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In [1] a two-dimensional generalized Lotka-Volterra model was established. In this paper we analyze that model which (after scaling) contains five parameters. The generalized model includes explosive, conservative, and stable systems [-23]. The condition for supercritical Hopf bifurcation is established. The model also shows zip bifurcation [14]. Some integrable cases are given together with the first integrals. The model is related to nonlinear chemical and biological systems, e.g. the oscillatory BZ-reaction.AMS subject dassification (1991). 92D25.

Purpose We aimed to develop and assess the psychometric characteristics of the Hungarian language version of two well-being capability measures, the ICEpop CAPability measure for Adults/Older people (ICECAP-A/-O), and to establish population norms. Methods A cross-sectional survey was performed involving a representative sample of the Hungarian population. Socio-demographic characteristics, the use and provision of informal care were recorded. The Minimum European Health Module (MEHM), EQ-5D-5L, WHO-5 well-being index, happiness and life satisfaction visual analogue scale (VAS), Satisfaction with Life Scale (SWLS) measures were applied alongside the ICECAP-A (age-group 18–64) and ICECAP-O (age-group 65+). Results Altogether 1568 and 453 individuals completed the ICECAP-A/-O questionnaires, respectively. Cronbach’s alpha was 0.86 for both measures (internal consistency). Subgroup analyses showed positive associations between ICECAP-A/-O scores and marital status, employment, income, health status (MEHM) and informal care use (construct validity). Pearson correlations were strong (r > 0.5; p < 0.01) between ICECAP-A/-O indexes and EQ-5D-5L, WHO-5, happiness and satisfaction VAS and SWLS scores (convergent validity). The age, education, and marital status were no longer significant in the multiple regression analysis. Test–retest average (SD) scores were 0.88 (0.11) and 0.89 (0.10) for the ICECAP-A, and equally 0.86 (0.09) for the ICECAP-O (reliability). Conclusion This is the first study to provide ICECAP-A/-O population norms. Also, it is the first to explore associations with WHO-5 well-being index which, alongside the MEHM measures, enable estimates from routinely collected international health statistics. The Hungarian ICECAP-A/-O proved to be valid and reliable measurement tools. Socio-demographic characteristics had minor or no impact on ICECAP-A/-O. Other influencing factors deserve further investigation in future research.