a system of two delay-coupled Mathieu equations, resulting in a slow flow which contains delayed variables. This previous treatment involved a convenient approximation which involved replacing delay terms in the slow flow by non-delay terms. The current paper explores the effect of keeping delay terms in the slow flow with the hope of illus...
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