https://doi.org/10.1140/epjp/s13360-025-06519-2
Regular Article
Investigation of spatial pattern in mussel-algae model with higher-order interactions and PD control
1
College of Automation amd College of Artificial Intelligence, Nanjing University of Posts and Telecommunications, 210023, Nanjing, China
2
School of Mathematics and Statistics, Xinyang Normal University, 464000, Xinyang, China
3
School of Mathematics, Southeast University, 211189, Nanjing, China
4
Guizhou Key Laboratory of Economics System Simulation, Guizhou University of Finance and Economics, Guiyang, 550025, Guiyang, China
Received:
15
April
2025
Accepted:
3
June
2025
Published online:
20
June
2025
Higher-order interactions (HOIs) , as critical drivers of complex dynamical behaviors in ecosystems, have garnered increasing attention in scientific research. Existing studies have demonstrated their significant regulatory effects on multispecies coexistence and biodiversity. However, the mechanisms through which HOIs influence ecosystem spatial dynamics remain poorly understood. In this paper, we propose a reaction-diffusion mussel-algae model incorporating HOIs and introduce proportional-derivative (PD) control mechanisms. We analyze the stability of the model in the absence of diffusion and provide the conditions for Turing instability driven by diffusion. Using the HOIs coefficient as the bifurcation parameters and based on the multiple scale method, we derive the amplitude equations for the two-dimensional Turing pattern at the Turing bifurcation threshold. We determine the selectivity and stability of the pattern formation. Numerical simulations in two-dimensional space show that HOIs can not only realize the change of the structure of Turing patterns but also affect its evolution rate. By applying PD control, the occurrence of Turing instability is effectively suppressed. In addition, under the influence of HOIs, more complex spatial patterns appear in the three-dimensional space.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2025
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
