X–factorable transformation–based control of interconnected Lotka–Volterra systems

Lőrinc Márton; Katalin M. Hangos; Lőrinc Márton; Katalin M. Hangos

doi:10.3934/mbe.2026065

Mathematical Biosciences and Engineering

2026, Volume 23, Issue 6: 1774-1798. doi: 10.3934/mbe.2026065

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Research article

X–factorable transformation–based control of interconnected Lotka–Volterra systems

Lőrinc Márton ^{1
,
,},
Katalin M. Hangos ^2,3

1.
Department of Electrical Engineering, Sapientia Hungarian University of Transylvania, Corunca, Romania
2.
Systems and Control Laboratory, HUN-REN Institute for Computer Science and Control, Budapest, Hungary
3.
Department of Electrical Engineering and Information Systems, University of Pannonia, Veszprém, Hungary

Received: 22 December 2025 Revised: 20 April 2026 Accepted: 07 May 2026 Published: 22 May 2026

A dynamic model of interconnected Lotka–Volterra systems has been developed both with static and delayed interconnections. We have shown that the X-transformed model of interconnected Lotka–Volterra systems naturally admits a quasi-polynomial (QP) representation, facilitating systematic analysis and control design. In order to analyze local asymptotic stability around a positive equilibrium, we have shown that the X-factorable transformation preserves local diagonal stability. We propose a decentralized setpoint-tracking controller design based on the transformed model that guarantees population persistence in the subsystems of the network. The proposed controller design is computationally simple and ensures that the controlled system is locally diagonally stable around the prescribed setpoint. Moreover, larger controller gains improve disturbance attenuation, mitigating the effect of the disturbance offset term on control performance.
- network dynamics,
- Lotka-Volterra systems,
- quasi-polynomial systems,
- X-factorable transformation,
- setpoint control
Citation: Lőrinc Márton, Katalin M. Hangos. X–factorable transformation–based control of interconnected Lotka–Volterra systems[J]. Mathematical Biosciences and Engineering, 2026, 23(6): 1774-1798. doi: 10.3934/mbe.2026065

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Abstract

A dynamic model of interconnected Lotka–Volterra systems has been developed both with static and delayed interconnections. We have shown that the X-transformed model of interconnected Lotka–Volterra systems naturally admits a quasi-polynomial (QP) representation, facilitating systematic analysis and control design. In order to analyze local asymptotic stability around a positive equilibrium, we have shown that the X-factorable transformation preserves local diagonal stability. We propose a decentralized setpoint-tracking controller design based on the transformed model that guarantees population persistence in the subsystems of the network. The proposed controller design is computationally simple and ensures that the controlled system is locally diagonally stable around the prescribed setpoint. Moreover, larger controller gains improve disturbance attenuation, mitigating the effect of the disturbance offset term on control performance.

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