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Displaying similar documents to “Topological and measurable dynamics of Lorenz maps”

Breaking the continuity of a piecewise linear map

Viktor Avrutin, Michael Schanz, Björn Schenke (2012)

ESAIM: Proceedings

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Knowledge about the behavior of discontinuous piecewise-linear maps is important for a wide range of applications. An efficient way to investigate the bifurcation structure in 2D parameter spaces of such maps is to detect specific codimension-2 bifurcation points, called organizing centers, and to describe the bifurcation structure in their neighborhood. In this work, we present the organizing centers in the 1D discontinuous piecewise-linear...

Doubling bifurcation of a closed invariant curve in 3D maps

Laura Gardini, Iryna Sushko (2012)

ESAIM: Proceedings

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The object of the present paper is to give a qualitative description of the bifurcation mechanisms associated with a closed invariant curve in three-dimensional maps, leading to its doubling, not related to a standard doubling of tori. We propose an explanation on how a closed invariant attracting curve, born via Neimark-Sacker bifurcation, can be transformed into a repelling one giving birth to a new attracting closed invariant curve ...

Degenerate Hopf bifurcations and the formation mechanism of chaos in the Qi 3-D four-wing chaotic system

Hongtao Liang, Yanxia Tang, Li Li, Zhouchao Wei, Zhen Wang (2013)

Kybernetika

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In order to further understand a complex 3-D dynamical system proposed by Qi et al, showing four-wing chaotic attractors with very complicated topological structures over a large range of parameters, we study degenerate Hopf bifurcations in the system. It exhibits the result of a period-doubling cascade to chaos from a Hopf bifurcation point. The theoretical analysis and simulations demonstrate the rich dynamics of the system.