Darboux Polynomials for Lotka–Volterra Systems in Three Dimensions
Darboux Polynomials for Lotka–Volterra Systems in Three Dimensions
We consider Lotka-Volterra systems in three dimensions depending on three real parameters. By using elementary algebraic methods we classify the Darboux polynomials (also known as second integrals) for such systems for various values of the parameters, and give the explicit form of the corresponding cofactors. More precisely, we show that …