##
**Control and synchronization of chaos in RCL-shunted Josephson junction with noise disturbance using only one controller term.**
*(English)*
Zbl 1246.34060

Summary: This paper investigates the control and synchronization of the shunted nonlinear resistive-capacitive-inductance junction (RCLSJ) model under the condition of noise disturbance with only one single controller. Based on the sliding mode control method, the controller is designed to eliminate the chaotic behavior of Josephson junctions and realize the achievement of global asymptotic synchronization of coupled system. Numerical simulation results are presented to demonstrate the validity of the proposed method. The approach is simple and easy to implement and provides reference for chaos control and synchronization in relevant systems.

### MSC:

34H10 | Chaos control for problems involving ordinary differential equations |

37D45 | Strange attractors, chaotic dynamics of systems with hyperbolic behavior |

PDF
BibTeX
XML
Cite

\textit{D.-Y. Chen} et al., Abstr. Appl. Anal. 2012, Article ID 378457, 14 p. (2012; Zbl 1246.34060)

Full Text:
DOI

### References:

[1] | T. G. Zhou, D. C. Wang, F. L. Liu, L. Fang, X. J. Zhao, and S. L. Yan, “Simulation of chaos in different models of Josephson junctions,” Journal of System Simulation, vol. 22, no. 3, pp. 666-669, 2010. |

[2] | C. R. Nayak and V. C. Kuriakose, “Dynamics of coupled Josephson junctions under the influence of applied fields,” Physics Letters A, vol. 365, no. 4, pp. 284-289, 2007. |

[3] | S. Das, S. Datta, and D. Sahdev, “Mode-locking, hysteresis and chaos in coupled Josephson junctions,” Physica D, vol. 101, no. 3-4, pp. 333-345, 1997. · Zbl 0891.34051 |

[4] | E. Kurt and M. Canturk, “Chaotic dynamics of resistively coupled DC-driven distinct Josephson junctions and the effects of circuit parameters,” Physica D, vol. 238, no. 22, pp. 2229-2237, 2009. · Zbl 1188.94052 |

[5] | X. S. Yang and Q. D. Li, “A computer-assisted proof of chaos in Josephson junctions,” Chaos, Solitons & Fractals, vol. 27, no. 1, pp. 25-30, 2006. · Zbl 1083.37034 |

[6] | T. Kawaguchi, “Directed transport and complex dynamics of vortices in a Josephson junction network driven by modulated currents,” Physica C, vol. 470, no. 20, pp. 1133-1136, 2010. |

[7] | S. Al-Khawaja, “Chaotic dynamics of underdamped Josephson junctions in a ratchet potential driven by a quasiperiodic external modulation,” Physica C, vol. 420, no. 1-2, pp. 30-36, 2005. |

[8] | K. Kadowaki, I. Kakeya, T. Yamamoto, T. Yamazaki, M. Kohri, and Y. Kubo, “Dynamical properties of Josephson vortices in mesoscopic intrinsic Josephson junctions in single crystalline Bi2Sr2CaCu2O8+\delta ,” Physica C, vol. 437-438, pp. 111-117, 2006. |

[9] | P. D. Shaju and V. C. Kuriakose, “Vortex dynamics in S-shaped Josephson junctions,” Physica C, vol. 434, no. 1, pp. 25-30, 2006. |

[10] | S. Candia, Ch. Leemann, S. Mouaziz, and P. Martinoli, “Investigation of vortex dynamics in Josephson junction arrays with magnetic flux noise measurements,” Physica C, vol. 369, no. 1-4, pp. 309-312, 2002. |

[11] | T. Kawaguchi, “Depinning mechanism and driven dynamics of vortices in disordered Josephson junction arrays,” Physica C, vol. 392-396, part 1, pp. 364-368, 2003. |

[12] | J. Affolter, A. Eichenberger, S. Rosse, P. Scheuzger, C. Leemann, and P. Martinoli, “Phase and vortex dynamics in Josephson junction arrays with percolative disorder,” Physica B, vol. 280, no. 1-4, pp. 241-242, 2000. |

[13] | M. MacHida, T. Koyama, A. Tanaka, and M. Tachiki, “Theory of the superconducting phase and charge dynamics in intrinsic Josephson-junction systems: microscopic foundation for longitudinal Josephson plasma and phenomenological dynamical equations,” Physica C, vol. 331, no. 1, pp. 85-96, 2000. |

[14] | H. Kashiwaya, T. Matsumoto, H. Shibata et al., “Switching dynamics and MQT in Bi2201 intrinsic Josephson junctions,” Physica C, vol. 469, no. 15-20, pp. 1593-1595, 2009. |

[15] | M. Hayashi, M. Suzuki, J. Onuki, and H. Ebisawa, “Nonlinear dynamics of intrinsic Josephson junctions under an applied current,” Physica C, vol. 463-465, pp. 993-996, 2007. |

[16] | J. M. Dias and A. Dourado, “A self-organizing fuzzy controller with a fixed maximum number of rules and an adaptive similarity factor,” Fuzzy Sets and Systems, vol. 103, no. 1, pp. 27-48, 1999. |

[17] | D. Y. Chen, L. Shi, H. T. Chen, and X. Y. Ma, “Analysis and control of a hyperchaotic system with only one nonlinear term,” Nonlinear Dynamics, vol. 67, no. 3, pp. 1745-1752, 2012. |

[18] | J. Ma, Q. Y. Wang, W. Y. Jin, et al., “Control chaos in the Hindmarsh-Rose neuron by using intermittent feedback with one variable,” Chinese Physics Letters, vol. 25, no. 10, pp. 3582-3585, 2008. |

[19] | M. Rafikov and J. M. Balthazar, “On control and synchronization in chaotic and hyperchaotic systems via linear feedback control,” Communications in Nonlinear Science and Numerical Simulation, vol. 13, no. 7, pp. 1246-1255, 2008. · Zbl 1221.93230 |

[20] | Z. Ruo-Xun and Y. Shi-Ping, “Chaos in fractional-order generalized lorenz system and its synchronization circuit simulation,” Chinese Physics B, vol. 18, no. 8, pp. 3295-3303, 2009. |

[21] | A. S. de Paula and M. A. Savi, “A multiparameter chaos control method based on OGY approach,” Chaos, Solitons & Fractals, vol. 40, no. 3, pp. 1376-1390, 2009. · Zbl 1197.34110 |

[22] | D. Y. Chen, W. L. Zhao, X. Y. Ma, and R. F. Zhang, “No-chattering sliding mode control chaos in Hindmarsh-Rose neurons with uncertain parameters,” Computers & Mathematics with Applications, vol. 61, no. 10, pp. 3161-3171, 2011. · Zbl 1222.37106 |

[23] | D. Y. Chen, R. F. Zhang, X. Y. Ma, et al., “Chaotic synchronization and anti-synchronization for a novel class of multiple chaotic systems via a sliding mode control scheme,” Nonlinear Dynamics, vol. 69, no. 1-2, pp. 35-55, 2011. · Zbl 1253.93017 |

[24] | B. Yurke, R. Movshovich, P. G. Kaminsky et al., “Vacuum-noise squeezing at microwave frequencies using Josephson-parametric amplifier,” Physica B, vol. 169, no. 1-4, pp. 432-435, 1991. |

[25] | F. Müller, H. Schulze, R. Behr, J. Kohlmann, and J. Niemeyer, “The Nb-Al technology at PTB-a common base for different types of Josephson voltage standards,” Physica C, vol. 354, no. 1-4, pp. 66-70, 2001. |

[26] | E. Il’ichev, G. S. Krivoy, and R. P. J. IJsselsteijn, “Low frequency noise of high-Tc radio-frequency SQUIDs based on grain boundary Josephson junctions,” Physica C, vol. 377, no. 4, pp. 516-520, 2002. |

[27] | Y. Zhao and W. Wang, “Chaos synchronization in a Josephson junction system via active sliding mode control,” Chaos, Solitons & Fractals, vol. 41, no. 1, pp. 60-66, 2009. · Zbl 1198.34127 |

[28] | A. Ucar, K. E. Lonngren, and E. W. Bai, “Chaos synchronization in RCL-shunted Josephson junction via active control,” Chaos, Solitons & Fractals, vol. 31, no. 1, pp. 105-111, 2007. |

[29] | J. J. Yan, C. F. Huang, and J. S. Lin, “Robust synchronization of chaotic behavior in unidirectional coupled RCLSJ models subject to uncertainties,” Nonlinear Analysis. Real World Applications, vol. 10, no. 5, pp. 3091-3097, 2009. · Zbl 1171.37019 |

[30] | M. B. Gaifullin, K. Hirata, S. Ooi, S. Savel’ev, Yu. I. Latyshev, and T. Mochiku, “Synchronization in stacked array of the Josephson junctions in Bi2Sr2CaCu2O8+\delta ,” Physica C, vol. 468, no. 15-20, pp. 1896-1898, 2008. |

[31] | G. Filatrella and N. F. Pedersen, “Synchronization of intrinsic Josephson junctions to a cavity,” Physica C, vol. 408-410, no. 1-4, pp. 560-561, 2004. |

[32] | W. X. Qin and G. Chen, “Coupling schemes for cluster synchronization in coupled Josephson equations,” Physica D, vol. 197, no. 3-4, pp. 375-391, 2004. · Zbl 1066.34046 |

[33] | U. E. Vincent, A. Ucar, J. A. Laoye, and S. O. Kareem, “Control and synchronization of chaos in RCL-shunted Josephson junction using backstepping design,” Physica C, vol. 468, no. 5, pp. 374-382, 2008. |

[34] | A. N. Njah, K. S. Ojo, G. A. Adebayo, and A. O. Obawole, “Generalized control and synchronization of chaos in RCL-shunted Josephson junction using backstepping design,” Physica C, vol. 470, no. 13-14, pp. 558-564, 2010. |

[35] | C. B. Whan, C. J. Lobb, and M. G. Forrester, “Effect of inductance in externally shunted Josephson tunnel junctions,” Journal of Applied Physics, vol. 77, no. 1, pp. 382-389, 1995. |

[36] | J. Lü, S. Yu, H. Leung, and G. Chen, “Experimental verification of multidirectional multiscroll chaotic attractors,” IEEE Transactions on Circuits and Systems I, vol. 53, no. 1, pp. 149-165, 2006. |

[37] | S. Yu, J. Lü, X. Yu, and G. Chen, “Design and implementation of grid multiwing hyperchaotic lorenz system family via switching control and constructing super-heteroclinic loops,” IEEE Transactions on Circuits and Systems I, vol. 59, no. 5, pp. 1015-1028, 2012. |

[38] | J. Lü and G. Chen, “Generating multiscroll chaotic attractors: theories, methods and applications,” International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, vol. 16, no. 4, pp. 775-858, 2006. · Zbl 1097.94038 |

[39] | J. Lü, F. Han, X. Yu, and G. Chen, “Generating 3-D multi-scroll chaotic attractors: a hysteresis series switching method,” Automatica, vol. 40, no. 10, pp. 1677-1687, 2004. · Zbl 1162.93353 |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.