Modelling the leaping cycle by modified Lotka-Volterra equations with applications to technology and safety

A bounded version of the Lotka – Volterra model based on logistic differential equations is suggested to emulate cyclic behaviour in complex evolutionary and other systems. The model provides reasonable approximations for the so-called leaping cycles and other oscillational processes when the main state variables are limited by physical constraints. The model represents a basic model-building block that can be used in system dynamics and other frameworks and applications that require fundamental understanding and modelling of principal features of complex cyclic processes. Two application areas – technological progress and industrial safety – are specifically considered here. The model is shown to emulate techno-economic cycles reasonably well and give an appropriate qualitative description of risk and safety variations in the industrial environment. Simulations using the suggested model are quantitatively compared with the results of agent-based simulations. While a simple model cannot match all details of complex agent-based simulations of the risk and benefit dilemma, the bounded Lotka – Volterra model still gives a reasonable approximation of the process. The conceptual implications of the model are, nevertheless, significant, pointing to common cyclic mechanisms taking place in complex evolutionary systems that may belong to different branches of science.