scholarly journals Fuzzy cell mapping on dynamical systems

2013 ◽  
Vol 8 (19) ◽  
pp. 973-983
Author(s):  
Song Y ◽  
Edwards D ◽  
S Manoranjan V
Keyword(s):  
Dynamical Systems ◽  
Cell Mapping ◽  
Fuzzy Cell

Using Generalized Cell Mapping to Approximate Invariant Measures on Compact Manifolds

1997 ◽  
Vol 07 (11) ◽  
pp. 2487-2499 ◽  
Author(s):  
Rabbijah Guder ◽  
Edwin Kreuzer
Keyword(s):  
Dynamical Systems ◽  
Invariant Measures ◽  
Nonlinear Dynamical Systems ◽  
Powerful Method ◽  
Cell Mapping ◽  
Generalized Cell Mapping ◽  
Nonlinear Dynamical ◽  
Long Term Behavior ◽  
Mapping Theory

In order to predict the long term behavior of nonlinear dynamical systems the generalized cell mapping is an efficient and powerful method for numerical analysis. For this reason it is of interest to know under what circumstances dynamical quantities of the generalized cell mapping (like persistent groups, stationary densities, …) reflect the dynamics of the system (attractors, invariant measures, …). In this article we develop such connections between the generalized cell mapping theory and the theory of nonlinear dynamical systems. We prove that the generalized cell mapping is a discretization of the Frobenius–Perron operator. By applying the results obtained for the Frobenius–Perron operator to the generalized cell mapping we outline for some classes of transformations that the stationary densities of the generalized cell mapping converges to an invariant measure of the system. Furthermore, we discuss what kind of measures and attractors can be approximated by this method.

A subdomain synthesis method for global analysis of nonlinear dynamical systems based on cell mapping

2018 ◽  
Vol 95 (1) ◽  
pp. 715-726 ◽  
Author(s):  
Zigang Li ◽  
Jun Jiang ◽  
Jing Li ◽  
Ling Hong ◽  
Ming Li
Keyword(s):  
Dynamical Systems ◽  
Nonlinear Dynamical Systems ◽  
Global Analysis ◽  
Synthesis Method ◽  
Cell Mapping ◽  
Nonlinear Dynamical

Fuzzy Cell Mapping

2012 ◽  
pp. 161-174
Author(s):  
Jian-Qiao Sun ◽  
Ling Hong
Keyword(s):  
Cell Mapping ◽  
Fuzzy Cell

GLOBAL ANALYSIS OF DYNAMICAL SYSTEMS USING POSETS AND DIGRAPHS

1995 ◽  
Vol 05 (04) ◽  
pp. 1085-1118 ◽  
Author(s):  
C. S. HSU
Keyword(s):  
Dynamical Systems ◽  
Nonlinear Dynamical Systems ◽  
Global Analysis ◽  
Ordered Sets ◽  
Cell Mapping ◽  
Basic Notion ◽  
Nonlinear Dynamical ◽  
Global Evolution ◽  
Computation Algorithms ◽  
Primitive Notion

In this paper the resources of the theory of partially ordered sets (posets) and the theory of digraphs are used to aid the task of global analysis of nonlinear dynamical systems. The basic idea underpinning this approach is the primitive notion that a dynamical systems is simply an ordering machine which assigns fore-and-after relations for pairs of states. In order to make the linkage between the theory of posets and digraphs and dynamical systems, cell mapping is used to put dynamical systems in their discretized form and an essential concept of self-cycling sets is used. After a discussion of the basic notion of ordering, appropriate results from the theory of posets and digraphs are adapted for the purpose of determining the global evolution properties of dynamical systems. In terms of posets, evolution processes and strange attractors can be studied in a new light. It is believed that this approach offers us a new way to examine the multifaceted complex behavior of nonlinear systems. Computation algorithms are also discussed and an example of application is included.

Fuzzy Cell Mapping Applied to Autonomous Systems

2001 ◽  
Author(s):  
Y. Song ◽  
D. Edwards ◽  
V. S. Manoranjan
Keyword(s):  
Nonlinear Systems ◽  
Analytical Methods ◽  
Autonomous Systems ◽  
Global Behavior ◽  
Cell Mapping ◽  
Strongly Nonlinear ◽  
Scientific Disciplines ◽  
Fuzzy Cell ◽  
Engineering Physics ◽  
Viable Method

Abstract Nonlinear systems appear in many scientific disciplines such as engineering, physics, chemistry, biology, economics, and demography. Therefore methods of analysis of nonlinear systems, which can provide a good understanding of their behavior have wide applications. Although there are several analytical methods (See Hsu [3] and references therein), determining the global behavior of strongly nonlinear systems is still a substantially difficult task. The direct approach of numerical integration is a viable method. However, such an approach is sometimes prohibitively time consuming even with the powerful present-day computers.

Identification of Multivariable Fuzzy Systems through Fuzzy Cell Mapping

1993 ◽  
Vol 26 (2) ◽  
pp. 153-157
Author(s):  
Li-Min Jia ◽  
Xi-Di Zhang
Keyword(s):  
Fuzzy Systems ◽  
Cell Mapping ◽  
Fuzzy Cell

Fuzzy cell-to-cell mapping

2002 ◽  
Author(s):  
H. Aydin ◽  
A.M. Erkmen
Keyword(s):  
Cell Mapping ◽  
Fuzzy Cell

Improved generalized cell mapping for global analysis of dynamical systems

2009 ◽  
Vol 52 (3) ◽  
pp. 787-800 ◽  
Author(s):  
HaiLin Zou ◽  
JianXue Xu
Keyword(s):  
Dynamical Systems ◽  
Global Analysis ◽  
Cell Mapping ◽  
Generalized Cell Mapping

A fuzzy cell mapping method for a sub-optimal control implementation

1994 ◽  
Vol 2 (2) ◽  
pp. 247-254 ◽  
Author(s):  
J.Y. Yen ◽  
W.C. Chao ◽  
S.S. Lu
Keyword(s):  
Optimal Control ◽  
Mapping Method ◽  
Cell Mapping ◽  
Fuzzy Cell ◽  
Control Implementation
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