A counterexample of a theorem by Tsolas et al. and an independent result by Zaborszky et al. [with reply]

Recent results on the composition of the stability boundary by N.A. Tsolas et al. (IEEE Trans. Circuits Syst., vol.CAS-32, no.10, pp.1041-9, Oct. 1985) and J. Zaborszky et al. (Proc. IFAC Symp. Power Syst. Power Plant. Contr., Beijing, China, Aug. 1986, pp.597-603) claimed that it consisted of the stable manifolds of index-one unstable equilibria and their closures. A counterexample shows the potential existence of additional structures within the boundary. This finding invalidates numerous theorems published in the literature. The author concedes that the counterexample to the theorem in the paper by N.A. Tsolas et al. is unassailable and identifies the error in his proof