Abstract. We consider the predator-prey system with a fairly general functional response of Holling type and give a necessary and sufficient condition under which this system has exactly one stable limit cycle. Our result extends previous results and is an answer to a conjecture which was recently presented by Sugie, Miyamoto and Morino.

Formation constants in water of 1:1 benzo-18-crown-6 (B18C6)–metal ion complexes and the B18C6 solubility in water were determined at 25 °C by conductometry or potentiometry with ion-selective electrodes and spectrophotometry, respectively. The selectivity sequences of B18C6 for metal ions in water are Pb2+>Ba2+>Sr2+>Ag+>K+>Tl+>Na+>Rb+. In each case of alkali and alkaline earth metal ions, the more closely a metal ion fits into the B18C6 cavity, the more stable is the B18C6–metal ion complex. Although the solvation power of water for an alkali metal ion is not the largest of all solvents, the formation constant of a given B18C6–alkali metal ion complex in water is by far the smallest of all solvents. The transfer activity coefficients (γ) from water to nonaqueous solvents of the B18C6–metal ion complexes were then calculated from the formation constants of the B18C6 complexes, γ values of B18C6 (obtained from solubilities of B18C6), and γ values of the uncomplexed metal ions. The γ value of B18C6 is larger than those of B18C6–alkali metal ion complexes. This shows that when B18C6 forms a complex with an alkali metal ion, the B18C6 complex becomes more soluble in nonaqueous solvents than in water, compared with uncomplexed B18C6.