Limit Cycles Appearing from a Generalized Heteroclinic Loop with an Elementary Saddle and a Nilpotent Saddle by Perturbing Piecewise Hamiltonian Systems [PDF]
, 2022 Jin Zhou +2 more
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Excitability in a nonlinear magnetoacoustic resonator
, 2006 We report a nonlinear acoustic system displaying excitability. The considered system is a magnetostrictive material where acoustic waves are parametrically generated.
F. Plaza +8 more
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, 2009 In this paper, the dynamical attractor and heteroclinic orbit have been employed to make the late-time behaviors of the model insensitive to the initial condition and thus alleviate the fine-tuning problem in the torsion cosmology.
C. G. Böhmer +6 more
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On the singular hyperbolicity of star flows
, 2014 We prove for a generic star vector field $X$ that, if for every chain recurrent class $C$ of $X$ all singularities in $C$ have the same index, then the chain recurrent set of $X$ is singular hyperbolic.
Gan, Shaobo, Shi, Yi, Wen, Lan
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Dynamics of surface diffeomorphisms relative to homoclinic and heteroclinic orbits [PDF]
, 2003 The Nielsen-Thurston theory of surface diffeomorphisms shows that useful dynamical information can be obtained about a surface diffeomorphism from a finite collection of periodic orbits.In this paper, we extend these results to homoclinic and ...
Collins, Pieter
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Global bifurcation for monotone fronts of elliptic equations
, 2020 In this paper, we present two results on global continuation of monotone front-type solutions to elliptic PDEs posed on infinite cylinders. This is done under quite general assumptions, and in particular applies even to fully nonlinear equations as well ...
Chen, Robin Ming +2 more
core
Unfolding of a Quadratic Integrable System with Two Centers and Two Unbounded Heteroclinic Loops
Journal of Differential Equations, 1997 The authors present a complete study of quadratic 3-parameter unfoldings of the integrable quadratic system \[ \dot x=- y-3x^2+ y^2,\;\dot y= x(1-2y) \leqno (1)_0 \] belonging to the class \(Q^{\mathbb{R}_3}\) (according to H. Zoladek), or the class \(m=a=0\) (according to Chinese classification). System \((1)_0\) has two centers \((0,0)\) and \((0,1)\)
Dumortier, Freddy, Li, C., Zhang, Z.
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Superinflation, quintessence, and the avoidance of the initial singularity [PDF]
, 2000 We consider the dynamics of a spatially flat universe dominated by a self-interacting nonminimally coupled scalar field. The structure of the phase space and complete phase portraits for the conformal coupling case are given.
Brenig, L. +5 more
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Heteroclinic networks for brain dynamics. [PDF]
Front Netw Physiol, 2023 Meyer-Ortmanns H.
europepmc +1 more source
Analytical study of the Lorenz system: Existence of infinitely many periodic orbits and their topological characterization. [PDF]
Proc Natl Acad Sci U S A, 2023 Pinsky T.
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