Existence of periodic orbits for high-dimensional autonomous systems
نویسندگان
چکیده
منابع مشابه
Existence of Periodic Orbits for High-dimensional Autonomous Systems
We give a result on existence of periodic orbits for autonomous differential systems with arbitrary finite dimension. It is based on a Poincaré-Bendixson property enjoyed by a new class of monotone systems introduced in L. A. Sanchez, Cones of rank 2 and the PoincaréBendixson property for a new class of monotone systems, Journal of Differential Equations 216 (2009), 1170-1190. A concrete applic...
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There has been extensive work on the existence of periodic solutions for nonlinear second order autonomous differantial equations, but little work regarding the third order problems. The popular Poincare-Bendixon theorem applies well to the former but not the latter (see [2] and [3]). We give a necessary condition for the existence of periodic solutions for the third order autonomous system...
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We study the stability of periodic orbits of autonomous Hamiltonian systems with N+1 degrees of freedom or equivalently of 2N -dimensional symplectic maps, with N ≥ 1. We classify the different stability types, introducing a new terminology which is perfectly suited for systems with many degrees of freedom, since it clearly reflects the configuration of the eigenvalues of the corresponding mono...
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there has been extensive work on the existence of periodic solutions for nonlinear second order autonomous differantial equations, but little work regarding the third order problems. the popular poincare-bendixon theorem applies well to the former but not the latter (see [2] and [3]). we give a necessary condition for the existence of periodic solutions for the third order autonomous systems, t...
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In this work we describe how to prove with computer assistance the existence of fixed points and periodic orbits for infinite dimensional discrete dynamical systems. The method is based on Krawczyk operator. As an example we prove the existence of three fixed points, one period–2 and one period–4 orbit for the Kot-Schaffer growth-dispersal model.
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 2010
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2009.08.058