Algebraic solutions of polynomial differential equations and foliations in dimension two

1988 ◽  
pp. 192-232 ◽  
Author(s):  
Alcides Lins Neto
Keyword(s):  
Differential Equations ◽  
Polynomial Differential Equations ◽  
Algebraic Solutions

The number of limit cycles of certain polynomial differential equations

1984 ◽  
Vol 98 (3-4) ◽  
pp. 215-239 ◽  
Author(s):  
T. R. Blows ◽  
N. G. Lloyd
Keyword(s):  
Differential Equations ◽  
Limit Cycles ◽  
Small Amplitude ◽  
Two Dimensional ◽  
Differential Systems ◽  
Quadratic Systems ◽  
Polynomial Differential Equations ◽  
Image Position ◽  
Cubic Systems

SynopsisTwo-dimensional differential systemsare considered, where P and Q are polynomials. The question of interest is the maximum possible numberof limit cycles of such systems in terms of the degree of P and Q. An algorithm is described for determining a so-called focal basis; this can be implemented on a computer. Estimates can then be obtained for the number of small-amplitude limit cycles. The technique is applied to certain cubic systems; a class of examples with exactly five small-amplitude limit cycles is constructed. Quadratic systems are also considered.

scholarly journals Algorithms and algebraic solutions of decay chain differential equations for stable and unstable nuclide fractionation

2020 ◽  
Vol 246 ◽  
pp. 106907
Author(s):  
Austin Ladshaw ◽  
Alexander I. Wiechert ◽  
Yong-ha Kim ◽  
Costas Tsouris ◽  
Sotira Yiacoumi
Keyword(s):  
Differential Equations ◽  
Decay Chain ◽  
Algebraic Solutions
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