Article
The boundary focus–saddle bifurcation in planar piecewise linear systems. Application to the analysis of memristor oscillators
Author/s | Ponce Núñez, Enrique
Ros Padilla, Francisco Javier Vela Felardo, Elisabet |
Department | Universidad de Sevilla. Departamento de Matemática Aplicada II (ETSI) |
Publication Date | 2018-10 |
Deposit Date | 2024-01-29 |
Published in |
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Abstract | Among the boundary equilibrium bifurcations in planar continuous piecewise linear systems with two zones separated by a straight line, the focus–saddle bifurcation corresponds with a one-parameter transition from a situation ... Among the boundary equilibrium bifurcations in planar continuous piecewise linear systems with two zones separated by a straight line, the focus–saddle bifurcation corresponds with a one-parameter transition from a situation without equilibria to a configuration with two equilibria, namely a focus and a saddle point. Depending on the dynamics of the two linear systems involved, the focus can appear surrounded by a limit cycle, by a saddle-loop (homoclinic connection) or by nothing else. After introducing a criticality coefficient whose sign discriminates the different possible situations, the focus–saddle bifurcation is quantitatively characterized for the first time. The analysis requires to work in a more general framework, as is the family of planar refracting linear systems with two zones, for which a new result about existence and uniqueness of limit cycles and saddle-loops is also shown. The achieved results are applied to the study of oscillations in an electronic circuit involving a single memristor cell, showing rigorously the appearance of limit cycles via the focus–saddle bifurcation analyzed in the paper. © 2018 Elsevier Ltd |
Funding agencies | Ministerio de Economia, Industria y Competitividad (MINECO). España Consejería de Economía y Conocimiento, Junta de Andalucía |
Project ID. | MTM2014-56272-C2-1-P
MTM2015-65608-P P12-FQM-1658 |
Citation | Ponce, E., Ros, F.J. y Vela, E. (2018). The boundary focus–saddle bifurcation in planar piecewise linear systems. Application to the analysis of memristor oscillators. Nonlinear Analysis: Real World Applications, 43, 495-514. https://doi.org/10.1016/j.nonrwa.2018.03.011. |
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