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A cubic system with eight small-amplitude limit cycles

✍ Scribed by Shucheng Ning; Shilong Ma; Keng Huat Kwek; Zhiming Zheng

Publisher
Elsevier Science
Year
1994
Tongue
English
Weight
356 KB
Volume
7
Category
Article
ISSN
0893-9659

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✦ Synopsis

In E.M. James and N.G. Lloyd's paper A Cubic System with Eight Small-Amplitude Limit Cycles [l], a set of conditions is given that ensures the origin to be a fine focus of order eight and eight limit cycles to bifurcate from the origin by perturbing parameters. We find that one of the conditions, as = e*a7, where 666/97 < (T* < 103/15, can be weakened as as = (~*a7 or as = OraT, where 283/125 < (21 < 284/125.

In [l], deriving above conditions is reduced to finding the real solutions of a system of some algebraic equations and inequalities. When verifying these conditions by solving this system in a different ordering, we find another real solution to the system, which is leading to above improvement of the conditions.

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