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X-factorable transformation-based control of interconnected Lotka-Volterra systems
Lőrinc Márton1, Katalin M Hangos2,3
1Department of Electrical Engineering, Sapientia Hungarian University of Transylvania, Corunca, Romania.
Mathematical Biosciences and Engineering : MBE
|July 14, 2026
Summary
A new dynamic model for interconnected Lotka-Volterra systems was developed. This model simplifies analysis and control design, ensuring system stability and population persistence in ecological networks.
Area of Science:
- Ecology
- Systems Biology
- Control Theory
Background:
- Interconnected Lotka-Volterra systems are fundamental models in ecology.
- Analyzing their stability and control is complex due to interconnections, especially with delays.
Purpose of the Study:
- To develop a dynamic model for interconnected Lotka-Volterra systems.
- To facilitate systematic analysis and control design for these systems.
- To propose a decentralized controller for setpoint tracking and disturbance rejection.
Main Methods:
- Developed a dynamic model incorporating static and delayed interconnections.
- Applied an X-transformed model to achieve a quasi-polynomial (QP) representation.
- Designed a decentralized setpoint-tracking controller based on the transformed model.
Main Results:
- The X-transformed model naturally admits a QP representation.
- The transformation preserves local diagonal stability for stability analysis.
- The proposed controller guarantees population persistence and local diagonal stability.
- Controller gains enhance disturbance attenuation.
Conclusions:
- The developed model and transformation simplify the analysis of interconnected Lotka-Volterra systems.
- A computationally simple, decentralized controller ensures stability and performance.
- The approach is effective for population dynamics and network control.
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