|
|
Homoclinic and heteroclinic chaos in nonlinear systems driven by trichotomous noise |
You-Ming Lei(雷佑铭), Hong-Xia Zhang(张红霞) |
Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an 710072, China |
|
|
Abstract The homoclinic and heteroclinic chaos in nonlinear systems subjected to trichotomous noise excitation are studied. The Duffing system and the Josephson-junction system are taken for example to calculate the corresponding amplitude thresholds for the onset of chaos on the basis of the stochastic Melnikov process with the mean-square criterion. It is shown that the amplitude threshold for the onset of chaos can be adjusted by changing the internal parameters of trichotomous noise, thereby inducing or suppressing chaotic behaviors in the two systems driven by trichotomous noise. The effects of trichotomous noise on the systems are verified by vanishing the mean largest Lyapunov exponent and demonstrated by phase diagrams and time histories.
|
Received: 28 October 2016
Revised: 15 December 2016
Accepted manuscript online:
|
PACS:
|
05.45.-a
|
(Nonlinear dynamics and chaos)
|
|
05.45.Pq
|
(Numerical simulations of chaotic systems)
|
|
02.50.Ey
|
(Stochastic processes)
|
|
Fund: Project supported by the National Natural Science Foundation of China (Grant No. 11672231), the Natural Science Foundation of Shaanxi Province, China (Grant No. 2016JM1010), the Fundamental Research Funds for the Central Universities, China (Grant No. 3102015ZY073), and the Seed Foundation of Innovation and Creation for Graduate Students in Northwestern Polytechnical University, China. |
Corresponding Authors:
Hong-Xia Zhang
E-mail: zhanghongxia@mail.nwpu.edu.cn
|
Cite this article:
You-Ming Lei(雷佑铭), Hong-Xia Zhang(张红霞) Homoclinic and heteroclinic chaos in nonlinear systems driven by trichotomous noise 2017 Chin. Phys. B 26 030502
|
[1] |
Koch B P and Leven R W 1985 Physica D 16 1
|
[2] |
Ariaratnam S T, Xie W C and Vrscay E R 1989 Dyn. Stability Syst. 4 111
|
[3] |
Shaw S W and Rand R H 1989 Inter. J. Non-Linear Mech. 24 41
|
[4] |
Xie W C 1994 Nonlinear Stochastic Dynamics, AMD 192 215
|
[5] |
Lin H and Yim S C S 1996 ASME J. Appl. Mech. 63 509
|
[6] |
Awrejcewicz J and Sendkowski D 2004 Phys. Lett. A 330 371
|
[7] |
Awrejcewicz J and Pyryev Y 2006 Nonlinear Anal., Real World Appl. 7 12
|
[8] |
Awrejcewicz J and Holicke M 2006 Math. Probl. Eng. 2006 1
|
[9] |
Lei Y M and Xu W 2007 Acta Phys. Sin. 56 5103 (in Chinese)
|
[10] |
Zhang W, Yao M H and Zhang J H 2009 J. Sound Vib. 319 541
|
[11] |
Yang X W, Tian R L, Cao Q J and Wu Q L 2012 Chin. Phys. B 21 20503
|
[12] |
Elston T C and Doering C R 1996 J. Stat. Phys. 83 359
|
[13] |
Horsthemke W and Lefever R 1984 Noise-induced Transitions (Berlin: Springer)
|
[14] |
Bena I, Van den Broeck C, Kawai R and Lindenberg K 2002 Phys. Rev. E 66 045603
|
[15] |
Gitterman M 2003 Phys. Rev. E 67 057103
|
[16] |
Li J H and Han Y X 2006 Phys. Rev. E 74 051115
|
[17] |
Lei Y M, Fu R, Yang Y and Wang Y Y 2016 J. Sound Vib. 363 68
|
[18] |
Li P, Nie L R, Lü X M and Zhang Q B 2011 Chin. Phys. B 20 100502
|
[19] |
Mankin R, Ainsaar A and Reiter E 2000 Phys. Rev. E 61 6359
|
[20] |
Mankin R, Ainsaar A and Reiter E 1999 Phys. Rev. E 60 1374
|
[21] |
Mankin R, Laas K, Laas T and Reiter E 2008 Phys. Rev. E 78 031120
|
[22] |
Laas K, Mankin R and Rekker A 2009 Phys. Rev. E 79 051128
|
[23] |
Gitterman M 2012 Physica A 391 5343
|
[24] |
Mankin R, Soika E and Lumi N 2014 Physica A 411 128
|
[25] |
Mankin R, Ainsaar A, Haljas A and Reiter E 2002 Phys. Rev. E 65 051108
|
[26] |
Mankin R, Soika E and Sauga A 2008 WSEAS Trans. Syst. 7 239
|
[27] |
Soika E, Mankin R and Priimets J 2012 Proc. Est. Acad. Sci., Phys. Math. 61 113
|
[28] |
Guo F, Li H and Liu J 2014 Physica A 409 1
|
[29] |
Soika E and Mankin R 2010 WSEAS Trans. Biol. Biomed. 7 21
|
[30] |
Zhong S C, Wei K, Gao S L and Ma H 2015 J. Stat. Phys. 159 195
|
[31] |
Lin L F, Chen C and Wang H Q 2016 J. Stat. Mech. 2016 023201
|
[32] |
Yang T T, Zhang H Q, Xu Y and Xu W 2014 Inter. J. Non-Linear Mech. 67 42
|
[33] |
Zhang H Q, Yang T T, Xu Y and Xu W 2015 Eur. Phys. J. B 88 1
|
[34] |
Birx D L and Pipenberg S J 1992 IEEE International Joint Conference on Neural Network, June 7-11, 1992, p. 881
|
[35] |
Frey M and Simiu E 1993 Physica D 63 321
|
[36] |
Privault N 1994 Stochastics, Stochastics Rep. 51 83
|
[37] |
Kendall B 2001 Chaos, Solitons & Fractals 12 321
|
[38] |
Cveticanin L and Zukovic M 2009 J. Sound Vib. 326 768
|
[39] |
Sharma A, Patidar V, Purohit G and Sud K K 2012 Commun. Nonlinear Sci. Numer. Simul. 17 2254
|
[40] |
Srinil N and Zanganeh H 2012 Ocean Eng. 53 83
|
[41] |
Li Y, Yuan Y, Mandic D P and Yang B J 2009 Chin. Phys. B 18 958
|
[42] |
Likharev K K and Semenov V K 1991 IEEE Trans. Appl. Supercond. 1 3
|
[43] |
Makhlin Y, Schön G and Shnirman A 2001 Rev. Mod. Phys. 73 357
|
[44] |
Wang J S, Liang B L and Fan H Y 2008 Chin. Phys. B 17 697
|
[45] |
Wiggins S 1988 SIAM J. Appl. Math. 48 262
|
[46] |
Wolf A, Swift J B, Swinney H L and Vastano J A 1985 Physica D 16 285
|
[47] |
Sano M and Sawada Y 1985 Phys. Rev. Lett. 55 1082
|
[48] |
He T and Habib S 2013 Chaos 23 033123
|
No Suggested Reading articles found! |
|
|
Viewed |
|
|
|
Full text
|
|
|
|
|
Abstract
|
|
|
|
|
Cited |
|
|
|
|
Altmetric
|
blogs
Facebook pages
Wikipedia page
Google+ users
|
Online attention
Altmetric calculates a score based on the online attention an article receives. Each coloured thread in the circle represents a different type of online attention. The number in the centre is the Altmetric score. Social media and mainstream news media are the main sources that calculate the score. Reference managers such as Mendeley are also tracked but do not contribute to the score. Older articles often score higher because they have had more time to get noticed. To account for this, Altmetric has included the context data for other articles of a similar age.
View more on Altmetrics
|
|
|