ABSTRACT

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.

摘要

建议使用基于逻辑微分方程的 Lotka – Volterra 模型的有界版本来模拟复杂进化和其他系统中的循环行为。当主要状态变量受物理约束限制时，该模型为所谓的跳跃周期和其他振荡过程提供了合理的近似值。该模型代表了一个基本的模型构建块，可用于系统动力学和其他需要对复杂循环过程的主要特征进行基本理解和建模的框架和应用程序。这里特别考虑了两个应用领域——技术进步和工业安全。该模型被证明可以很好地模拟技术经济周期，并对工业环境中的风险和安全变化进行适当的定性描述。使用建议模型的模拟与基于代理的模拟的结果进行定量比较。虽然一个简单的模型无法匹配基于代理的复杂风险和收益困境模拟的所有细节，但有界 Lotka – Volterra 模型仍然给出了该过程的合理近似值。然而，该模型的概念含义是重要的，它指出了在可能属于不同科学分支的复杂进化系统中发生的共同循环机制。虽然一个简单的模型无法匹配基于代理的复杂风险和收益困境模拟的所有细节，但有界 Lotka – Volterra 模型仍然给出了该过程的合理近似值。然而，该模型的概念含义是重要的，它指出了在可能属于不同科学分支的复杂进化系统中发生的共同循环机制。虽然一个简单的模型无法匹配基于代理的复杂风险和收益困境模拟的所有细节，但有界 Lotka – Volterra 模型仍然给出了该过程的合理近似值。然而，该模型的概念含义是重要的，它指出了在可能属于不同科学分支的复杂进化系统中发生的共同循环机制。