On the existence and uniqueness of limit cycles in planar continuous piecewise linear systems without symmetry

Keywords

Uniqueness, Piecewise linear function, Mathematics, Piecewise, Limit (mathematics)

References

• Limit cycles for planar piecewise linear differential systems via first integralsJaume Llibre, Eduardo Núñez, Antonio E. Teruel — 2002
• Qualitative Theory of Planar Differential SystemsFreddy Dumortier, Llibre, Jaume 1952-, Artés, Joan C. — 2006
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• Phase portraits of planar control systemsJaume Llibre, Jorge Sotomayor — 1996
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• Limit cycle studies for circuits containing one Esaki diodeLeopold Flatto — 1964
• Bifurcation Sets of Continuous Piecewise Linear Systems with Two ZonesE. Freire, Enrique Ponce, F. Rodrigo — 1998
• Planar systems of piecewise linear differential equations with a line of discontinuityFotios Giannakopoulos, Karin Pliete — 2001
• Neuronal Networks with Gap Junctions: A Study of Piecewise Linear Planar Neuron ModelsStephen Coombes — 2008
• Mathematical problems for the next centurySteve Smale — 1998
• Canonical Discontinuous Planar Piecewise Linear SystemsE. Freire, Enrique Ponce, Francisco Torres — 2012
• On the uniqueness and nonexistence of limit cycles for predator?prey systemsDongmei Xiao, Zhifeng Zhang — 2003
• Algorithms for finding hidden oscillations in nonlinear systems. The Aizerman and Kalman conjectures and Chua’s circuitsV. O. Bragin, V. I. Vagaitsev, Н. В. Кузнецов — 2011
• Cubic Lienard equations with linear dampingFreddy Dumortier, Christiane Rousseau — 1990
• Bifurcation Sets of Symmetrical Continuous Piecewise Linear Systems with Three ZonesE. Freire, Enrique Ponce, F. Rodrigo — 2002
• Relaxation oscillations in a system with a piecewise smooth drag coefficientS. J. Hogan — 2003

Cited by

• On the uniqueness of limit cycles in discontinuous Lienard-type systemsFangfang Jiang, Jitao Sun — 2014
• Birth of limit cycles for a class of continuous and discontinuous differential systems in (d + 2)–dimensionJaume Llibre, Marco Antônio Teixeira, Iris de Oliveira Zeli — 2015
• Limit Cycles Bifurcating from the Periodic Orbits of a Discontinuous Piecewise Linear Differentiable Center with Two ZonesJaume Llibre, Douglas D. Novaes, Marco Antônio Teixeira — 2015
• A Multiple Time Scale Coupling of Piecewise Linear Oscillators. Application to a Neuroendocrine SystemSoledad Fernández-García, Mathieu Desroches, Martin Krupa — 2015
• Structural stability of planar bimodal linear systemsJosep Ferrer, Marta Peña, Antoni Susín — 2013
• Canards in piecewise-linear systems: explosions and super-explosionsMathieu Desroches, E. Freire, S. J. Hogan — 2013
• Limit Cycle and Boundary Equilibrium Bifurcations in Continuous Planar Piecewise Linear SystemsEnrique Ponce, Javier Ros, Elísabet Vela — 2015
• Existence and Uniqueness of Limit Cycle in Discontinuous Planar Differential SystemsFangfang Jiang, Jitao Sun — 2016
• Uniqueness and Non-uniqueness of Limit Cycles for Piecewise Linear Differential Systems with Three Zones and No SymmetryJaume Llibre, Enrique Ponce, Clàudìa Valls — 2015
• On the Limit Cycles for a Class of Continuous Piecewise Linear Differential Systems with Three ZonesMaurício Firmino Silva Lima, Claudio Pessoa, Weber F. Pereira — 2012
• Dynamical analysis of periodic bursting in piece-wise linear planar neuron modelYing Ji, Xiaofang Zhang, Minjie Liang — 2015
• Existence of Chaotic Invariant Set in a Class of 4-Dimensional Piecewise Linear Dynamical SystemsSong-Mei Huan, Xiao‐Song Yang — 2014
• Limit Cycles Bifurcating from a Period Annulus in Continuous Piecewise Linear Differential Systems with Three ZonesMaurício Firmino Silva Lima, Claudio Pessoa, Weber F. Pereira — 2015
• Jump bifurcations in some degenerate planar piecewise linear differential systems with three zonesRodrigo D. Euzébio, Rubens Pazim, Enrique Ponce — 2016
• Bursting Behavior in the Piece-Wise Linear Planar Neuron Model with Periodic StimulationYing Ji, Yawei Wang — 2015
• LIMIT CYCLES OF PIECEWISE LINEAR DIFFERENTIAL SYSTEMS WITH THREE ZONES AND NO SYMMETRYJaume Llibre, Enrique Ponce, Audia Valls — 2015
• On the existence of discontinuous periodic solutions for a class of Liénard systems with impulsesFangfang Jiang, Jitao Sun — 2016
• Periodic Orbits Analysis in a Class of Planar Liénard Systems with State-Triggered JumpsFangfang Jiang, Wei Lü, Jitao Sun — 2016
• Limit cycle bifurcations near generalized homoclinic loop in piecewise smooth differential systemsLijun Wei, Xiang Zhang — 2015
• On the existence and uniqueness of a limit cycle for a Liénard system with a discontinuity lineFangfang Jiang, Junping Shi, Qing‐Guo Wang — 2016

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