Optimal control of patterns toward desired morphologies in a networked reaction-diffusion plankton system

Jiaqi Yang; Ning Li; Botong Zhang; Jiaqi Yang; Ning Li; Botong Zhang

doi:10.3934/era.2026263

Electronic Research Archive

2026, Volume 34, Issue 9: 5941-5967. doi: 10.3934/era.2026263

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Optimal control of patterns toward desired morphologies in a networked reaction-diffusion plankton system

1.
College of Sciences, Northeastern University, Shenyang 110819, China
2.
Dongfang Green Energy (Hebei) Co., Ltd., Hebei 061000, China

Received: 28 April 2026 Revised: 28 June 2026 Accepted: 06 July 2026 Published: 13 July 2026

In this paper, we investigated the formation and optimal control of spatial patterns in a plankton ecosystem. Based on a reaction-diffusion model with time delay and cross-diffusion, linear stability analysis revealed the conditions for Turing instability and Hopf oscillations, providing a dynamical explanation for plankton patchiness and periodic red tide outbreaks. A networked reaction-diffusion model was further constructed to account for ecological connectivity. Through global sensitivity analysis, the most influential parameters were identified, and node-dependent control as well as time-dependent optimal control was implemented. Extensive numerical simulations verified that when the network topology and average connectivity varied separately or simultaneously, the proposed control strategy could effectively steer the system toward the target spatial pattern, maintaining the average relative error below 8%. Moreover, the control method could significantly reduce system deviations in the short term, thereby effectively mitigating the adverse effects of time delay. This work provides a quantitative framework for understanding and regulating spatial heterogeneity in plankton ecosystems, with potential implications for red tide management.
- networks,
- reaction-diffusion,
- Turing pattern,
- global sensitivity analysis,
- optimal control
Citation: Jiaqi Yang, Ning Li, Botong Zhang. Optimal control of patterns toward desired morphologies in a networked reaction-diffusion plankton system[J]. Electronic Research Archive, 2026, 34(9): 5941-5967. doi: 10.3934/era.2026263

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Abstract

In this paper, we investigated the formation and optimal control of spatial patterns in a plankton ecosystem. Based on a reaction-diffusion model with time delay and cross-diffusion, linear stability analysis revealed the conditions for Turing instability and Hopf oscillations, providing a dynamical explanation for plankton patchiness and periodic red tide outbreaks. A networked reaction-diffusion model was further constructed to account for ecological connectivity. Through global sensitivity analysis, the most influential parameters were identified, and node-dependent control as well as time-dependent optimal control was implemented. Extensive numerical simulations verified that when the network topology and average connectivity varied separately or simultaneously, the proposed control strategy could effectively steer the system toward the target spatial pattern, maintaining the average relative error below 8%. Moreover, the control method could significantly reduce system deviations in the short term, thereby effectively mitigating the adverse effects of time delay. This work provides a quantitative framework for understanding and regulating spatial heterogeneity in plankton ecosystems, with potential implications for red tide management.

References

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