Rational bases of $GL(2,\mathbb R)$-comitants and of $GL(2,\mathbb R)$-invariants for the planar system of differential equations with nonlinearities of the fourth degree

This paper is devoted to the construction of minimal rational bases of $GL(2,\mathbb R)$-comitants and minimal rational bases of $GL(2,\mathbb R)$-invariants for the bidimensional system of differential equations with nonlinearities of the fourth degree. For this system, three minimal rational bases of $GL(2,\mathbb R)$-comitants and two minimal rational bases of $GL(2,\mathbb R)$-invariants were constructed. It was established that any minimal rational basis of $GL(2,\mathbb R)$-comitants contains 13 comitants and each minimal rational basis of $GL(2,\mathbb R)$-invariants contains 11 invariants.