Results 31 to 40 of about 169 (74)
Constructing dynamical systems possessing homoclinic bifurcation points of codimension two [PDF]
, 1995 A procedure is derived which allows for a systematic construction of three-dimensional ordinary differential equations possessing homoclinic solutions. These are proved to admit homoclinic bifurcation points of codimension two.
Sandstede, Björn
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Continuation for thin film hydrodynamics and related scalar problems
, 2018 This chapter illustrates how to apply continuation techniques in the analysis of a particular class of nonlinear kinetic equations that describe the time evolution through transport equations for a single scalar field like a densities or interface ...
A Dhooge +94 more
core +1 more source
Saddle-nodes and period-doublings of smale horseshoes: a case study near resonant homoclinic bellows [PDF]
, 2020 In unfoldings of resonant homoclinic bellows interesting bifurcation phenomena occur: two suspensed Smale horseshoes can collide and disappear in saddle-node bifurcations (all periodic orbits disappear through saddle-node bifurcations, there are no other
Ale Jan Homburg +3 more
core +3 more sources
Appearance of discrete Lorenz attractors in the transitions from saddle to saddle-focus
, 2023 Triply degenerate fixed points appear in global bifurcations -- homoclinic and heteroclinic tangencies. In order to get Lorenz-like attractors, the dynamics of the first return map along the homoclinic or heteroclinic cycle should be effectively at least
Ovsyannikov, Ivan
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On the existence of non-hyperbolic ergodic measures as the limit of periodic measures
, 2016 [GIKN] and [BBD1] propose two very different ways for building non hyperbolic measures, [GIKN] building such a measure as the limit of periodic measures and [BBD1] as the $\omega$-limit set of a single orbit, with a uniformly vanishing Lyapunov exponent.
Bonatti, Christian, Zhang, Jinhua
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Periodic measures and partially hyperbolic homoclinic classes
, 2016 In this paper, we give a precise meaning to the following fact, and we prove it: $C^1$-open and densely, all the non-hyperbolic ergodic measures generated by a robust cycle are approximated by periodic measures.
Bonatti, Christian, Zhang, Jinhua
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Dynamical systems and their applications in neuroscience [PDF]
, 2007 This thesis deals with dynamical systems, numerical software for the continuation study of dynamical systems, and some important neurobiological applications.
Sautois, Bart
core +1 more source
Dominated splitting and zero volume for incompressible three-flows
, 2008 We prove that there exists an open and dense subset of the incompressible 3-flows of class C^2 such that, if a flow in this set has a positive volume regular invariant subset with dominated splitting for the linear Poincar\'e flow, then it must be an ...
Araujo, Vitor, Bessa, Mario
core +1 more source
Fast and slow waves in the FitzHugh-Nagumo equation [PDF]
, 1995 It is known that the FitzHugh-Nagumo equation possesses fast and slow travelling waves. Fast waves are perturbations of singular orbits consisting of two pieces of slow manifolds and connections between them, whereas slow waves are perturbations of ...
Krupa, Martin +2 more
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Stabilization of heterodimensional cycles [PDF]
, 2020 . We consider diffeomorphisms f with heteroclinic cycles associated to saddles P and Q of different indices. We say that a cycle of this type can be stabilized if there are diffeomorphisms close to f with a robust cycle associated to hyperbolic sets ...
C Bonatti, L J Díaz, S Kiriki
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