| Bibliography | Avrutin, V.; Levi, P.; Schanz, M.: Border-Collision induced Bifurcation Phenomena and multi-parametric Bifurcations in a piecewise-quadratic map on the Interval.
In: Proceedings of Fifth EUROMECH Nonlinear Dynamics Conf. (ENOC'2005).
University of Stuttgart, Faculty of Computer Science, Electrical Engineering, and Information Technology.
pp. 1-10, english.
Eindhoven, NL: Springer-Verlag, January 2005.
Article in Proceedings (Conference Paper).
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| CR-Schema | G.1.10 (Numerical Analysis Applications)
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| Abstract | This article describes some bifurcation phenomena, induced by border-collisions in a piecewise--quadratic map on interval representing a special kind of Poincaré return map for dynamical systems of the Lorenz type. It is shown that the structure of the 2D parameter space of this map is dominated by singularities, which we denote as big bang bifurcation points. These bifurcations can be observed only if two parameters are varied simultaneously and cause an infinite number of different periodic dynamics. The investigated system shows an infinite number of the big bang bifurcations, which lead to the complex self-similar structure of the 2D parameter space.
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| Department(s) | University of Stuttgart, Institute of Parallel and Distributed Systems, Image Understanding
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| Entry date | October 30, 2005 |
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