Minimal Resonance Dynamics in Complex Adaptive Systems: A Simulation Study of Compression, Tension, and Structural Singularization

This paper introduces the Minimal Model of Resonance Dynamics (MMRD), a nonlinear dynamical framework designed to explore the interaction between adaptive resonance, structural compression, and systemic tension in complex adaptive systems (CAS). The model formalizes the Compression–Resonance–Tension Index (CRTI), defined as: CRTI = R / (C + T + ε) where R represents adaptive resonance (diversity, exploration capacity, and feedback responsiveness), C represents structural compression (efficiency-driven rigidity and standardization), and T represents systemic tension (external or internal stress acting on the system). To investigate the dynamical behavior underlying CRTI trajectories, the study introduces a system of coupled differential equations describing the co-evolution of resonance, compression, and tension within a system. Numerical simulations are used to explore how feedback loops between these variables generate different dynamical regimes. The model reveals three characteristic system states: • Resilient regime – high adaptive resonance with moderate structural compression • Declining resilience regime – increasing structural compression and reduced adaptive response • Singularization regime – resonance collapse caused by runaway compression–tension feedback loops Simulation results demonstrate that declining CRTI values can emerge well before systemic collapse occurs, suggesting that CRTI may function as a leading indicator of structural fragility in complex adaptive systems. The MMRD framework is structurally comparable to classical nonlinear models of regime shifts, including ecological tipping-point models and other dynamical systems exhibiting hysteresis and bifurcation behavior. By focusing on the balance between adaptive capacity and structural rigidity, the model offers a minimal dynamical representation of how efficiency-driven optimization can erode systemic resilience. The paper provides a computational foundation for future empirical validation studies and contributes to the broader effort to develop quantitative diagnostics for stability and collapse in complex adaptive systems. complex adaptive systems nonlinear dynamics dynamical systems modeling resilience dynamics regime shifts tipping points compression–resonance–tension index CRTI minimal model of resonance dynamics systemic fragility stability analysis computational simulation bifurcation dynamics resilience modeling