6533b7d4fe1ef96bd1262777

RESEARCH PRODUCT

Space‐time dynamical models

Antonio CasellesPantaleón D. RomeroJoan C. Micó

subject

Space timeMathematical analysisComplex systemSpace (mathematics)Theoretical Computer ScienceSet (abstract data type)Systems theoryControl and Systems EngineeringComputer Science (miscellaneous)Partial derivativeCyberneticsApplied mathematicsState-transition equationEngineering (miscellaneous)Social Sciences (miscellaneous)Mathematics

description

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 w...

yearjournalcountryeditionlanguage
2008-09-17Kybernetes
https://doi.org/10.1108/03684920810884397