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On the Limit Cycles of the Polynomial Differential Systems with a Linear Node and Homogeneous Nonlinearities

✍ Scribed by Llibre, Jaume; Yu, Jiang; Zhang, Xiang


Book ID
125485115
Publisher
World Scientific Publishing Company
Year
2014
Tongue
English
Weight
312 KB
Volume
24
Category
Article
ISSN
0218-1274

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✦ Synopsis


We consider the class of polynomial differential equations αΊ‹ = Ξ»x + P~n~(x, y), ẏ = ΞΌy + Q~n~(x, y) in ℝ^2^ where P~n~(x, y) and Q~n~(x, y) are homogeneous polynomials of degree n > 1 and Ξ» β‰  ΞΌ, i.e. the class of polynomial differential systems with a linear node with different eigenvalues and homogeneous nonlinearities. For this class of polynomial differential equations, we study the existence and nonexistence of limit cycles surrounding the node localized at the origin of coordinates.


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