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A class of the characteristic collective dynamic behaviors, i.e., the frozen random patterns, in a globally coupled both-discontinuous-and-non-invertible-map lattices are studied. The coupling-strength dependences of the mean order parameters and the largest Lyapunov exponents are calculated and analyzed. The result shows that, given the initial values for the dynamical variables, the system will reach its complete or partial synchronization state when the coupling strength is beyond some critical value, where the frozen random pattern appears. These phenomena reveal that there are coexisting attractors in the system, and thus the structure and the distribution of the frozen random patterns sensitively depend on the choice of the initial dynamics variables. The interesting event is that the system can be modulated to some regular states of motion by the coupling among lattices even when the single maps are in the chaotic states, which may have some important applications in controlling chaos. The rich dynamical behaviors mentioned above are due to the interplay between the discontinuity and the non-invertibility in the map.
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Keywords:
- coupled map lattices /
- discontinuous map /
- collective dynamics
[1] Kanoke K 1992 Chaos 2 279
[2] Kanoke K 1991 Physica D 54 5
[3] Hu G, Qu Z L 1994 Phys. Rev. Lett. 72 68
[4] Batista A M, Pinto S E de S, Viana R L, Lopes S R 2002 Phys. Rev. E 65 056209
[5] Santos A M,Viana R L, Lopes S R, Pinto S E de S, Batista A M 2006 Physica A 367 145
[6] Yang W M 1994 Spatio-temproal Chaos and Coupled Map Lattices (Shanghai: Education And Technology Press of Shanghai) (in Chinese) [杨维明 1994 时空混沌和耦合映像格子(上海: 上海教育科技出版社)]
[7] Wiesenfeld K, Hadley P 1989 Phys. Rev. Lett. 62 1335
[8] Sompolinsky H, Golomb D 1991 Phys. Rev. A 43 6990
[9] Wiesenfeld K, Bracikowski C, James G, Roy R 1990 Phys. Rev. Lett. 65 1749
[10] Sompolinsky H, Golomb D, Kleinfeld D 1991 Phys. Rev. A 43 6990
[11] Wang T, Wang K J, Jia N 2011 Neural Computing 74 1673
[12] Grudzinski K, Zebrowski J J 2004 Physica A 336 153
[13] Budd C J, Piiroinenb P T 2006 Physica D 220 127
[14] He D R, Wang B H, Bauer M, Habip S, Krueger U, Martienssen W, Christiansen B 1994 Physica D 79 335
[15] Qu S X, Cristiansen B, He D R 1995 Phys. Lett. A 201 413
[16] Qu S X, Lu Y Z, Zhang L, He D R 2008 Chin. Phys. B 17 4418
[17] Ren H P, Liu D 2005 Chin. Phys. 14 1352
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[1] Kanoke K 1992 Chaos 2 279
[2] Kanoke K 1991 Physica D 54 5
[3] Hu G, Qu Z L 1994 Phys. Rev. Lett. 72 68
[4] Batista A M, Pinto S E de S, Viana R L, Lopes S R 2002 Phys. Rev. E 65 056209
[5] Santos A M,Viana R L, Lopes S R, Pinto S E de S, Batista A M 2006 Physica A 367 145
[6] Yang W M 1994 Spatio-temproal Chaos and Coupled Map Lattices (Shanghai: Education And Technology Press of Shanghai) (in Chinese) [杨维明 1994 时空混沌和耦合映像格子(上海: 上海教育科技出版社)]
[7] Wiesenfeld K, Hadley P 1989 Phys. Rev. Lett. 62 1335
[8] Sompolinsky H, Golomb D 1991 Phys. Rev. A 43 6990
[9] Wiesenfeld K, Bracikowski C, James G, Roy R 1990 Phys. Rev. Lett. 65 1749
[10] Sompolinsky H, Golomb D, Kleinfeld D 1991 Phys. Rev. A 43 6990
[11] Wang T, Wang K J, Jia N 2011 Neural Computing 74 1673
[12] Grudzinski K, Zebrowski J J 2004 Physica A 336 153
[13] Budd C J, Piiroinenb P T 2006 Physica D 220 127
[14] He D R, Wang B H, Bauer M, Habip S, Krueger U, Martienssen W, Christiansen B 1994 Physica D 79 335
[15] Qu S X, Cristiansen B, He D R 1995 Phys. Lett. A 201 413
[16] Qu S X, Lu Y Z, Zhang L, He D R 2008 Chin. Phys. B 17 4418
[17] Ren H P, Liu D 2005 Chin. Phys. 14 1352
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