Export file:


  • RIS(for EndNote,Reference Manager,ProCite)
  • BibTex
  • Text


  • Citation Only
  • Citation and Abstract

Turing instabilities and pattern formation in a benthic nutrient-microorganism system

1. Institute for Chemistry and Biology of the Marine Environment, Carl von Ossietzky Universität Oldenburg, PF 2503, 26111 Oldenburg

In general, the distributions of nutrients and microorganisms in sediments show complex spatio-temporal patterns, which often cannot be explained as resulting exclusively from the temporal fluctuations of environmental conditions and the inhomogeneity of the studied sediment's material. We studied the dynamics of one population of microorganisms feeding on a nutrient in a simple model, taking into account that the considered bacteria can be in an active or in a dormant state. Using this model, we show that the formation of spatio-temporal patterns can be the consequence of the interaction between predation and transport processes. Employing the model on a two-dimensional vertical domain, we show by simulations which patterns can arise. Depending on the strength of bioirrigation, we observe stripes or "hot spots'' (or "cold spots'') with high (or low) microbiological activity. A detailed study regarding the effect of non-homogeneous (depth dependent) forcing by bioirrigation shows that different patterns can appear in different depths.
  Article Metrics

Keywords pattern formation; reaction-diffusion models; Turing instability; sediment.

Citation: Martin Baurmann, Wolfgang Ebenhöh, Ulrike Feudel. Turing instabilities and pattern formation in a benthic nutrient-microorganism system. Mathematical Biosciences and Engineering, 2004, 1(1): 111-130. doi: 10.3934/mbe.2004.1.111


This article has been cited by

  • 1. Martin Baurmann, Thilo Gross, Ulrike Feudel, Instabilities in spatially extended predator–prey systems: Spatio-temporal patterns in the neighborhood of Turing–Hopf bifurcations, Journal of Theoretical Biology, 2007, 245, 2, 220, 10.1016/j.jtbi.2006.09.036
  • 2. Gui-Quan Sun, Guang Zhang, Zhen Jin, Li Li, Predator cannibalism can give rise to regular spatial pattern in a predator–prey system, Nonlinear Dynamics, 2009, 58, 1-2, 75, 10.1007/s11071-008-9462-z
  • 3. Quan-Xing Liu, Zhen Jin, Formation of spatial patterns in an epidemic model with constant removal rate of the infectives, Journal of Statistical Mechanics: Theory and Experiment, 2007, 2007, 05, P05002, 10.1088/1742-5468/2007/05/P05002
  • 4. Luo-Luo Jiang, Tao Zhou, Matjaž Perc, Bing-Hong Wang, Effects of competition on pattern formation in the rock-paper-scissors game, Physical Review E, 2011, 84, 2, 10.1103/PhysRevE.84.021912
  • 5. Malay Banerjee, Santo Banerjee, Turing instabilities and spatio-temporal chaos in ratio-dependent Holling–Tanner model, Mathematical Biosciences, 2012, 236, 1, 64, 10.1016/j.mbs.2011.12.005
  • 6. Malay Banerjee, Syed Abbas, Existence and non-existence of spatial patterns in a ratio-dependent predator–prey model, Ecological Complexity, 2015, 21, 199, 10.1016/j.ecocom.2014.05.005
  • 7. Subhendu Chakraborty, P.K. Tiwari, S.K. Sasmal, Santanu Biswas, Sabyasachi Bhattacharya, Joydev Chattopadhyay, Interactive effects of prey refuge and additional food for predator in a diffusive predator-prey system, Applied Mathematical Modelling, 2017, 47, 128, 10.1016/j.apm.2017.03.028
  • 8. M. Banerjee, V. Volpert, Prey-predator model with a nonlocal consumption of prey, Chaos: An Interdisciplinary Journal of Nonlinear Science, 2016, 26, 8, 083120, 10.1063/1.4961248
  • 9. Ulrike Feudel, , Complexity and Synergetics, 2018, Chapter 15, 179, 10.1007/978-3-319-64334-2_15
  • 10. Subhendu Chakraborty, The influence of generalist predators in spatially extended predator–prey systems, Ecological Complexity, 2015, 23, 50, 10.1016/j.ecocom.2015.06.003
  • 11. PENG ZHOU, JINGYU WANG, XIAODONG LI, ZHEN JIN, EMERGENCE OF TRAVELING PATTERN IN A PREDATOR–PREY SYSTEM, International Journal of Modern Physics C, 2009, 20, 11, 1861, 10.1142/S0129183109014783
  • 12. Kunal Chakraborty, Kunal Das, T. K. Kar, Modeling and analysis of a marine plankton system with nutrient recycling and diffusion, Complexity, 2015, 21, 1, 229, 10.1002/cplx.21559
  • 13. Daniel Wetzel, Pattern analysis in a benthic bacteria-nutrient system, Mathematical Biosciences and Engineering, 2015, 13, 2, 10.3934/mbe.2015004
  • 14. Florian Centler, Ingo Fetzer, Martin Thullner, Modeling population patterns of chemotactic bacteria in homogeneous porous media, Journal of Theoretical Biology, 2011, 287, 82, 10.1016/j.jtbi.2011.07.024
  • 15. Martin Thullner, Philippe Van Cappellen, Pierre Regnier, Modeling the impact of microbial activity on redox dynamics in porous media, Geochimica et Cosmochimica Acta, 2005, 69, 21, 5005, 10.1016/j.gca.2005.04.026
  • 16. Subhendu Chakraborty, P.K. Tiwari, A.K. Misra, J. Chattopadhyay, Spatial dynamics of a nutrient–phytoplankton system with toxic effect on phytoplankton, Mathematical Biosciences, 2015, 264, 94, 10.1016/j.mbs.2015.03.010
  • 17. Malay Banerjee, , Applications of Chaos and Nonlinear Dynamics in Science and Engineering - Vol. 4, 2015, Chapter 8, 257, 10.1007/978-3-319-17037-4_8
  • 18. Jian Gao, Changgui Gu, Super Multi-Armed and Segmented Spiral Pattern in a Reaction-Diffusion Model, IEEE Access, 2019, 7, 140391, 10.1109/ACCESS.2019.2943421

Reader Comments

your name: *   your email: *  

Copyright Info: 2004, Martin Baurmann, et al., licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

Download full text in PDF

Export Citation

Copyright © AIMS Press All Rights Reserved