Cui, Jing’an; Chen, Lansun Stable positive periodic solution of time dependent Lotka-Volterra periodic mutualistic system. (English) Zbl 0808.34055 Acta Math. Sci. 14, No. 1, 19-23 (1994). The main result of this paper is: Consider a Lotka-Volterra mutualistic system in a periodic environment, \(dx_ i/dt = x_ i\) \((r_ i(t) + \sum^ n_{j = 1} a_{ij} (t)x_ j)\) \((i = 1, \dots, n)\), with \(a_{ii} (t) < 0\) and \(a_{ij} (t) \geq 0\) \((i \neq j)\) and with \(\omega\)-periodic \((0 < \omega < + \infty)\) functions \(r_ i (t)\) and \(a_{ij} (t)\). Assume \(\int^ \omega_ 0 r_ i(t) dt > 0\) and let \(\overline a_{ij} = \max_{0 \leq t \leq \omega} a_{ij} (t)\). If the leading principal minors of the matrix \((\overline a_{ij})\) alternate in sign, then the system has a unique and globally asymptotically stable positive \(\omega\)-periodic solution. This result extends a somewhat similar result for time-independent Lotka-Volterra mutualistic systems. The paper implicitly assumes continuity of the \(a_{ij} (t)\)’s. It ends with the “Note: The proof of theorem 2 has some errors, but it can be corrected easily”. The corrections should have been indicated and were not. Reviewer: C.A.Braumann (Evora) Cited in 2 Documents MSC: 34D20 Stability of solutions to ordinary differential equations 34C25 Periodic solutions to ordinary differential equations 92D25 Population dynamics (general) Keywords:stable periodic solutions; Lotka-Volterra mutualistic system in a periodic environment PDFBibTeX XMLCite \textit{J. Cui} and \textit{L. Chen}, Acta Math. Sci. 14, No. 1, 19--23 (1994; Zbl 0808.34055)