Limit Cycles of Differential Equations

By Colin Christopher, Chengzhi Li. 2007

238 citations recorded by the source corpus.

Subfields: Geometry and Topology, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/175ef2e0465b915651a28bafcc71bc02dbc87ba7

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In Numerical Analysis

Citations in the corpus

Limit cycles for discontinuous quadratic differential systems with two zones (2014, background): “The limit cycles of continuous planar quadratic polynomial differential systems has been studied intensively, see for instance the books [7, 17] and the hundreds of references quoted therein.”
Hopf and homoclinic bifurcations for near-Hamiltonian systems (2017, background): “Most of them consider the cases of f (x, y) = 0 and g(x, y) = g1(x)y, where g1(x) is a polynomial in x, for instance see books [1,6].”
On the limit cycles of polynomial vector field (2011, background): “This has been studied intensively perturbing the periodic orbits of the centers of the quadratic polynomial differential systems see the book of Christopher and Li [6], and the references quoted there.”
On extended Chebyshev systems with positive accuracy (2017, background): “In fact these studies provide lower bounds for the so called weak Hilbert 16th problem, see [2, 14].”
On the number of zeros of Abelian integrals (2008, background): “Li (see part 2 of the book [10] and references therein).”
Abelian Integrals and Limit Cycles (2012, background): “For more details, see for example [33] and the second part of [6].”
Center conditions at infinity for Abel differential equations (2010, background): “Many deep partial results have been obtained (see [7], [8], [28]–[30], [34], [38], [42], [44], [45], [48], [55], [58], [63], [65], [72] and references therein) but general center conditions are not known even for F.”