Connection-based framework for assessing natural complexity in nonlinear adaptive systems
Viviane M. Gomes, Gabriel Wainer, Flavio A. Gomes, Weber Martins, João R. B. Paiva, Marcella Scoczynski Ribeiro Martins, Clóves Gonçalves Rodrigues, A. Paulo Coimbra, Wesley Pacheco Calixto · Chaos Solitons & Fractals · 2025
This study introduces a quantitative framework for assessing natural complexity in adaptive systems, based on connection measures weighted by sensitivity indices. The methodology integrates system modeling, sensitivity analysis, and complexity assessment, enabling continuous monitoring and decision support in dynamic environments. Natural complexity is defined as an optimal level at which the system behaves in accordance with its nature, sustaining coherence between structure and function. By employing sensitivity-weighted connections, the framework captures both internal organization and adaptive dynamics, overcoming limitations of traditional metrics such as Shannon entropy and fractal dimension, which often neglect interaction intensity and temporal variability. The framework is validated through two case studies: a computational model of an Intensive Care Unit and a real-world startup acceleration ecosystem. In the Intensive Care Unit, periods of overload were identified through peaks in complexity, associated with an increased number of highly sensitive parameter connections. In contrast, in the startup ecosystem, systemic idleness was reflected by lower complexity levels, driven by weakly influential interactions among actors. These findings highlight the responsiveness and interpretability of the proposed metric compared to conventional approaches, particularly in tracking adaptive states over time. This connection-based framework supports the management of adaptive information systems, offering a dynamic and scalable complexity assessment tool. Its applicability spans medical informatics, business management, and distributed systems optimization, providing real-time insights that improve resilience and efficiency. In addition, the approach aligns with industry 4.0 paradigms, facilitating preventive analyses and adaptive decision-making in advanced technological environments. By offering a unified methodology for complexity evaluation, this research advances understanding and control of complex adaptive systems. • Natural complexity quantifies adaptive system behavior via connection modeling. • Sensitivity-weighted connections enable dynamic system complexity assessment. • The metric ψ ( c , γ c ) identifies idleness, regularity, and overload states. • Validation performed in ICU and startup acceleration real-world case studies. • Framework improves decision-making, resource allocation, and resilience planning.