Behavioral Traits as Dynamical Systems: Utilizing Entropy to Analyze Longitudinal Psychometric Data in Coupled Ordinary Differential Equations

Traits such as neuroticism persist across species despite exhibiting characteristics typically regarded as maladaptive. This paper introduces a systems-based framework for understanding trait-stability, integrating findings from the Swedish Adoption/Twin Study on Aging (SATSA) with a biologically grounded system of coupled ordinary differential equations. To enable dynamical modeling, Shannon entropy is extracted from longitudinal Likert-scale psychometric data, and is treated as a population-level signal of behavioral dispersion, reducing high-dimensional Likert data into low-dimensional trajectories. These trajectories serve as dynamical variables in the ODE framework, which is governed by principles from evolutionary biology, including mutation-selection balance, genetic pleiotropy, and metabolic constraints. The model is benchmarked against a null (uncoupled) system and additionally validated through multiple stress tests using RMSE, R^2, and dynamic time warping metrics. By embedding environmental feedback as a recursive driver of phenotypic expression, traits such as neuroticism are framed not as stochastic byproducts, but as emergent, multi-stable attractors within a biologically constrained system. The resulting Entropy-Coupled Trait ODEs (ECTO) reveal structured attractor dynamics and demonstrate that entropy functions not merely as a descriptive measure, but as a functional driver of behavioral evolution. This approach provides a scalable, mathematically grounded foundation for modeling phenotypic traits, with future applications to machine learning, multi-omic behavioral modeling, and related complex systems domains. By bridging psychometrics, evolutionary theory, and systems modeling, this work offers a general method for understanding long-term trait stability through recursive information-theoretic dynamics.