Results 1 to 10 of about 169 (74)
Codimension-4 resonant homoclinic bifurcations with orbit flips and inclination flips [PDF]
Acta Mathematica Sinica, English Series, 2015 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Zhang, Tian Si, Zhu, De Ming
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Bifurcations of orbit and inclination flips heteroclinic loop with nonhyperbolic equilibria. [PDF]
ScientificWorldJournal, 2014 The bifurcations of heteroclinic loop with one nonhyperbolic equilibrium and one hyperbolic saddle are considered, where the nonhyperbolic equilibrium is supposed to undergo a transcritical bifurcation; moreover, the heteroclinic loop has an orbit flip ...
Geng F, Zhao J.
europepmc +6 more sources
A topological approach to stability of pulses bifurcating from an inclination-flip homoclinic orbit [PDF]
Methods and Applications of Analysis, 2000 The paper deals with the linear stability problem of multiple pulse solutions of a parabolic system, which bifurcate from an inclination-flip homoclinic orbit. A topological approach is applied to the eigenvalue problem and a relation between the distribution of the eigenvalues and the geometry of the homoclinic orbits is proven.
Shunsaku Nii
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Resonant Homoclinic Bifurcations with Orbit Flips and Inclination Flips
Applied Mathematics, 2013 Homoclinic bifurcation with one orbit flip, two inclination flips and resonance in the tangent directions of homoclinic orbit is considered. By studying the associated successor functions constructed from a local active coordinate system, we prove the existence of double 1-periodic orbit, 1-homoclinic orbit, and also some coexistence conditions of 1 ...
Tiansi Zhang
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Dynamics of excitable cells: spike-adding phenomena in action [PDF]
, 2023 Open Access funding provided thanks to the CRUE-CSIC agreement with Springer Nature. RB, AL, AM, CM, MAM and SS have been supported by the Spanish Research projects PGC2018-096026-B-I00 and PID2021-122961NB-I00.
Barrio, R. +9 more
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Homoclinic puzzles and chaos in a nonlinear laser model [PDF]
, 2020 We present a case study elaborating on the multiplicity and self-similarity of homoclinic and heteroclinic bifurcation structures in the 2D and 3D parameter spaces of a nonlinear laser model with a Lorenz-like chaotic attractor.
Meijer, H. G. E. +2 more
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Codimension 3 bifurcation from orbit-flip homoclinic orbit of weak type [PDF]
, 2015 This article is devoted to the research of a new codimension 3 homoclinic orbit bifurcation, which is the orbit-flip of weak type. Such kind of homoclinic orbit is a degenerate case of the orbit-flip homoclinic orbit.
Deng, Guifeng, Lu, Qiuying, Luo, Hua
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Classification of fold/hom and fold/Hopf spike-adding phenomena [PDF]
, 2021 The Hindmarsh-Rose neural model is widely accepted as an important prototype for fold/hom and fold/Hopf burstings. In this paper, we are interested in the mechanisms for the production of extra spikes in a burst, and we show the whole parametric panorama
Barrio R. +3 more
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Spike-adding structure in fold/hom bursters [PDF]
, 2020 Square-wave or fold/hom bursting is typical of many excitable dynamical systems, such as pancreatic or other endocrine cells. Besides, it is also found in a great variety of fast-slow systems coming from other neural models, chemical reactions, laser ...
Barrio Gil, Roberto +3 more
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Elements of Applied Bifurcation Theory [PDF]
, 2023 This is a book on nonlinear dynamical systems and their bifurcations under parameter variation. It provides a reader with a solid basis in dynamical systems theory, as well as explicit procedures for application of general mathematical results to ...
Kuznetsov, Yuri A.
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