scholarly journals Computational complexity of solving polynomial differential equations over unbounded domains

2016 ◽  
Vol 626 ◽  
pp. 67-82 ◽  
Author(s):  
Amaury Pouly ◽  
Daniel S. Graça
Keyword(s):  
Computational Complexity ◽  
Differential Equations ◽  
Unbounded Domains ◽  
Polynomial Differential Equations

scholarly journals On local fractional operators View of computational complexity: Diffusion and relaxation defined on cantor sets

2016 ◽  
Vol 20 (suppl. 3) ◽  
pp. 755-767 ◽  
Author(s):  
Xiao-Jun Yang ◽  
Zhi-Zhen Zhang ◽  
Tenreiro Machado ◽  
Dumitru Baleanu
Keyword(s):  
Computational Complexity ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Complex Systems ◽  
Exact Solutions ◽  
Fractional Derivatives ◽  
Cantor Sets ◽  
Fractional Operators ◽  
Fractional Partial Differential Equations ◽  
Comparative Results

This paper treats the description of non-differentiable dynamics occurring in complex systems governed by local fractional partial differential equations. The exact solutions of diffusion and relaxation equations with Mittag-Leffler and exponential decay defined on Cantor sets are calculated. Comparative results with other versions of the local fractional derivatives are discussed.

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.

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