Birth of bilayered torus and torus breakdown in a piecewise-smooth dynamical system

by: Zhanybai T Zhusubaliyev, Erik Mosekilde

Physics Letters A, Vol. 351, No. 3. (27 February 2006), pp. 167-174.

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Abstract

Border-collision bifurcations arise when the periodic trajectory of a piecewise-smooth system under variation of a parameter crosses into a region with different dynamics. Considering a three-dimensional map describing the behavior of a DC/DC power converter, the Letter discusses a new type of border-collision bifurcation that leads to the birth of a "bilayered torus". This torus consists of the union of two saddle cycles, their unstable manifolds, and a stable focus cycle. When changing the parameters, the bilayered torus transforms through a border-collision bifurcation into a resonance torus containing the stable cycle and a saddle. The Letter also presents scenarios for torus destruction through homoclinic and heteroclinic tangencies.

@article{citeulike:502292, abstract = {Border-collision bifurcations arise when the periodic trajectory of a piecewise-smooth system under variation of a parameter crosses into a region with different dynamics. Considering a three-dimensional map describing the behavior of a DC/DC power converter, the Letter discusses a new type of border-collision bifurcation that leads to the birth of a "bilayered torus". This torus consists of the union of two saddle cycles, their unstable manifolds, and a stable focus cycle. When changing the parameters, the bilayered torus transforms through a border-collision bifurcation into a resonance torus containing the stable cycle and a saddle. The Letter also presents scenarios for torus destruction through homoclinic and heteroclinic tangencies.}, author = {Zhusubaliyev, Zhanybai T. and Mosekilde, Erik }, citeulike-article-id = {502292}, doi = {10.1016/j.physleta.2005.10.080}, journal = {Physics Letters A}, month = {February}, number = {3}, pages = {167--174}, posted-at = {2006-02-12 05:58:02}, priority = {2}, title = {Birth of bilayered torus and torus breakdown in a piecewise-smooth dynamical system}, url = {http://dx.doi.org/10.1016/j.physleta.2005.10.080}, volume = {351}, year = {2006} }

RIS record

TY - JOUR ID - citeulike:502292 L3 - citeulike-article-id:502292 TI - Birth of bilayered torus and torus breakdown in a piecewise-smooth dynamical system JF - Physics Letters A VL - 351 IS - 3 SP - 167 EP - 174 N2 - Border-collision bifurcations arise when the periodic trajectory of a piecewise-smooth system under variation of a parameter crosses into a region with different dynamics. Considering a three-dimensional map describing the behavior of a DC/DC power converter, the Letter discusses a new type of border-collision bifurcation that leads to the birth of a "bilayered torus". This torus consists of the union of two saddle cycles, their unstable manifolds, and a stable focus cycle. When changing the parameters, the bilayered torus transforms through a border-collision bifurcation into a resonance torus containing the stable cycle and a saddle. The Letter also presents scenarios for torus destruction through homoclinic and heteroclinic tangencies. AU - Zhusubaliyev, Zhanybai AU - Mosekilde, Erik PY - 2006/02/27/ UR - http://dx.doi.org/10.1016/j.physleta.2005.10.080 ER -

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