On existence of periodic orbits for the FitzHugh nerve system
نویسندگان
چکیده
منابع مشابه
On the Generic Existence of Periodic Orbits in Hamiltonian Dynamics
We prove several generic existence results for infinitely many periodic orbits of Hamiltonian diffeomorphisms or Reeb flows. For instance, we show that a Hamiltonian diffeomorphism of a complex projective space or Grassmannian generically has infinitely many periodic orbits. We also consider symplectomorphisms of the two-torus with irrational flux. We show that such a symplectomorphism necessar...
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Consider the Hamiltonian system i = 1 , . . . , N. Here, H E C2(R2N, R). In this paper, we investigate the existence of periodic orbits of (HS) on a given energy surface X = { z E W Z N ; H ( z) = c} ( c > 0 is a constant). The surface I: is required to verify certain geometric assumptions: B bounds a star-shaped compact region B and u 8 c B c pS for some ellipsoid %‘c RZN, 0 < (Y < p. We exhib...
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15 صفحه اولExistence of Periodic Orbits for Singular-hyperbolic Sets
It is well known that on every compact 3-manifold there is a C flow displaying a singular-hyperbolic isolated set which has no periodic orbits [BDV], [M1]. By contrast, in this paper we prove that every singular-hyperbolic attracting set of a C flow on a compact 3manifold has a periodic orbit. 2000 Math. Subj. Class. Primary: 37D30; Secondary: 37D45.
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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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ژورنال
عنوان ژورنال: Quarterly of Applied Mathematics
سال: 1996
ISSN: 0033-569X,1552-4485
DOI: 10.1090/qam/1417226