自然科學模型在空間交互行為分析之應用

Abstract

本文簡要系統地介紹區域科學裏空間交互行為分析中常被應用的自然科學模型之間縱向與橫向的相互關係。包括靜態的熱力學之Entropy概念與重力定理，以及動態的生態基礎成長模型、logit模型和空間競爭模型間的相關性與在區域科學上的應用。最後並探討前述動態模型中之混沌特性與非線性之相關。

This paper serves three purposes. First, it gives a systematic review of interactions between some natural science concepts and regional science phenomena in both static and dynamic states. Second, it aims to understand why non-linear feature is crucial in the emergence of chaotic behavior. What role does "non-linear" play in a chaotic dynamic system? And finally, simulating the non-linear dynamic system to observe its features. This review shows that maximum entropy concept can be applied in the spatial interaction model, and result in a gravity type model; based on this gravity model, a logit discrete choice model is followed; consequently, a dynamic logit model will generate a logistic type growth model. It shows that these biological or physical based models are correlated and correspond to regional phenomena. From optimal entropy to generated dynamic logit model, they are vertically related.Horizontally, each natural science model interprets certain regional science phenomenon. Simulation results show that non-linear dynamic system is not only able to perform all regular trajectories of linear dynamic system, but also perform non-periodic irregular motion patterns given different initial conditions. The chaotic systems do not cause different irregular trajectories given the same initial conditions and parameter values. The "stochastic" term in describing chaotic behavior refers to its unpredictable and random time series path. Also, non-periodic evolution is extremely sensitive depending on the initial conditions. Non-linear is the necessary condition for the emergence of chaos; the level of parameter value is the sufficient condition for chaotic dynamic system.