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A (purely) graph-theoretic approach to synchronization of nonlinear dynamical networks

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  • Sahaya Arokiadoss, Aandrew Baggio
  • Arunkumar, G.

Abstract

Synchronizing nonlinear dynamical networks typically requires solving matrix inequalities or detailed system models, which fail for large networks. This paper offers a simple fix: a purely graph-theoretic framework using only a single Lipschitz-like bound on the dynamics. Coupling strengths are computed directly from the digraph, bypassing inequality solvers entirely. The method succeeds where existing approaches encounter infeasibility due to connectivity patterns. It examines only n−1 directed paths per strongly connected component versus n(n−1)2 undirected paths before, achieving O(n3) complexity. Results show network connectivity can be exploited to synchronize a large class of nonlinear dynamical networks.

Suggested Citation

  • Sahaya Arokiadoss, Aandrew Baggio & Arunkumar, G., 2026. "A (purely) graph-theoretic approach to synchronization of nonlinear dynamical networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 692(C).
    • Handle: RePEc:eee:phsmap:v:692:y:2026:i:c:s037843712600244x
    DOI: 10.1016/j.physa.2026.131508
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