2007/05/31 by Quan-Xing Liu, Bai-Lian Li, Zhen Jin
Biochemistry, Genetics and Molecular Biology · Computer Science · Environmental Science · Physics and Astronomy · #Ecosystem dynamics and resilience #Nonlinear Dynamics and Pattern Formation #cond-mat.stat-mech #nlin.PS #q-bio.OT #q-bio.PE #stochastic dynamics and bifurcation
paper · pdf · doi:10.1088/1742-5468/2008/05/p05011
published as J. Stat. Mech. (2008) P05011 · Some typos errors are proof, and some strong relate references are added
arxiv created 2007/12/07 · openalex publication_date 2008/05/23 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30
It is known that natural systems are undeniably subject to random fluctuations, arising from either environmental variability or internal effects. In this paper, we present a spatial version of the phytoplankton–zooplankton model that includes some important factors such as external periodic forces, noise, and diffusion processes. The spatially extended phytoplankton–zooplankton system is from the original study by Scheffer (Scheffer 1991 Oikos 62 271). Our results show that the spatially extended system exhibits a resonant pattern and frequency-locking phenomena. The system also shows that the noise and the external periodic forces play a constructive role in the Scheffer's model: (i) the noise can enhance the oscillation of phytoplankton species' density and form large clusters in space when the noise intensity is within a certain interval; (ii) the external periodic forces can induce 4:1 and 1:1 frequency-locking and spatially homogeneous oscillation phenomena to appear; and (iii) resonant patterns are observed in the system when the spatial noises and external periodic forces are both turned on. Moreover, we find that the 4:1 frequency locking transforms into 1:1 frequency locking when the noise intensity is increased. In addition to elucidating our results outside the domain of Turing instability, we provide further analysis of linear stability with the help of numerical calculation using the Maple software. Significantly, oscillations are enhanced in the system when the noise term is present. These results indicate that the oceanic plankton bloom may be partly due to interplay between the stochastic factors and external forces instead of deterministic factors. These results also may help us to understand the effects arising from the undeniable susceptibility to random fluctuations in oceanic plankton bloom.