Boundary and Interior Control in a Diffusive Lotka-Volterra Model

Fernandes Barreira J, Sônego M, Zuazua Iriondo E (2025)

Publication Language: English

Publication Status: Submitted

Publication Type: Unpublished / Preprint

Future Publication Type: Journal article

Publication year: 2025

Open Access Link: https://dcn.nat.fau.eu/wp-content/uploads/LVM.pdf

Abstract

We investigate the controllability of a generalized diffusive LotkaVolterra competition model for two species, incorporating boundary controls and an interior multiplicative control. Considering a smooth, bounded N-dimensional domain, we analyze ecologically pertinent scenarios characterized by constraints on both the controls and system states. Our results demonstrate how integrated control strategies can effectively overcome the limitations identified in previous studies. We prove two main results: (1) asymptotic controllability to single-species survival steady states under arbitrary system parameters, ensured by a combination of boundary and interior controls which act jointly to stabilize the system; and (2) finitetime controllability to a specific heterogeneous coexistence steady state via a two-phase strategy - first steering the system near the target with boundary control, then activating an interior multiplicative control in a localized region. The strong synergy between the two control mechanisms is crucial in both cases. We also analyze extinction dynamics and homogeneous coexistence, and support our findings with numerical simulations. The work concludes with perspectives for future research.

Authors with CRIS profile

Joao Fernandes Barreira Lehrstuhl für Dynamics, Control, Machine Learning and Numerics (Alexander von Humboldt-Professur) Maicon Sônego Lehrstuhl für Dynamics, Control, Machine Learning and Numerics (Alexander von Humboldt-Professur) Enrique Zuazua Iriondo Lehrstuhl für Dynamics, Control, Machine Learning and Numerics (Alexander von Humboldt-Professur)

How to cite

APA:

Fernandes Barreira, J., Sônego, M., & Zuazua Iriondo, E. (2025). Boundary and Interior Control in a Diffusive Lotka-Volterra Model. (Unpublished, Submitted).

MLA:

Fernandes Barreira, Joao, Maicon Sônego, and Enrique Zuazua Iriondo. Boundary and Interior Control in a Diffusive Lotka-Volterra Model. Unpublished, Submitted. 2025.

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