Limit cycles for $Z_{2n}$-equivariant systems without infinite equilibria
Electronic Journal of Differential Equations, 2016 We analyze the dynamics of a class of $\mathbb{Z}_{2n}$-equivariant differential equations of the form $\dot{z}=pz^{n-1}\bar{z}^{n-2}+sz^{n}\bar{z}^{n-1}-\bar{z}^{2n-1}$, where z is complex, the time t is real, while p and s are complex parameters ...
Isabel S. Labouriau, Adrian C. Murza
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Non-contact robotic manipulation of floating objects: exploiting emergent limit cycles. [PDF]
Front Robot AI, 2023 Jacquart S, Obayashi N, Hughes J.
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Polynomial differential systems with explicit non-algebraic limit cycles
Electronic Journal of Differential Equations, 2012 Up to now all the examples of polynomial differential systems for which non-algebraic limit cycles are known explicitly have degree at most 5. Here we show that already there are polynomial differential systems of degree at least exhibiting explicit ...
Rebiha Benterki, Jaume Llibre
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Variational and phase response analysis for limit cycles with hard boundaries, with applications to neuromechanical control problems. [PDF]
Biol Cybern, 2022 Wang Y, Gill JP, Chiel HJ, Thomas PJ.
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Synchronization of Coupled Limit Cycles [PDF]
Journal of Nonlinear Science, 2011 Journal of Nonlinear Science ...
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Non-existence of limit cycles for planar vector fields
Electronic Journal of Differential Equations, 2014 This article presents sufficient conditions for the non-existence of limit cycles for planar vector fields. Classical methods for the nonexistence of limit cycles are connected with the theory developed here.
Jaume Gine
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Science Journal of University of Zakho, 2017 The main purpose of this paper is to study the existence of polynomial inverse integrating factor and first integral, and non-existence of limit cycles for all systems. Furthermore, we consider some applications.
Ahmed M. Hussien
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Coexistence of chaotic attractor and unstable limit cycles in a 3D dynamical system. [PDF]
Open Res Eur, 2021 Constantinescu D, Tigan G, Zhang X.
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Non-existence of limit cycles via inverse integrating factors
Electronic Journal of Differential Equations, 2011 It is known that if a planar differential systems has an inverse integrating factor, then all the limit cycles contained in the domain of definition of the inverse integrating factor are contained in the zero set of this function.
Leonardo Laura-Guarachi +2 more
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Unstable eigenvectors and reduced amplitude spaces specifying limit cycles of coupled oscillators with simultaneously diagonalizable matrices: with applications from electric circuits to gene regulation. [PDF]
Eur Phys J B, 2022 Mongkolsakulvong S, Frank TD.
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