Crisis Response Modes in Collaborative Business Ecosystems: A Mathematical Framework from Plasticity to Antifragility

Javaneh Ramezani (), Luis Gomes and Paula Graça
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Javaneh Ramezani: NOVA School of Science and Technology, UNINOVA-CTS, NOVA University of Lisbon, 2829-516 Caparica, Portugal
Luis Gomes: NOVA School of Science and Technology, UNINOVA-CTS and LASI, NOVA University of Lisbon, 2829-516 Caparica, Portugal
Paula Graça: NOVA School of Science and Technology, UNINOVA-CTS, NOVA University of Lisbon, 2829-516 Caparica, Portugal

Mathematics, 2025, vol. 13, issue 15, 1-33

Abstract: Collaborative business ecosystems (CBEs) are increasingly exposed to disruptive events (e.g., pandemics, supply chain breakdowns, cyberattacks) that challenge organizational adaptability and value creation. Traditional approaches to resilience and robustness often fail to capture the full range of systemic responses. This study introduces a unified mathematical framework to evaluate four crisis response modes—plasticity, resilience, transformative resilience, and antifragility—within complex adaptive networks. Grounded in complex systems and collaborative network theory, our model formalizes both internal organizational capabilities (e.g., adaptability, learning, innovation, structural flexibility) and strategic interventions (e.g., optionality, buffering, information sharing, fault-injection protocols), linking them to pre- and post-crisis performance via dynamic adjustment functions. A composite performance score is defined across four dimensions (Innovation, Contribution, Prestige, and Responsiveness to Business Opportunities), using capability–strategy interaction matrices, weighted performance change functions, and structural transformation modifiers. The sensitivity analysis and scenario simulations enable a comparative evaluation of organizational configurations, strategy impacts, and phase-transition thresholds under crisis. This indicator-based formulation provides a quantitative bridge between resilience theory and practice, facilitating evidence-based crisis management in networked business environments.

Keywords: resilience; antifragility; transformative resilience; plasticity; organizational capabilities; coping strategies; collaborative networks; business ecosystems; complex adaptive systems; performance evaluation; AHP; sensitivity analysis (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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