Relationships between Darboux Integrability and Limit Cycles for a Class of Able Equations
نویسندگان
چکیده
We consider the class of polynomial differential equation x = 2 ( , ) ( , ) ( , ) n n m n m P x y P x y P x y + + + + , 2 ( , ) ( , ) ( , ) n n m n m y Q x y Q x y Q x y + + = + + . For , 1 m n ≥ where i P and i Q are homogeneous polynomials of degree i. Inside this class of polynomial differential equation we consider a subclass of Darboux integrable systems. Moreover, under additional conditions we proved such Darboux integrable systems can have at most 1 limit cycle.
منابع مشابه
Relationships between Darboux Integrability and Limit Cycles for a Class of Able Equations
We consider the class of polynomial differential equation x&= , 2(,)(,)(,)nnmnmPxyPxyPxy++++2(,)(,)(,)nnmnmyQxyQxyQxy++&=++. For where and are homogeneous polynomials of degree i. Inside this class of polynomial differential equation we consider a subclass of Darboux integrable systems. Moreover, under additional conditions we proved such Darboux integrable systems can have at most 1 limit cycle.
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