Results 11 to 20 of about 3,260 (131)

Coexistence of algebraic and non-algebraic limit cycles for quintic polynomial differential systems

Electronic Journal of Differential Equations, 2017
In the work by Gine and Grau [11], a planar differential system of degree nine admitting a nested configuration formed by an algebraic and a non-algebraic limit cycles explicitly given was presented.
Ahmed Bendjeddou, Rachid Cheurfa
doaj   +2 more sources

Planar chemical reaction systems with algebraic and non-algebraic limit cycles. [PDF]

J Math Biol
Abstract The Hilbert number H(n) is defined as the maximum number of limit cycles of a planar autonomous system of ordinary differential equations (ODEs) with right-hand sides containing polynomials of degree at most $$n \in {{\mathbb {N}}}$$ n
Craciun G, Erban R.
europepmc   +6 more sources

Algebraic Limit Cycles Bifurcating from Algebraic Ovals of Quadratic Centers [PDF]

International Journal of Bifurcation and Chaos, 2018
In the integrability of polynomial differential systems it is well known that the invariant algebraic curves play a relevant role. Here we will see that they can also play an important role with respect to limit cycles.In this paper, we study quadratic polynomial systems with an algebraic periodic orbit of degree [Formula: see text] surrounding a ...
Jaume Llibre, Yun Tian 0001
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Algebraic Limit Cycles in Piecewise Linear Differential Systems [PDF]

International Journal of Bifurcation and Chaos, 2018
This paper is devoted to study the algebraic limit cycles of planar piecewise linear differential systems. In particular, we present examples exhibiting two explicit hyperbolic algebraic limit cycles, as well as some one-parameter families with a saddle-node bifurcation of algebraic limit cycles.
Claudio A. Buzzi, Armengol Gasull, Joan Torregrosa   +2 more
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Algebraic limit cycles of planar cubic systems

Sibirskie Elektronnye Matematicheskie Izvestiya, 2020
Algebraic limit cycles of differential systems of the form \[\dot{x}=x+P_3(x,y),\quad \dot{y}=y+Q_3(x,y), \] where \(P_3(x,y)\) and \(Q_3(x,y)\) are homogeneous cubic polynomials, are studied. Note that the results of Theorem 1 were obtained much earlier in the monograph [\textit{V. N. Gorbuzov} and \textit{A. A.
Volokitin, E. P., Cheresiz, V. M.
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Algebraic theory of quantum synchronization and limit cycles under dissipation

SciPost Physics, 2022
Synchronization is a phenomenon where interacting particles lock their motion and display non-trivial dynamics. Despite intense efforts studying synchronization in systems without clear classical limits, no comprehensive theory has been found. We develop such a general theory based on novel necessary and sufficient algebraic criteria for persistently ...
Buča, B, Booker, C, Jaksch, D
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The classification of limits of 2n-cycle algebras

Indiana University Mathematics Journal, 1999
We obtain a complete classification of the locally finite algebras and the operator algebras, given as algebraic inductive limits and Banach algebraic inductive limits respectively, of direct systems: A_1 contained in A_2 contained in A_3 and so on. Here the A_k are 2n-cycle algebras, where n is at least 3 and the inclusions are of rigid type.
Donsig, Allan P., Power, S. C.
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Algebraic Analysis of Bifurcation and Limit Cycles for Biological Systems [PDF]

, 2008
In this paper, we show how to analyze bifurcation and limit cycles for biological systems by using an algebraic approach based on triangular decomposition, Gröbner bases, discriminant varieties, real solution classification, and quantifier elimination by partial CAD.
Niu, Wei, Wang, Dongming
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Counterexample to a Conjecture on the Algebraic Limit Cycles of Polynomial Vector Fields [PDF]

Geometriae Dedicata, 2005
In Geometriae Dedicata 79 (2000), 101{108, Rudolf Winkel conjectured: For a given algebraic curve f = 0 of degree m > 4 there is in general no polynomial vector ¯eld of degree less than 2m ¡ 1 leaving invariant f = 0 and having exactly the ovals of f = 0 as limit cycles. Here we show that this conjecture is not true.
Llibre Saló, Jaume, Pantazi, Chara
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Robust Nonlinear Regulation of Limit Cycle Oscillations in UAVs Using Synthetic Jet Actuators

Robotics, 2014
In this paper, a synthetic jet actuators (SJA)-based nonlinear robust controller is developed, which is capable of completely suppressing limit cycle oscillations (LCO) in UAV systems with parametric uncertainty in the SJA dynamics and unmodeled external
Natalie Ramos Pedroza, William MacKunis, Vladimir V. Golubev   +2 more
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