×
Zhao, Wenbo; Ma, Caocuan; Zheng, Taotao; Sun, Xiao-Ke

Periodic solutions of multispecies mutualism system with infinite delays. (English) Zbl 1470.92270

Abstr. Appl. Anal. 2014, Article ID 127876, 5 p. (2014).
Summary: We studied the delayed periodic mutualism system with Gilpin-Ayala effect. Some new and interesting sufficient conditions are obtained to guarantee the existence of periodic solution for the multispecies mutualism system with infinite delays. Our method is based on Mawhin’s coincidence degree. To the best knowledge of the authors, there is no paper considering the existence of periodic solutions for \(n\)-species mutualism system with infinite delays.

MSC:

92D25 Population dynamics (general)
34C25 Periodic solutions to ordinary differential equations
PDF BibTeX XML Cite
\textit{W. Zhao} et al., Abstr. Appl. Anal. 2014, Article ID 127876, 5 p. (2014; Zbl 1470.92270)
Full Text: DOI

References:

[1] Fan, M.; Wang, K.; Jiang, D., Existence and global attractivity of positive periodic solutions of periodic \(n\)-species Lotka-Volterra competition systems with several deviating arguments, Mathematical Biosciences, 160, 1, 47-61 (1999) · Zbl 0964.34059
[2] Xia, Y. H.; Han, M., New conditions on the existence and stability of periodic solution in lotka-volterra’s population system, SIAM Journal on Applied Mathematics, 69, 6, 1580-1597 (2009) · Zbl 1181.92084
[3] Xia, Y., Periodic solution of certain nonlinear differential equations: via topological degree theory and matrix spectral theory, International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, 22, 8 (2012) · Zbl 1258.34114
[4] Gu, X.; Wang, H.; Wong, P. J. Y.; Xia, Y., Existence and stability of periodic solution to delayed nonlinear differential equations, Abstract and Applied Analysis, 2014 (2014) · Zbl 1470.34178
[5] Yang, F.; Jiang, D.; Ying, A., Existence of positive solution of multidelays facultative mutualism system, Journal of Engineering Mathematics, 3, 64-68 (2002) · Zbl 1055.34137
[6] Chen, F.; Shi, J.; Chen, X., Periodicity in a Lotka-Volterra facultative mutualism system with several delays, Journal of Engineering Mathematics, 21, 3, 403-409 (2004)
[7] Xia, Y. H.; Cao, J.; Cheng, S. S., Periodic solutions for a Lotka-Volterra mutualism system with several delays, Applied Mathematical Modelling, 31, 9, 1960-1969 (2007) · Zbl 1167.34343
[8] Gaines, R. E.; Mawhin, J. L., Coincidence Degree and Nonlinear Differential Equations (1977), Berlin, Germany: Springer, Berlin, Germany · Zbl 0339.47031
[9] LaSalle, J. P., The Stability of Dynamical System (1976), Philadelphia, Pa, USA: Society for Industrial and Applied Mathematics, Philadelphia, Pa, USA · Zbl 0364.93002
[10] Berman, A.; Plemmons, R. J., Nonnegative Matrices in the Mathematical Science (1929), New York, NY, USA: Academic Press, New York, NY, USA
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.