System Analysis Based on Volterra Equations

Peschel Μ, Breitenecker F, Grauer Μ, & Mende W (1983). System Analysis Based on Volterra Equations. IFAC Proceedings Volumes 16 (17): 277-283. DOI:10.1016/S1474-6670(17)61838-X.

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Abstract

Ecological systems can be described by chains and cycles of rate-coupled growing systems. Based on this description for arbitrary nonlinear instationary systems governed by sets of ordinary differential equations a new flexible structure design procedure is introduced, which allows to describe the system by a system of Volterra equations (Volterra-representation of the system). By a nonlinear transformation the Volterra equations can be changed to a system of differential equations, where the righthand-side consist only of a product (of powers) of the states (Riccati-representation). This unified system description by Volterra- or Riccati-representation) allows to use mathematical tools for the analysis of Volterra systems for a large class of nonlinear systems. The Riccati-representation allows to characterize the dynamics of the (original) system by means of five basic modes of growth. Examples show the advantages of this new approach from the theoretical and practical point of view (replication equation, model for world energy consumption and world population).

Item Type: Article
Uncontrolled Keywords: System analysis; time-varying systems; multivariable systems; modelling; ecology; biocybernetics
Depositing User: Luke Kirwan
Date Deposited: 04 Jul 2017 12:35
Last Modified: 04 Jul 2017 12:35
URI: http://pure.iiasa.ac.at/14719

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