Controllability and Observability of Microbial Purification Systems in Small–Micro Water Bodies: A Complex Network Theory Perspective

As critical terminal units within watershed aquatic ecosystems, small–micro water bodies exhibit dynamic water quality responses to coupled environmental factors. Due to disparities in hydrological connectivity, limited self-purification capacity, and external pollution inputs, certain small-micro water bodies (e.g., stagnant systems with weak groundwater exchange and affected by non-point source pollution) are prone to pollution intensification and ecological degradation, presenting significant challenges in watershed management. This study proposes a novel analytical framework grounded in complex network theory to addresses the controllability and observability challenges of biological purification systems under pollutant overload conditions.

The research methodology involves three key phases: First, a hydro-bio-chemical coupled kinetic model of contaminant migration and transformation, as well as their state-space representations, are constructed. And then, they are mapped onto a directed network with heterogeneous node weights and adaptive edges. Subsequently, complex network metrics are employed to evaluate the full-state structural controllability and observability of photosynthetic bacteria-mediated purification systems, identifying critical input and monitoring nodes. Finally, case studies elucidate the performance enhancement mechanisms through network topology optimization.

Our results demonstrate that topology-guided regulation significantly enhances purification efficiency in low-connectivity, long hydraulic retention time systems, while optimized sensor placement improves system observability. This finding provides novel insights for the targeted remediation of environmentally stressed small–micro water bodies, with substantial practical implications for differentiated water governance and resilient water resource management. Field applications require adaptive adjustments based on site-specific hydrological characteristics to ensure operational efficacy.