-
By extending and nonlinearly coupling two one-dimensional parabolic discrete maps, a new two-dimensional parabolic discrete map is achieved. By using stability analysis of fixed points and bifurcation analysis of map, the complex dynamical behavior and attractor evolution of the proposed two-dimensional discrete map are investigated, and its peculiar dynamical characteristics, such as the coexisting bifurcation modes and fast-slow periodic oscillation effects, etc., are illustrated. The research results indicate that two-dimensional parabola discrete map has two control parameters with different functions of adjustable dynamical behaviors and adjustable dynamic amplitudes, and there emerge nonlinear physical phenomena of Hopf bifurcation, bifurcation mode coexisting, locked-frequency and periodic oscillation fast-slow effect. Furthermore, the corresponding theoretical analysis and numerical simulation results are verified based on a digital circuit realized by microcontroller.
-
Keywords:
- two-dimensional discrete map /
- bifurcation /
- attractor /
- parameter
[1] Liu Z, Zhu X H, Hu W, Jiang F 2007 Int. J. Bifur. Chaos 17 1735
[2] Lin F Y, Liu J M 2004 IEEE J. Quantum Electron. 40 815
[3] Long M, Qiu S S 2007 Chin. Phys. 16 2254
[4] Bao B C, Xu J P, Liu Z 2009 Chin. Phys. B 18 4742
[5] Zheng F, Tian X J, Li X Y, Wu B 2008 Chin. Phys. B 17 1685
[6] May R M 1976 Nature 261 459
[7] Feigenbaum M J 1978 J. Statistical Phys. 19 25
[8] Yu W P, Wei X P 2006 Acta Phys. Sin. 55 3969 (in Chinese) [于万波、魏小鹏 2006 55 3969]
[9] Bao B C, Hu W, Liu Z, Kang Z S, Xu J P 2009 Acta Phys. Sin. 58 2440 (in Chinese) [包伯成、胡 文、刘 中、康祝圣、许建平 2009 58 2440]
[10] Bao B C, Xu J P, Liu Z 2009 Acta Phys. Sin. 58 2949 (in Chinese) [包伯成、许建平、刘 中 2009 58 2949]
[11] Wang X Y, Liang Q Y 2005 Chin. J. Theoretical and Applied Mechanics 37 522 (in Chinese) [王兴元、梁庆永 2005 力学学报 37 522]
[12] Bao B C, Kang Z S, Xu J P, Hu W 2009 Acta Phys. Sin. 58 1420 (in Chinese) [包伯成、康祝圣、许建平、胡 文 2009 58 1420]
[13] Wang X Y, Luo C 2005 Chin. J. Theoretical and Applied Mechanics 37 346 (in Chinese) [王兴元、骆 超 2005 力学学报 37 346]
[14] Wang X Y, Wang M J 2008 Acta Phys. Sin. 57 731 (in Chinese) [王兴元、王明军 2008 57 731]
[15] Wang L M 2009 J. Northwest Normal Univ. (Natural Science) 45 26 (in Chinese) [王立军 2009 西北师范大学学报(自然科学版) 45 26]
[16] Wang X Y, Luo C 2006 J. Software 17 729
[17] Li Z G, Xu D L 2004 Chaos, Solitons and Fractals 22 477
[18] Zhang X F, Chen Z Y, Ji Y, Bi Q S 2009 Chin. J. Theoretical and Applied Mechanics 41 765 (in Chinese) [张晓芳、陈章耀、季 颖、毕勤胜 2009 力学学报 41 765]
[19] Li C B, Wang D C 2009 Acta Phys. Sin. 58 764 (in Chinese) [李春彪、王德纯 2009 58 764]
[20] Li C B, Wang H K, Chen S 2010 Acta Phys. Sin. 59 783 (in Chinese) [李春彪、王翰康、陈 谡 2010 59 783]
-
[1] Liu Z, Zhu X H, Hu W, Jiang F 2007 Int. J. Bifur. Chaos 17 1735
[2] Lin F Y, Liu J M 2004 IEEE J. Quantum Electron. 40 815
[3] Long M, Qiu S S 2007 Chin. Phys. 16 2254
[4] Bao B C, Xu J P, Liu Z 2009 Chin. Phys. B 18 4742
[5] Zheng F, Tian X J, Li X Y, Wu B 2008 Chin. Phys. B 17 1685
[6] May R M 1976 Nature 261 459
[7] Feigenbaum M J 1978 J. Statistical Phys. 19 25
[8] Yu W P, Wei X P 2006 Acta Phys. Sin. 55 3969 (in Chinese) [于万波、魏小鹏 2006 55 3969]
[9] Bao B C, Hu W, Liu Z, Kang Z S, Xu J P 2009 Acta Phys. Sin. 58 2440 (in Chinese) [包伯成、胡 文、刘 中、康祝圣、许建平 2009 58 2440]
[10] Bao B C, Xu J P, Liu Z 2009 Acta Phys. Sin. 58 2949 (in Chinese) [包伯成、许建平、刘 中 2009 58 2949]
[11] Wang X Y, Liang Q Y 2005 Chin. J. Theoretical and Applied Mechanics 37 522 (in Chinese) [王兴元、梁庆永 2005 力学学报 37 522]
[12] Bao B C, Kang Z S, Xu J P, Hu W 2009 Acta Phys. Sin. 58 1420 (in Chinese) [包伯成、康祝圣、许建平、胡 文 2009 58 1420]
[13] Wang X Y, Luo C 2005 Chin. J. Theoretical and Applied Mechanics 37 346 (in Chinese) [王兴元、骆 超 2005 力学学报 37 346]
[14] Wang X Y, Wang M J 2008 Acta Phys. Sin. 57 731 (in Chinese) [王兴元、王明军 2008 57 731]
[15] Wang L M 2009 J. Northwest Normal Univ. (Natural Science) 45 26 (in Chinese) [王立军 2009 西北师范大学学报(自然科学版) 45 26]
[16] Wang X Y, Luo C 2006 J. Software 17 729
[17] Li Z G, Xu D L 2004 Chaos, Solitons and Fractals 22 477
[18] Zhang X F, Chen Z Y, Ji Y, Bi Q S 2009 Chin. J. Theoretical and Applied Mechanics 41 765 (in Chinese) [张晓芳、陈章耀、季 颖、毕勤胜 2009 力学学报 41 765]
[19] Li C B, Wang D C 2009 Acta Phys. Sin. 58 764 (in Chinese) [李春彪、王德纯 2009 58 764]
[20] Li C B, Wang H K, Chen S 2010 Acta Phys. Sin. 59 783 (in Chinese) [李春彪、王翰康、陈 谡 2010 59 783]
Catalog
Metrics
- Abstract views: 9329
- PDF Downloads: 888
- Cited By: 0
下载:
