Organizational Responsiveness in a Three-Dimensional Discrete Model of AI, ESG Disclosure, and Green Supply Chain Collaboration

Abstract

Artificial intelligence (AI) investment, environmental, social, and governance (ESG) disclosure, and green supply chain collaboration increasingly operate as an interconnected corporate sustainability system, yet their relationships are commonly examined through static or approximately linear models. This study develops a bounded three-dimensional discrete nonlinear framework in which firms periodically adjust AI-investment maturity, ESG disclosure quality, and green supply chain collaboration in response to cross-domain benefits and self-limiting organizational costs. The model contributes by separating structural complementarity from organizational responsiveness, allowing the same long-run configuration to remain feasible while its dynamic stability changes with adjustment speed. A logit adaptive rule keeps all states within the open unit interval, while Hill-type functions capture activation thresholds and saturation. Under the baseline calibration, the system exhibits three interior fixed points: stable low- and high-complementarity regimes separated by an unstable intermediate state. Schur-Jury analysis establishes local stability conditions, and Neimark--Sacker analysis shows that the low and high regimes lose stability at distinct responsiveness thresholds, with subcritical and supercritical bifurcations, respectively. Along the high-regime branch, increasing responsiveness generates quasiperiodic motion, intermittent chaotic subwindows, and re-entrant stable period-3 behavior. A positive leading Lyapunov exponent confirms deterministic chaos, while multi-start diagnostics show that quasiperiodic and chaotic dynamics can coexist with a stable period-3 attractor under different initial conditions over part of the parameter range. The findings show that stronger AI-ESG-green-supply-chain complementarity does not imply that faster organizational adjustment is always beneficial. Effective governance must therefore consider not only the strength of cross-domain reinforcement but also the pacing and damping of organizational responses.