Zhang, Zhengqiu; Wang, Zhicheng Periodic solution for a two-species nonautonomous competition Lotka-Volterra patch system with time delay. (English) Zbl 1003.34060 J. Math. Anal. Appl. 265, No. 1, 38-48 (2002). By using the continuation theorem of coincidence degree theory, the existence of a positive periodic solution to a two-species nonautonomous competition Lotka-Volterra patch system with time delay \[ \begin{aligned} x'_1(t)&=x_1(t)[r_1(t)-a_1(t)x_1(t)-b_1(t)y(t)]+D_1(t)[x_2(t)-x_1(t)],\cr x'_2(t)&=x_2(t)[r_2(t)-a_2(t)x_2(t)]+D_2(t)[x_1(t)-x_2(t)],\cr y'(t)&=y(t) \Biggl[r_3(t)-a_3(t)x_1(t)-b_3(t)y(t)-\beta(t)\int_{-\tau}^{0}K(s)y(t+s) ds\Biggr], \end{aligned} \] is established, where \(r_i(t), a_i(t)\), \(i=1,2,3\), \(D_i(t)\), \(i=1,2\), \(b_i(t)\) \(i=1,3\), and \(\beta(t)\) is any positive periodic continuous function with period \(\omega>0\), \(\tau\) is a nonnegative constant and \(K(s)\) is a continuous nonnegative function on \([-\tau,0]\). Reviewer: Yongkun Li (Kunming) Cited in 32 Documents MSC: 34K13 Periodic solutions to functional-differential equations 92D25 Population dynamics (general) Keywords:competition Lotka-Volterra system; positive periodic; continuation theorem of coincidence degree; topological degree PDFBibTeX XMLCite \textit{Z. Zhang} and \textit{Z. Wang}, J. Math. Anal. Appl. 265, No. 1, 38--48 (2002; Zbl 1003.34060) Full Text: DOI References: [1] Zhang, J. G.; Chen, L. S.; Chen, X. D., Persistence and global stability for two-species nonautonomous competition Lotka-Volterra patch-system with time delay, Nonlinear Anal., 37, 1019-1028 (1999) · Zbl 0949.34060 [2] Gaines, R. E.; Mawhin, J. L., Coincidence Degree and Nonlinear Differential Equations (1977), Springer-Verlag: Springer-Verlag Berlin · Zbl 0326.34021 [3] Li, Y., Periodic solution of a periodic delay predator-prey system, Proc. Amer. Math. Soc., 127, 1331-1335 (1999) · Zbl 0917.34057 [4] Li, Y., On a periodic neutral delay Lotka-Volterra system, Nonlinear Anal., 39, 767-778 (2000) · Zbl 0943.34058 [5] Ma, S. W.; Wang, Z. C.; Yu, J. S., Coincidence degree and periodic solutions of Duffing equations, Nonlinear Anal., 34, 443-460 (1998) · Zbl 0931.34048 [6] Ma, S. W.; Wang, Z. C.; Yu, J. S., An abstract existence theorem at resonance and its applications, J. Differential Equations, 145, 274-294 (1998) · Zbl 0940.34056 [7] Ma, S. W.; Wang, Z. C.; Yu, J. S., Periodic solutions of periodically perturbed functional-differential equations, Chinese Sci. Bull., 43, 1956-1959 (1998) · Zbl 0992.34054 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.