Abstract
We propose for symmetric three-dimensional piecewise linear systems with three zones a unified approach to analyze both Hopf and Hopf-pitchfork bifurcations. For the equilibrium at the origin, the crossing of a complex eigenvalue pair through the imaginary axis of complex plane, with the possible simultaneous crossing of a real eigenvalue, is considered. Some results related to the bifurcation of limit cycles are provided, and an illustrative example is included.
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Acknowledgment
Authors are partially supported by the Ministerio de Ciencia y Tecnología, Plan Nacional I+D+I, in the frame of projects MTM2010-20907 and MTM2012-31821, and by the Consejería de Economía, Innovación, Ciencia y Empleo de la Junta de Andalucía under grant FQM-1658.
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Ponce, E., Ros, J., Vela, E. (2015). A Unified Approach to Piecewise Linear Hopf and Hopf-Pitchfork Bifurcations. In: Tost, G., Vasilieva, O. (eds) Analysis, Modelling, Optimization, and Numerical Techniques. Springer Proceedings in Mathematics & Statistics, vol 121. Springer, Cham. https://doi.org/10.1007/978-3-319-12583-1_12
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DOI: https://doi.org/10.1007/978-3-319-12583-1_12
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