The Interaction of Natural Science Models in Spatial Interaction Behavior

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 sciencephenomena in both static and dynamic states. Second it aims to understand whynon-linear feature is crucial in the emergence of chaotic behavior. What roledoes \"non-linear\" play in a chaotic dynamic system? And finally simulatingthe non-linear dynamic system to observe its features. This review shows thatmaximum entropy concept can be applied in the spatial interaction model andresult in a gravity type model; based on this gravity model a logit discretechoice model is followed; consequently a dynamic logit model will generate alogistic type growth model. It shows that these biological or physical basedmodels are correlated and correspond to regional phenomena. From optimalentropy to generated dynamic logit model they are vertically related.Horizontally each natural science model interprets certain regional sciencephenomenon. Simulation results show that non-linear dynamic system is not onlyable to perform all regular trajectories of linear dynamic system but alsoperform non-periodic irregular motion patterns given different initialconditions. The chaotic systems do not cause different irregular trajectoriesgiven the same initial conditions and parameter values. The \"stochastic\" termin describing chaotic behavior refers to its unpredictable and random timeseries path. Also non-periodic evolution is extremely sensitive depending onthe initial conditions. Non-linear is the necessary condition for theemergence of chaos; the level of parameter value is the sufficient conditionfor chaotic dynamic system.