Wang, Kaifa; Zhang, Na; Niu, Decao Periodic oscillations in a spatially explicit model with delay effect for vegetation dynamics in freshwater marshes. (English) Zbl 1228.92080 J. Biol. Syst. 19, No. 2, 131-147 (2011). Summary: Time delay is incorporated into a spatially explicit model for vegetation dynamics in freshwater marshes and the effect of the delay is investigated by using qualitative analysis and numerical simulations. If the specific rate of plant senescence is sufficiently small then spatial homogeneity will be induced eventually for any delay, while if it is large, then a switches may occurs as time delay increases and there is a periodic oscillations if it exceed a critical value. Thus, the delay time in the ecosystem may be one of the important factors to induce temporal fluctuation in nature. Cited in 3 Documents MSC: 92D40 Ecology 34K60 Qualitative investigation and simulation of models involving functional-differential equations 34K11 Oscillation theory of functional-differential equations 92C80 Plant biology 65C20 Probabilistic models, generic numerical methods in probability and statistics Keywords:delay time; stability; periodic solution; pattern formation PDFBibTeX XMLCite \textit{K. Wang} et al., J. Biol. Syst. 19, No. 2, 131--147 (2011; Zbl 1228.92080) Full Text: DOI References: [1] DOI: 10.1086/508671 · doi:10.1086/508671 [2] DOI: 10.2307/1939378 · doi:10.2307/1939378 [3] Wang W., Acta Phytoecological Sinica 20 pp 449– [4] Wang W., Acta Phytoecological Sinica 20 pp 460– [5] DOI: 10.1111/j.1526-100X.2007.00332.x · doi:10.1111/j.1526-100X.2007.00332.x [6] DOI: 10.2307/3898453 · doi:10.2307/3898453 [7] DOI: 10.1046/j.1365-2486.2002.00512.x · doi:10.1046/j.1365-2486.2002.00512.x [8] DOI: 10.2307/1940184 · doi:10.2307/1940184 [9] DOI: 10.2307/2259151 · doi:10.2307/2259151 [10] DOI: 10.2307/3543812 · doi:10.2307/3543812 [11] DOI: 10.1007/978-1-4612-1224-9_3 · doi:10.1007/978-1-4612-1224-9_3 [12] DOI: 10.1016/j.chaos.2007.10.045 · Zbl 1152.34059 · doi:10.1016/j.chaos.2007.10.045 [13] DOI: 10.1016/j.nonrwa.2009.01.027 · Zbl 1181.37119 · doi:10.1016/j.nonrwa.2009.01.027 [14] DOI: 10.1137/0149050 · Zbl 0676.92013 · doi:10.1137/0149050 [15] DOI: 10.1006/jmaa.1995.1239 · Zbl 0833.34069 · doi:10.1006/jmaa.1995.1239 [16] DOI: 10.1137/0133023 · Zbl 0372.35044 · doi:10.1137/0133023 [17] DOI: 10.1016/S0362-546X(98)00186-2 · Zbl 0940.35010 · doi:10.1016/S0362-546X(98)00186-2 [18] DOI: 10.1016/j.tree.2007.10.013 · doi:10.1016/j.tree.2007.10.013 [19] DOI: 10.1007/s10867-009-9165-9 · doi:10.1007/s10867-009-9165-9 [20] Wang R. H., J. R. Soc. Interface 37 pp 705– [21] DOI: 10.1007/978-1-4612-9892-2 · doi:10.1007/978-1-4612-9892-2 [22] Kuang Y., Delay Differential Equations with Applications in Population Dynamics (1993) · Zbl 0777.34002 [23] Ye Q., Introduction to Reaction-Diffusion Equations (1990) · Zbl 0774.35037 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.