Oil Production, Net Energy, and Capital Dynamics: A System-Coupled Lotka–Volterra Approach

Net energy—defined as the energy remaining after accounting for the energy required for resource extraction and processing—shapes the fundamental physical constraints of energy systems. Although the extended Energy Return on Investment (EROIext) incorporates extraction, refining, transportation, and end-use infrastructure, its long-term structural dynamics remain underexplored. This study applies a Single-Cycle Lotka–Volterra (SCLV) model to examine interactions between resource stock, capital accumulation, and EROIext in the global petroleum system. The model is calibrated using historical data from 1965 to 2012 to explore structural trajectories under simplified assumptions. Results indicate that production peaks endogenously around 2041 within the model framework, while EROIext declines and falls below unity by 2081 under the assumed structural relationships. These years represent model-derived structural outcomes rather than deterministic forecasts. Capital stock reaches its maximum at the same energetic threshold (EROIext = 1), marking an internally generated transition in the resource–capital system. An entropy-based indicator is introduced as a thermodynamic proxy mirroring the decline in energetic efficiency within the modeled subsystem. These findings show how energetic reinvestment constraints generate endogenous peak and threshold behavior in resource-dependent systems. The analysis offers a structural perspective on interactions between depletion, capital accumulation, and net energy under simplified thermodynamic assumptions. These results provide insights into long-term structural constraints of the oil system, which may inform energy planning and policy discussions under conditions of declining net energy availability.