A An Integrable Class of Polynomial Differential Systems with an Explicit Limit Cycle
DOI:
https://doi.org/10.5269/bspm.83362Abstract
We consider a multi-parameter family of polynomial differential systems. Under suitable conditions on the parameters,
we establish the integrability of the system and derive an explicit expression for a first integral.
Moreover, we prove that the system admits a unique algebraic limit cycle, which is explicitly determined,
and that no other periodic orbits exist. Finally, illustrative examples are presented to demonstrate the applicability of our results.
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