Steady States of Globally and Locally Coupled Maps

다국어 초록 (Multilingual Abstract)

We consider a coupled logistic map system that is interacting locally and globally simultaneously.
We find numerically that the maps can be in steady states and investigate how widely the regions of the steady states are distributed in the parameter space. For purpose, we try to find a method to classify the regions of steady states in parameter space systematically by using some macroscopic measures. We also discuss some special aspects and stability of the steady states. Routes to the steady states are also investigated by comparing our case with the case of continuous-time oscillator systems.

참고문헌 (Reference)

1 P. Hadley, 38 : 8712-, 1988

2 Yumei Zhai, 69 : 026208-, 2004

3 P. M. Varangis, 78 : 2353-, 1997

4 A. Hohl, 78 : 4745-, 1997

5 J. Benford, 62 : 969-, 1989

6 I. Schreiber, 5 : 258-, 1982

7 S. Daan, 70 : 297-, 1978

8 P. Hadley, 52 : 1619-, 1988

9 G. B. Ermentrout, 50 : 125-, 1990

10 M. Yoshimoto, 280 : 539-, 1997

11 M. F. Crowley, 93 : 2496-, 1989

12 K. Kaneco, 63 : 219-, 1994

13 Y. Shibata, 72 : 1644-, 1994

14 M. Cencini, 130 : 58-, 1999

15 Y-J. Han, 38 : 642-, 2001

16 D. V. Ramana Reddy, 129 : 15-, 1999

17 K. Bar-Eli, 14 : 242-, 1985

18 R. Herrero, 84 : 5312-, 2000

19 D. V. R. Reddy, 85 : 3381-, 2000

20 K. Konishi, 678 : 017201-, 2003

21 C. Masoller, 94 : 134102-, 2005

22 N. B.Ouchi, 10 : 359-, 2000

23 S. Manrubia, 60 : 1579-, 1999

24 Lord Rayleigh, "The Theory of Sound, 2nd ed" Dover 1945

25 A.T. Winfree, "The Geometry of Biological Time" Springer 1980

26 A. Pikovsky, "Synchronization-A Universal Concept in Nonlinear Science" Cambridge University Press 2001

27 J.D. Murray, "Mathematical Biology, 2nd ed." Springer 1993