The Poincar E-bendixson Theorem for Monotone Cyclic Feedback Systems with Delay
نویسندگان
چکیده
We consider cyclic nearest neighbor systems of di erential delay equations, in which the coupling between neighbors possesses a monotonicity property. Using a discrete (integer-valued) Lyapunov function, we prove that the Poincar e-Bendixson theorem holds for such systems. We also obtain results on piecewise monotonicity and stability of periodic solutions of such systems.
منابع مشابه
The Poincar -Bendixson Theorem for Monotone Cyclic Feedback Systems
where we agree to interpret x ~ as x n. [As there will be a frequent need to make such interpretat ions, due to the cyclic nature of the feedback in (0.1), let us agree that all indices (superscripts) of all variables are to be taken modu lo n.] We assume the nonlineari ty f = (fl, f2,...,fn) is defined on a n o n e m p t y open set 0 c R n with the p roper ty that each coordinate project ion O...
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