函数f(x;A,B)=-x+(Acosx+B)/sinx的性质

The properties of the function f(x; A, B)= -x + (Acosx + B)/sinx

讨论了函数f(x;A,B)=-x+(Acosx+B)/sinx在不同系数情况下的单调性,并给出了反函数的存在性,完整地刻划了其性态。这类函数在给出线性自治RDDEx(t)+ax(t)+bx(t-τ)+dx(t-τ)=0零解渐进稳定的充要条件,并直接从方程的系数预报稳定性与非稳定性中起重要作用。

The monotony of and the existence of the inverse function of the function f (x; A, B) = - x+ (Acosx + B) /sinx under the different coefficients are discussed, and the behavior of the inverse function is fully described. This function plays an important role in the establishing necessary and sufficient conditions for asymptotic stability of zero solution and predicting stability or instability directly from the coefficients of the equation x(t)+a(x(t)+bx(t-τ)+dx(t-τ)=0.