Collective dynamics and accelerated distributed optimization on cooperation–competition complex networks

Jiaxu Liu, Hanlin Wang, Shengze Cai and Chao Xu

Chaos, Solitons & Fractals, 2026, vol. 210, issue P1

Abstract: This paper investigates the collective dynamics and distributed optimization problems over cooperative–competitive complex networks. While discrete-time approaches have been widely explored, continuous-time solutions that reveal the underlying physical dynamics of antagonistic interactions remain scarce. To bridge this gap, we propose a novel continuous-time framework incorporating second-order momentum dynamics and a static topological coupling mechanism. Rigorous theoretical analysis, based on a comprehensive Lyapunov function, guarantees global exponential convergence to the optimal solution. Distinct from state-of-the-art first-order algorithms, the proposed method introduces an inertial mechanism that relaxes restrictive initial conditions, offering an initialization-free solution. Furthermore, we uncover a discriminative filtering mechanism inherent in the algorithm, which effectively isolates heterogeneous tasks in multi-agent systems. Numerical simulations on signed grid topologies validate the proposed strategy. In heterogeneous environmental monitoring scenarios, the results demonstrate emergent collective behaviors, physical consistency, and accelerated convergence.

Keywords: Distributed optimization; Cooperation–competition complex network; Exponential convergence; Collective dynamics; Sensor fusion (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:210:y:2026:i:p1:s096007792600771x

DOI: 10.1016/j.chaos.2026.118630

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