Abstract
In this paper, we characterize all the irreducible Darboux polynomials and polynomial first integrals of the FitzHugh-Nagumo system by the called characteristic curves method which involves the theory of weight homogeneous polynomials. It has been ever widely used to give a complete classification of Darboux polynomials of some systems. However, it does not work for the FitzHugh-Nagumo system. Thus, we introduce an “assistant” system and classify its invariant algebraic surfaces finally.
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