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Limit Cycles for Piecewise Linear Differential Systems via Poincaré–Miranda Theorem

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Extended Abstracts Spring 2018

Part of the book series: Trends in Mathematics ((RPCRMB,volume 11))

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In Gasull and Mañosa (Periodic orbits of discrete and continuous dynamical systems via Poincaré–Miranda theorem, Preprint 2018 [2]), we develop an effective procedure to prove the existence, determine the number, and locate periodic orbits of dynamical systems of both discrete and continuous nature. It is based on the use of the Poincaré–Miranda theorem. This note presents one of the results obtained in that paper: a new example of piecewise linear differential system with three limit cycles.

The authors are supported by Ministry of Economy, Industry and Competitiveness, State Research Agency of the Spanish Government through grants MTM2016-77278-P (MINECO/AEI/FEDER, UE, first author) and DPI2016-77407-P (MINECO/AEI/FEDER, UE, second author). The first author is also supported by the grant 2017-SGR-1617 from AGAUR, Generalitat de Catalunya. The second author acknowledges the group’s research recognition 2017-SGR-388 from AGAUR, Generalitat de Catalunya.

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Correspondence to Armengol Gasull .

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Gasull, A., Mañosa, V. (2019). Limit Cycles for Piecewise Linear Differential Systems via Poincaré–Miranda Theorem. In: Korobeinikov, A., Caubergh, M., Lázaro, T., Sardanyés, J. (eds) Extended Abstracts Spring 2018. Trends in Mathematics(), vol 11. Birkhäuser, Cham.

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