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Discrete Dynamics in Nature and Society
Volume 2014 (2014), Article ID 218053, 7 pages
http://dx.doi.org/10.1155/2014/218053
Research Article

Rich Spatiotemporal Dynamics of a Vegetation Model with Noise and Periodic Forcing

1National Key Laboratory for Electronic Measurement Technology, North University of China, Taiyuan, Shanxi 030051, China
2Key Laboratory of Instrumentation Science and Dynamic Measurement, Ministry of Education, North University of China, Taiyuan, Shanxi 030051, China

Received 1 September 2013; Revised 16 December 2013; Accepted 4 January 2014; Published 3 March 2014

Academic Editor: Ryusuke Kon

Copyright © 2014 Xia-Xia Zhao and Jian-Zhong Wang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The growth of vegetation is undeniably subject to random fluctuations arising from environmental variability and internal effects due to periodic forcing. To address these issues, we investigated a spatial version of a vegetation model including seasonal rainfall, noise, and diffusion. By numerical simulations, we found that noise can induce the pattern transition from stationary pattern to other patterns. More specifically, when noise intensity is small, patch invasion is induced. As noise intensity further increases, chaotic patterns emerge. For the system with noise and seasonal rainfall, it exhibits frequency-locking phenomena. Patterns transition may be a warning signal for the onset of desertification and thus the obtained results may provide some measures to protect vegetation, such as reducing random factors or changing irrigation on vegetation.