Results 11 to 20 of about 101,257 (246)
On the uniqueness of algebraic limit cycles for quadratic polynomial differential systems with two pairs of equilibrium points at infinity [PDF]
Geometriae Dedicata, 2017 Agraïments: The second author is partially supported by FCT/Portugal through UID/MAT/04459/2013.Algebraic limit cycles in quadratic polynomial differential systems started to be studied in 1958, and few years later the following conjecture appeared ...
Llibre, Jaume, Valls, Clàudia
core +4 more sources
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
openaire +5 more sources
Uniqueness of Algebraic Limit Cycles for Quadratic Systems
Journal of Mathematical Analysis and Applications, 2001 All known quadratic systems (QS) having an algebraic limit cycle are contained in five families. The degree of the algebraic curve containing the limit cycle is 4 in four of these families and 2 for the other one. Furthermore, it is also known that if there is another QS having an algebraic limit cycle, it should have at least degree 5. The main result
Chavarriga, Javier +2 more
openaire +4 more sources
Explicit non-algebraic limit cycles for polynomial systems
Journal of Computational and Applied Mathematics, 2007 We consider a system of the form x'=P_n(x,y)+xR_m(x,y), y'=Q_n(x,y)+yR_m(x,y), where P_n(x,y), Q_n(x,y) and R_m(x,y) are homogeneous polynomials of degrees n, n and m, respectively, with n<=m. We prove that this system has at most one limit cycle and that when it exists it can be explicitly found.
Gasull, A. +2 more
openaire +4 more sources
Number of Limit Cycles for Planar Systems with Invariant Algebraic Curves
Qualitative Theory of Dynamical Systems, 2023 AbstractFor planar polynomials systems the existence of an invariant algebraic curve limits the number of limit cycles not contained in this curve. We present a general approach to prove non-existence of periodic orbits not contained in this given algebraic curve.
Gasull, Armengol, Giacomini, Hector
openaire +5 more sources
AxiomsIn this paper, two classes of near-Hamiltonian systems with a nilpotent center are considered: the coexistence of algebraic limit cycles and small limit cycles.
Huimei Liu, Meilan Cai, Feng Li
doaj +3 more sources
Algebraic limit cycles of degree 4 for quadratic systems
Journal of Differential Equations, 2004 This interesting paper contains basic concepts on algebraic curves and some results on polynomial differential systems having invariant algebraic curves. The main result is the proof that quadratic systems have exactly four different families of algebraic limit cycles of degree four.
Chavarriga, Javier +2 more
openaire +3 more sources
Rational Lyapunov Functions and Stable Algebraic Limit Cycles [PDF]
IEEE Transactions on Automatic Control, 2014 The main goal of this technical note is to show that the class of systems described by a planar differential equation having a rational proper Lyapunov function has asymptotically stable sets which are either locally asymptotically stable equilibrium points, stable algebraic limit cycles or asymptotically stable algebraic graphics. The use of the Zubov
Emmanuel Moulay
openaire +4 more sources
Interpretability and Representability of Commutative Algebra, Algebraic Topology, and Topological Spectral Theory for Real-World Data. [PDF]
Adv Intell DiscovThis article investigates how persistent homology, persistent Laplacians, and persistent commutative algebra reveal complementary geometric, topological, and algebraic invariants or signatures of real‐world data. By analyzing shapes, synthetic complexes, fullerenes, and biomolecules, the article shows how these mathematical frameworks enhance ...
Ren Y, Wei GW.
europepmc +2 more sources
Limit Cycles of Polynomially Integrable Piecewise Differential Systems
Axioms, 2023 In this paper, we study how many algebraic limit cycles have the discontinuous piecewise linear differential systems separated by a straight line, with polynomial first integrals on both sides.
Belén García +3 more
doaj +1 more source