Border collision bifurcations and chaotic sets in a two-dimensional piecewise linear map |
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| Institution: | 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. State Key Laboratory of Advanced Design and Manufacture for Vehicle Body, Hunan University, Changsha, Hunan 410082, China;2. School of Mechanical and Mechatronic Engineering, FEIT, University of Technology Sydney, PO Box 123, Broadway, New South Wales 2007, Australia;3. School of Mechanical and Electric Engineering, Guangzhou University, Guangzhou, Guangdong 510006, China;4. School of Mechanical Engineering, Hunan Institute of Engineering, Xiangtan, Hunan 411104, China |
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| Abstract: | A two-dimensional piecewise linear continuous model is analyzed. It reflects the dynamics occurring in a circuit proposed as chaos generator, in a simplified case. The parameter space is investigated in order to classify completely regions of existence of stable cycles, and regions associated with chaotic behaviors. The border collision bifurcation curves are analytically detected, as well as the degenerate flip bifurcations of k-cycles and the homoclinic bifurcations occurring in cyclic chaotic regions leading to chaos in one-piece. |
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