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On the Limit Cycles of Linear Differential Systems with Homogeneous Nonlinearities
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- Journal:
- Canadian Mathematical Bulletin / Volume 58 / Issue 4 / 01 December 2015
- Published online by Cambridge University Press:
- 20 November 2018, pp. 818-823
- Print publication:
- 01 December 2015
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- Article
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We consider the class of polynomial differential systems of the form
$\dot{x} =\,\lambda x\,-\,y\,+\,{{P}_{n}}\left( x,\,y \right)$ , 
$\dot{y} =\,x\,+\,\lambda y\,+\,{{Q}_{n}}\left( x,\,y \right)$ where 
${{P}_{n}}$ and 
${{Q}_{n}}$ are homogeneous polynomials of degree 
$n$ . For this class of differential systems we summarize the known results for the existence of limit cycles, and we provide new results for their nonexistence and existence.
