The generalized polynomial Moon-Rand system

The Moon-Rand systems, developed to model control flexible space structures, are systems of differential equations in R3 of the form u̇=v,v̇=−u−uw,ẇ=−λw+f(u,v).We give a partially positive answer to a recently conjecture for a special class of such systems, called the generalized polynomial Moon-Rand systems in the case when λ∈(0,∞) and f is either a homogeneous cubic, quartic, quintic or sextic polynomial.