The generation mechanism of Turing-pattern in a Tree-grass competition model with cross diffusion and time delay-Reference-Cited by-同舟云学术

The generation mechanism of Turing-pattern in a Tree-grass competition model with cross diffusion and time delay

Published:2022 Issue:12 Volume:19 Page:12073-12103
ISSN:1551-0018
Container-title:Mathematical Biosciences and Engineering
language:
Short-container-title:MBE

Author:

Su Rina¹²,Zhang Chunrui³

Affiliation:

1. College of Mechanical and Electrical Engineering, Northeast Forestry University, Harbin, 150040, China

2. College of Mathematics and Physics, Inner Mongolia Minzu University, Tongliao, 028043, China

3. Department of Mathematics, Northeast Forestry University, Harbin, 150040, China

Abstract

<abstract><p>In this paper, we study the general mechanism of Turing-pattern in a tree-grass competition model with cross diffusion and time delay. The properties of four equilibrium points, the existence of Hopf bifurcation and the sufficient conditions for Turing instability caused by cross-diffusion are analyzed, respectively. The amplitude equation of tree-grass competition model is derived by using multi-scale analysis method, and its nonlinear stability is studied. The sensitivity analysis also verified that fire frequency plays a key role in tree-grass coexistence equilibrium. Finally, the Turing pattern of tree-grass model obtained by numerical simulation is consistent with the spatial structure of tree-grass density distribution observed in Hulunbuir grassland, China.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

Applied Mathematics,Computational Mathematics,General Agricultural and Biological Sciences,Modeling and Simulation,General Medicine

Reference39 articles.

1. J. I. House, S. Archer, D. D. Breshears, R. J. Scholes, Conundrums in mixed woody-herbaceous plant systems, J. Biogeogr., 30 (2003), 1763–1777. https://doi.org/10.1046/j.1365-2699.2003.00873.x

2. M. Sankaran, J. Ratnam, N. P. Hanan, Tree-grass co-existence in savannas revisited-insights from an examination of assumptions and mechanisms invoked in existing models, Ecol. Lett., 7 (2004), 480–490. https://doi.org/10.1111/j.1461-0248.2004.00596.x

3. F. S. Gilliam, W. J. Platt, R. K. Peet, Natural disturbances and the physiognomy of pine savannas: a phenomenological model, Appl. Veg. Sci., 9 (2006), 83–96. https://doi.org/10.1111/j.1654-109X.2006.tb00658.x

4. P. D'Odorico, L. Francesco, L. Ridolfi, A probabilistic analysis of fire-induced tree-grass coexistence in savannas, Am. Nat., 167 (2006), E79–E87. https://doi.org/10.1086/500617

5. W. J. Bond, F. Woodward, G. Midgley, The global distribution of ecosystems in a world without fire, New Phytol., 165 (2005), 525–538. https://doi.org/10.1111/j.1469-8137.2004.01252.x