Limit cycles of polynomial systems with homogeneous non-linearities
نویسندگان
چکیده
منابع مشابه
On the Limit Cycles of the Polynomial Differential Systems with a Linear Node and Homogeneous Nonlinearities
We consider the class of polynomial differential equations ẋ = λx + Pn(x, y), ẏ = μy + Qn(x, y) in R where Pn(x, y) and Qn(x, y) are homogeneous polynomials of degree n > 1 and λ 6= μ, 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 non–e...
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We consider a system of the form ẋ = Pn(x, y) + xRm(x, y), ẏ = Qn(x, y) + yRm(x, y), where Pn(x, y), Qn(x, y) and Rm(x, y) are homogeneous polynomials of degrees n, n and m, respectively, with n ≤ m. We prove that this system has at most one limit cycle and that when it exists it can be explicitly found. Then we study a particular case, with n = 3 and m = 4. We prove that this quintic polynomia...
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 1989
ISSN: 0022-247X
DOI: 10.1016/0022-247x(89)90021-8