Space‐time dynamical models

Abstract

Purpose

The purpose is to present a new formal approach based on a partial integro‐differential equation, the space‐time state transition equation (STSTE), and on a set of general equations with which space‐time dynamical models of complex systems, such as social systems and ecosystems, can be built.

Design/methodology/approach

The STSTE provides the partial derivative of the density of a state‐variable with regard to time as a sum of time rates and space‐time rates. Time rates describe the dynamics of the system for each space‐point irrespectively of the other points, whilst space‐time rates describe this evolution as a consequence of the relation of each space‐point with a given set of other points of the space. This relation contains integrals over the accessibility domains (sets of space‐points with which each space‐point is related).

Findings

The STSTE is provided for any system of space‐coordinates and is compared with the reaction‐diffusion models (RD). The reason why it is more convenient to work with the STSTE than with the RD to model complex systems in the context of social systems and ecosystems is indicated.

Practical implications

An urban system (the city of Valencia, Spain) is presented as an application; an analytical solution strategy is stated under the simplest hypothesis for computing space‐time rates, and a computer program for the situation is developed to obtain numerical solutions.

Originality/value

A numerical comparison between the new STSTE model and the RD shows that, the STSTE model produces better results than the reaction diffusion model in validation.

Citation

Micó, J.C., Caselles, A. and Romero, P.D. (2008), "Space‐time dynamical models", Kybernetes, Vol. 37 No. 7, pp. 1030-1058. https://doi.org/10.1108/03684920810884397