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Temporal Forcing Induced Pattern Transitions Near the Turing–Hopf Bifurcation in a Plankton System

Wen Wang

School of Control Science and Engineering, Shandong University, Jinan 250061, P. R. China

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Shutang Liu

http://orcid.org/0000-0003-2281-9378

School of Control Science and Engineering, Shandong University, Jinan 250061, P. R. China

E-mail Address: stliu618@163.com

Corresponding author.

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Zhibin Liu

School of Control Science and Engineering, Shandong University, Jinan 250061, P. R. China

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, and

Da Wang

Research Center for Dynamics and Control Science, Shandong Normal University, Jinan 250358, P. R. China

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https://doi.org/10.1142/S0218127420501369Cited by:7 (Source: Crossref)

Abstract

We explore the impact of time-periodic forcing on pattern transitions in a plankton system of reaction–diffusion type. Here, we mainly focus on the forced states near the Turing–Hopf bifurcation. A normal form analysis leads to the finding that weak forcing exhibits a destabilizing effect on the dynamics by exciting the transitions from a spatially homogeneous stationary state to a periodic oscillation in time. The results are obtained by studying the amplitude equations derived using weakly nonlinear analysis in the presence of forcing, which enables us to calculate the changes of states. Examples are given to confirm the theoretical results.

Keywords:

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