Generative AI Updates, Organizational Adaptation, and Enterprise Process Stability

Generative artificial intelligence (GenAI) is increasingly embedded in enterprise workflows, yet the models that support these workflows are updated at discrete and sometimes frequent intervals. Each update can improve technical effectiveness while simultaneously invalidating prompts, interfaces, controls, and employee routines. This study develops an impulsive dynamical system to analyze the resulting tension between technical improvement and organizational disruption. The continuous subsystem tracks enterprise process stability, organizational adaptation, and effective model capability between updates. The impulsive subsystem represents the instantaneous effects of a model release on workflow stability, learning, cognitive overload, and technical performance. Positive invariance of the state space is established, the existence of at least one periodic operating trajectory is proved, a closed-form periodic solution for the technical-effectiveness subsystem is derived, and a local stability condition is formulated through the spectral radius of the one-cycle Poincaré map. Numerical experiments compare high-frequency incremental updates, low-frequency major updates, higher governance investment, and cognitive-overload conditions. A long-run performance objective is then used to identify a joint update interval, update intensity, and governance investment policy. The results show that update interval and update intensity should not be selected independently. Small but frequent updates reduce the amplitude of process disruption but may impose persistent coordination costs, whereas large infrequent updates produce deeper stability losses. Organizational adaptation expands the robust operating region, while cognitive overload contracts it. Under the normalized baseline calibration, the best grid policy combines a moderate update interval, a moderate update intensity, and relatively high governance investment. The paper contributes a formal framework for treating GenAI model releases as organizational impulses rather than as purely technical upgrades.