A NONLINEAR DIFFERENTIAL EQUATION MODEL OF ENTREPRENEURIAL BEHAVIORAL DYNAMICS WITH EMPIRICAL PARAMETER ESTIMATION VIA PLS-SEM

This study develops a nonlinear differential equation model to describe the temporal evolution of entrepreneurial behavioral dynamics under the influence of digital technology intensity, entrepreneurship education exposure, and knowledge sharing intensity. Unlike conventional static econometric models, the proposed framework integrates empirical parameter estimation via Partial Least Squares Structural Equation Modeling (PLS-SEM) into a continuous-time nonlinear system. Data were collected from 278 MSME entrepreneurs and analyzed using SmartPLS 4. The results indicate that digital technology, entrepreneurship education, and knowledge sharing significantly enhance self-efficacy, which serves as a primary mediator translating external stimuli into sustained entrepreneurial action. The empirically estimated coefficients are incorporated into a nonlinear system that includes decay and saturation terms to realistically capture bounded growth, reinforcement effects, and adaptive behavioral dynamics. Equilibrium analysis demonstrates the existence of positive steady state levels for self-efficacy and entrepreneurial behavioral dynamics. In contrast, local stability analysis, based on the Jacobian eigenvalues, confirms that the equilibrium is locally asymptotically stable under realistic parameter constraints. These findings suggest that entrepreneurial behavior is self-regulating, nonlinear, and path-dependent, dynamically responding to both internal cognitive mechanisms and external stimuli. This study contributes to applied mathematical modeling by bridging behavioral entrepreneurship research with nonlinear dynamic systems analysis, offering a rigorous quantitative framework for understanding behavioral evolution in SMEs. It also provides practical implications for entrepreneurship education, digital ecosystem development, and policy interventions aimed at enhancing entrepreneurial performance in emerging markets. Future research may extend the model to include stochastic differential equations or optimal control strategies to capture environmental uncertainty and optimize entrepreneurial outcomes.