scholarly journals Fuzzy cell mapping on dynamical systems

2013 ◽  
Vol 8 (19) ◽  
pp. 973-983
Author(s):  
Song Y ◽  
Edwards D ◽  
S Manoranjan V

1997 ◽  
Vol 07 (11) ◽  
pp. 2487-2499 ◽  
Author(s):  
Rabbijah Guder ◽  
Edwin Kreuzer

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.



2018 ◽  
Vol 95 (1) ◽  
pp. 715-726 ◽  
Author(s):  
Zigang Li ◽  
Jun Jiang ◽  
Jing Li ◽  
Ling Hong ◽  
Ming Li


Author(s):  
Jian-Qiao Sun ◽  
Ling Hong
Keyword(s):  


1995 ◽  
Vol 05 (04) ◽  
pp. 1085-1118 ◽  
Author(s):  
C. S. HSU

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.



Author(s):  
Y. Song ◽  
D. Edwards ◽  
V. S. Manoranjan

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.



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






1994 ◽  
Vol 2 (2) ◽  
pp. 247-254 ◽  
Author(s):  
J.Y. Yen ◽  
W.C. Chao ◽  
S.S. Lu


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