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Non-hyperbolic boundary equilibrium bifurcations in planar Filippov systems: a case study approach

 

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Opened Access Non-hyperbolic boundary equilibrium bifurcations in planar Filippov systems: a case study approach
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Author: Di Bernardo, Mario
Pagano, Daniel Juan
Ponce Núñez, Enrique
Department: Universidad de Sevilla. Departamento de Matemática Aplicada II (ETSI)
Date: 2008
Published in: International Journal of Bifurcation and Chaos, 18 (5)
Document type: Article
Abstract: Boundary equilibrium bifurcations in piecewise smooth discontinuous systems are characterized by the collision of an equi- librium point with the discontinuity surface. Generically, these bi- furcations are of codimension one, but there are scenarios where the phenomenon can be of higher codimension. Here, the possible col- lision of a non-hyperbolic equilibrium with the boundary in a two- parameter framework and the nonlinear phenomena associated with such collision are considered. By dealing with planar discontinuous (Filippov) systems, some of such phenomena are pointed out through specific representative cases. A methodology for obtaining the corresponding bi-parametric bifurcation sets is developed.
Cite: Di Bernardo, M., Pagano, D.J. y Ponce Núñez, E. (2008). Non-hyperbolic boundary equilibrium bifurcations in planar Filippov systems: a case study approach. International Journal of Bifurcation and Chaos, 18 (5)
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URI: http://hdl.handle.net/11441/58705

DOI: 10.1142/S0218127408021051

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