The adjoining cell mapping and its recursive unraveling, Part I: Description of adaptive and recursive algorithms

Zufiria Zatarain, Pedro Jose and Guttalu, Ramesh S. (1993). The adjoining cell mapping and its recursive unraveling, Part I: Description of adaptive and recursive algorithms. "Nonlinear Dynamics", v. 4 ; pp. 204-226. ISSN 0924-090X.

Description

Title: The adjoining cell mapping and its recursive unraveling, Part I: Description of adaptive and recursive algorithms
Author/s:
  • Zufiria Zatarain, Pedro Jose
  • Guttalu, Ramesh S.
Item Type: Article
Título de Revista/Publicación: Nonlinear Dynamics
Date: 1993
ISSN: 0924-090X
Volume: 4
Subjects:
Freetext Keywords: Nonlinear autonomous dynamical systems, simple cell mapping, limit cycles, adjoining cell mapping, adaptivc integration, recursive algorithms
Faculty: E.T.S.I. Telecomunicación (UPM)
Department: Matemática Aplicada a las Tecnologías de la Información y las Comunicaciones
Creative Commons Licenses: Recognition - No derivative works - Non commercial

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Abstract

A new type of cell mapping, referred to as an adjoining cell mapping, is developed in this paper for autonomous dynamical systems employing the cellular state space. It is based on an adaptive time integration employed to compute an associated cell mapping for the system. This technique overcomes the problem of determining an appropriate duration of integration time for the simple cell mapping method. Employing the adjoining mapping principle, the first type of algorithm developed here is an adaptive mapping unraveling algorithm to determine equilibria and limit cycles of the dynamical system in a way similar to that of the simple cell mapping. In addition, it is capable of providing useful information regarding the behavior of dynamical systems possessing pathological dynamics and of systems with rapidly changing vector field. The adjoining property inherent in the adjoining cell mapping method, in general, permits development of new recursive algorithms for unraveling dynamics. The required computer memory for a practical implementation of such algorithms is considerably less than that required by the simple cell mapping algorithm since they allow for a recursive partitioning of state space for trajectory analysis. The second type of algorithm developed in this paper is a recursive unraveling algorithm based on adaptive integration and recursive partitioning of state space into blocks of cells with a view toward its practical implementation. It can find equilibria of the system in the same manner as the simple cell mapping method but is more efficient in locating periodic solutions.

More information

Item ID: 53500
DC Identifier: http://oa.upm.es/53500/
OAI Identifier: oai:oa.upm.es:53500
Official URL: https://link.springer.com/article/10.1007/BF00046321
Deposited by: Memoria Investigacion
Deposited on: 25 Mar 2019 17:23
Last Modified: 25 Mar 2019 17:23
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