✦ LIBER ✦

On a codimension-three bifurcation arising in a simple dynamo model

✍ Scribed by Anne C. Skeldon; Irene M. Moroz

Book ID: 104297402
Publisher: Elsevier Science
Year: 1998
Tongue: English
Weight: 661 KB
Volume: 117
Category: Article
ISSN: 0167-2789
DOI: 10.1016/s0167-2789(97)00316-3

No coin nor oath required. For personal study only.

✦ Synopsis

In this paper we investigate the dynamics associated with a degenerate codimension-two Takens-Bogdanov bifurcation which arises in a recently derived model for self-exciting dynamo action introduced by Hide et al. JR. Hide, A.C. Skeldon, D.J. Acheson, A study of two novel self-exciting single-disk homopolar dynamos: theory, Proc. R. Soc. Lond. A 452 (1996) 1369-1395]. The general unfolding of such a codimension-three bifurcation has already been discussed in an abstract setting by Li and Rousseau [Codimension-2 symmetric homoclinic bifurcations and application to 1 : 2 resonance, Can J. Math. 42 (1990) 191-212]. Here we describe the unfolding scenario in the context of the dynamo problem. In particular we compare the behaviour predicted by the normal form analysis with a bifurcation study of the full dynamo equations in the neighbourhood of the codimension-three point.

📜 SIMILAR VOLUMES

Codimension-three bifurcations in a Béna

Codimension-three bifurcations in a Bénard-Marangoni problem

✍ Hoyas, Sergio; Gil, Antonio; Fajardo, Pablo; Pérez-Quiles, María J. 📂 Article 📅 2013 🏛 The American Physical Society 🌐 English ⚖ 867 KB

A special point of Z2-codimension three

A special point of Z2-codimension three Hopf bifurcation in the Hodgkin-Huxley model

✍ B. Hassard; L.-J. Shiau 📂 Article 📅 1996 🏛 Elsevier Science 🌐 English ⚖ 278 KB

A curve in (Z,T,gNo, UN,)-pmameter space of degenerate Hopf bifurcation for the Hodgkin-Huxley model is described. The curve includes all six of the "doubly degenerate" points from our earlier work [1,2]. The curve includes one special point at which m = 1, where m is the modal parameter. The recog

Period-doubling bifurcations in a simple

Period-doubling bifurcations in a simple model

✍ T. Shimizu; N. Morioka 📂 Article 📅 1981 🏛 Elsevier Science 🌐 English ⚖ 172 KB

A stage-structured food chain model with

A stage-structured food chain model with stage dependent predation: Existence of codimension one and codimension two bifurcations

✍ B. Mukhopadhyay; R. Bhattacharyya 📂 Article 📅 2011 🏛 Elsevier Science 🌐 English ⚖ 439 KB

Bifurcation sequence in a simple model o

Bifurcation sequence in a simple model of migratory dynamics

✍ Jeppe Sturis; Erik Mosekilde 📂 Article 📅 1988 🏛 John Wiley and Sons 🌐 English ⚖ 469 KB

S-Shaped Bifurcation Branch in a Quasili

S-Shaped Bifurcation Branch in a Quasilinear Multivalued Model Arising in Climatology

✍ D. Arcoya; J.I. Diaz; L. Tello 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 247 KB

In this paper we show the existence of a continuous and unbounded connected S-shaped set [(Q, u)] where Q is the solar constant and u satisfies a quasilinear eventually multivalued stationary equation on a Riemannian manifold without boundary arising as a stationary energy balance model for the eart