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本文研究了一类既不连续又不可逆分段线性映像构成的全局耦合映像格子系统中的一类典型集体动力学行为, 即冻结化随机图案模式. 计算了平均同步序参量和最大李雅普诺夫指数随耦合强度的变化. 结果显示, 当耦合强度超过某个阈值后, 在给定动力学变量的初始下, 系统几乎都能达到完全或部分同步状态, 出现冻结化随机图案. 这些现象表明, 耦合映像格子系统中存在着多个共存的吸引子. 因此, 其冻结化图案的结构和分布敏感地依赖于格点动力学变量初始值的选取. 感兴趣地是, 即使当单映像处于混沌状态时, 格点间的耦合仍能将系统调制到规则的运动状态, 这种特征对于混沌控制具有重要的利用价值. 上述丰富动力学行为的出现是由于单映像中不连续性和不可逆性相互作用的结果.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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