Evaluating the Operation Mechanism of the Agricultural Industry–University–Research Collaborative Innovation Network: A B-Z Reaction-Based Approach

Abstract

This study is based on the data from co-authored papers, collaborative patents, and jointly authored varieties involving Chinese agricultural enterprises, universities, and research institutions from 2011 to 2023. We construct a three-dimensional dynamic equation system to model the agricultural industry–university–research (I-U-R) collaborative innovation network operation mechanism. Inspired by the Belousov–Zhabotinsky (B-Z) reaction, we model a three-variable oscillator with the state variables (network structure embeddedness, partner heterogeneity, and collaborative innovation output) to represent three primary substances in the chemical oscillators. This study investigates the network’s operational patterns and its determinants. Findings reveal that the patent network operates more efficiently than the paper and variety networks. Dependence on external government support increases with innovation complexity, coordination difficulty, and social value. Although a “structural optimization–resource agglomeration–output explosion” state is theoretically attainable under threshold conditions, the observed reality reflects “marginal structural optimization–continuous resource depletion–zero output growth”. Among the entities, eighteen are active leaders, forty-two constitute a stable but low-dynamism backbone, and ninety are general participants with limited innovation capacity. Significant structural contradictions highlight the need for targeted policy interventions to guide the network toward a more advanced and orderly state.