Results 21 to 30 of about 155,898 (247)
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.
Jaume Llibre
exaly +2 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.
Armengol Gasull +2 more
exaly +4 more sources
On the 16th Hilbert problem for algebraic limit cycles
Journal of Differential Equations, 2010 For a polynomial planar vector field of degree n ≥ 2 with generic invariant algebraic curves we show that the maximum number of algebraic limit cycles is 1 + (n − 1)(n − 2)/2 when n is even, and (n − 1)(n − 2)/2 when n is odd. Furthermore, these upper bounds are reached.
Jaume Llibre
exaly +3 more sources
Differential systems with algebraic and non-algebraic limit cycles explicitly given
Methods of Functional Analysis and Topology, 2022 R. Boukoucha
semanticscholar +2 more sources
Kolmogorov differential systems with prescribed algebraic limit cycles
Sibirskie Elektronnye Matematicheskie Izvestiya, 2021 R. Chouader, S. Benyoucef, A. Bendjeddou
semanticscholar +3 more sources
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
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
The algebraic curves of planar polynomial differential systems with homogeneous nonlinearities
Electronic Journal of Qualitative Theory of Differential Equations, 2021 We consider planar polynomial systems of ordinary differential equations of the form $\dot x = x + P_n(x,y)$, $\dot y = y + Q_n(x,y)$, where $P_n(x,y),\ Q_n(x,y)$ are homogeneous polynomials of degree $n$.
Vladimir Cheresiz, Evgenii Volokitin
doaj +1 more source
A CLASS OF KOLMOGOROV SYSTEM WITH EXACT ALGEBRAIC LIMIT CYCLES [PDF]
International Journal of Pure and Apllied Mathematics, 2015 S. Benyoucef, A. Bendjeddou
semanticscholar +2 more sources