Border collision bifurcations in discontinuous one-dimensional linear-hyperbolic maps |
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| Affiliation: | 1. Cátedras CONACYT - Benemérita Universidad Autónoma de Puebla - Facultad de Ciencias Físico-Matemáticas, Benemerita Universidad Autónoma de Puebla, Avenida San Claudio y 18 Sur, Colonia San Manuel, Puebla 72570, México;2. Tecnologico de Monterrey, Escuela de ingeniería y ciencias, San Luis Potosí, SLP, México;3. IPICYT/División de Matemáticas Aplicadas, Camino a la Presa San José 2055 col. Lomas 4a Sección, San Luis Potosí 78216, SLP, México;4. Coordinación Académica Región Altiplano Oeste, Universidad Autónoma de San Luis Potosí, Kilometro 1 Carretera a Santo Domingo, 78600 Salinas de Hidalgo, San Luis Potosí, México;1. Department of Mathematics, Middle East Technical University, 06531 Ankara, Turkey;2. METU, Mathematics Department, Turkey |
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| Abstract: | In this paper we consider a discontinuous one-dimensional map, which is linear on one side of a generic point and hyperbolic on the other side, coming from economic applications. However this kind of piecewise smooth models is widely used also in other different applied contexts, and is characterized by border collision bifurcations. The simple formulation of the functions involved in the model allows for analytical results and the border collision bifurcations curves associated with the attracting cycles of the model are here determined. Also coexistence of two attracting cycles is shown to occur in a family of cycles of even period whose periodicity regions are overlapped in pair. |
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