Finite-time anti-synchronization of a 6D Lorenz systems

Hu Tang; Kaiyu Liu; Zhengqiu Zhang; Hu Tang; Kaiyu Liu; Zhengqiu Zhang

doi:10.3934/math.20241703

AIMS Mathematics

2024, Volume 9, Issue 12: 35931-35948. doi: 10.3934/math.20241703

Previous Article Next Article

Research article

Finite-time anti-synchronization of a 6D Lorenz systems

1.
School of General Education, Hunan University of Information Technology, Changsha 410148, Hunan, China
2.
College of Mathematics, Hunan University, Changsha 410082, Hunan, China

Received: 14 October 2024 Revised: 27 November 2024 Accepted: 12 December 2024 Published: 25 December 2024
MSC : 34D06, 93D40

In this article, the finite time anti-synchronization (FTAS) of master-slave 6D Lorenz systems (MS6DLSS) is discussed. Without using previous study methods, by introducing new study methods, namely by adopting the properties of quadratic inequalities of one variable and utilizing the negative definiteness of the quadratic form of the matrix, two criteria on the FTAS are achieved for the discussed MS6DLSS. Up to now, the existing results on FTAS of chaotic systems have been achieved often by adopting the linear matrix inequality (LMI) method and finite time stability theorems (FTST). Adopting the new study methods studies the FTAS of the MS6DLSS, and the novel results on the FTAS are gotten for the MS6DLSS, which is innovative study work.
- FTAS,
- MS6DLSS,
- quadratic form of matrix,
- properties of quadratic inequalities of one variable
Citation: Hu Tang, Kaiyu Liu, Zhengqiu Zhang. Finite-time anti-synchronization of a 6D Lorenz systems[J]. AIMS Mathematics, 2024, 9(12): 35931-35948. doi: 10.3934/math.20241703

Related Papers:

Abstract

In this article, the finite time anti-synchronization (FTAS) of master-slave 6D Lorenz systems (MS6DLSS) is discussed. Without using previous study methods, by introducing new study methods, namely by adopting the properties of quadratic inequalities of one variable and utilizing the negative definiteness of the quadratic form of the matrix, two criteria on the FTAS are achieved for the discussed MS6DLSS. Up to now, the existing results on FTAS of chaotic systems have been achieved often by adopting the linear matrix inequality (LMI) method and finite time stability theorems (FTST). Adopting the new study methods studies the FTAS of the MS6DLSS, and the novel results on the FTAS are gotten for the MS6DLSS, which is innovative study work.

References

[1]	S. F. Al-Azzawi, A. S. Al-Obeidi, Dynamical analysis and anti-synchronization of a new 6D model with self-excited attractors, Appl. Math. J. Chin. Univ., 38 (2023), 27–43. https://doi.org/10.1007/s11766-023-3960-0 doi: 10.1007/s11766-023-3960-0
[2]	E. A. Assali, Different control strategies for predefined-time synchronization of nonidentical chaotic systems, Int. J. Syst. Sci., 55 (2024), 119–129. https://doi.org/10.1080/00207721.2023.2268771 doi: 10.1080/00207721.2023.2268771
[3]	S. F. Azzawi, M. M. Aziz, Chaos synchronization of non-linear dynamical systems via a novel analytical approach, Alex. Eng. J., 57 (2018), 3493–3500. https://doi.org/10.1016/j.aej.2017.11.017 doi: 10.1016/j.aej.2017.11.017
[4]	I. Bashkirtseva, L. Ryashko, M. J. Seoane, M. A. F. Sanjuan, Noise-induced complex dynamics and synchronization in the map-based Chialvo neuron model, Commun. Nonlinear Sci., 116 (2023), 106867. https://doi.org/10.1016/j.cnsns.2022.106867 doi: 10.1016/j.cnsns.2022.106867
[5]	E. C. Corrick, R. N. Drysdale, J. C. HeIIstrom, E. Capron, S. O. Rasmussen, X. Zhang, et al., Synchronous timing of abrupt climate changes during the last glacial period, Science, 369 (2020), 963–969. https://doi.org/10.1126/science.aay5538 doi: 10.1126/science.aay5538
[6]	S. Eshaghi, N. Kadkhoda, M. Inc, Chaos control and synchronization of a new fractional Laser chaotic system, Qual. Theory Dyn. Syst., 23 (2024), 241. https://doi.org/10.1007/s12346-024-01097-7 doi: 10.1007/s12346-024-01097-7
[7]	L. L. Huang, W. Y. Li, J. H. Xiang, G. L. Zhu, Adaptive finite-time synchronization of fractional order memristor chaotic system based on sliding-mode control, Eur. Phys. J. Spec. Top., 231 (2022), 3109–3118. https://doi.org/10.1140/epjs/s11734-022-00564-z doi: 10.1140/epjs/s11734-022-00564-z
[8]	A. A. K. Javan, A. Zare, Images encryption based on robust multi-mode finite time synchronization of fractional order hyper-chaotic Rikitake systems, Multimed. Tools Appl., 83 (2024), 1103–1123. https://doi.org/10.1007/s11042-023-15783-2 doi: 10.1007/s11042-023-15783-2
[9]	R. Kengne, R. Tehitnga, A. Mezatio, A. Fomethe, G. Litak, Finite-time synchronization of fractional order simplest two-component chaotic oscillators, Eur. Phys. J. B., 90 (2017), 88. https://doi.org/10.1140/epjb/e2017-70470-8 doi: 10.1140/epjb/e2017-70470-8
[10]	T. Kohyama, Y. Yamagami, H. Miura, S. Kido, H. Tatebe, M. Watanabe, The gulf stream and kuroshio current are synchronized, Science, 374 (2021), 341–346. https://doi.org/10.1126/science.abh3295 doi: 10.1126/science.abh3295
[11]	Q. Lai, G. W. Hu, U. Erkan, A. Toktas, A novel pixel-split image encryption scheme based on 2D Salomon map, Expert Syst. Appl., 213 (2023), 118845. https://doi.org/10.1016/j.eswa.2022.118845 doi: 10.1016/j.eswa.2022.118845
[12]	S. Lahmiri, C. Tadj, C. Gargour, S. Bekiros, Deep learning systems for automatic diagnosis of infantcry signals, Chaos Soliton. Fract., 154 (2022), 111700. https://doi.org/10.1016/j.chaos.2021.111700 doi: 10.1016/j.chaos.2021.111700
[13]	J. Li, J. M. Zheng, Finite-time synchronization of different dimensional chaotic systems with uncertain parameters and external disturbances, Sci. Rep., 12 (2022), 15407. https://doi.org/10.1038/s41598-022-19659-7 doi: 10.1038/s41598-022-19659-7
[14]	J. Li, Z. H. Zhou, S. Wan, Y. L. Zhang, Z. Shen, M. Li, et al., All-optical synchronization of remote optomechanical systems, Phys. Rev. Lett., 129 (2022), 063605. https://doi.org/10.1103/PhysRevLett.129.063605 doi: 10.1103/PhysRevLett.129.063605
[15]	F. N. Lin, G. M. Xue, B. Qin, S. G. Li, H. Liu, Event-triggered finite-time fuzzy control approach for fractional-order nonlinear chaotic systems with input delay, Chaos Soliton. Fract., 175 (2023), 114036. https://doi.org/10.1016/j.chaos.2023.114036 doi: 10.1016/j.chaos.2023.114036
[16]	E. N. Lorenz, Deterministic nonperiodic flow, J. Atmos. Sci., 20 (1963), 130–141. https://doi.org/10.1007/978-0-387-21830-4-2 doi: 10.1007/978-0-387-21830-4-2
[17]	X. Meng, C. C. Gao, B. P. Jiang, Z. T. Wu, Finite-time synchronization of variable-order fractional uncertain coupled systems via adaptive sliding mode control, Int. J. Control Autom. Syst., 20 (2022), 1535–1543. https://doi.org/10.1007/s12555-021-0051-y doi: 10.1007/s12555-021-0051-y
[18]	S. Q. Pang, Y. Feng, Y. J. Liu, Finite-time synchronization of chaotic systems with different dimension and secure communication, Math. Probl. Eng., 2016 (2016), 7693547. https://doi.org/10.1155/2016/7693547 doi: 10.1155/2016/7693547
[19]	W. Q. Pan, T. Z. Li, Finite-time synchronization of fractional-order chaotic systems with different structures under stochastic disturbances, Journal of Computer and Communications, 9 (2021), 120–137. https://doi.org/10.4236/jcc.2021.96007 doi: 10.4236/jcc.2021.96007
[20]	A. Roulet, C. Bruder, Quanyum synchronization and entanglement generation, Phys. Rev. Lett., 121 (2018), 063601. https://doi.org/10.1103/PhysRevLett.121.063601 doi: 10.1103/PhysRevLett.121.063601
[21]	E. Sakalar, T. Klausberger, B. Lasztoczi, Neurogliaform cells dynamically decouple neuronal synchrony between brain areas, Science, 377 (2022), 324–328. https://doi.org/10.1126/science.abo3355 doi: 10.1126/science.abo3355
[22]	R. Surendar, M. Muthtamilselvan, Sliding mode control on finite-time synchronization of nonlinear hyper mechanical fractional systems, Arab. J. Sci. Eng., 30 (2024), 088581. https://doi.org/10.1007/s13369-024-08858-1 doi: 10.1007/s13369-024-08858-1
[23]	S. Sweetha, R. Sakthivel, S. Harshavarthini, Finite-time synchronization of nonlinear fractional chaotic systems with stochastic faults, Chaos Soliton. Fract., 142 (2021), 110312. https://doi.org/10.1016/j.chaos.2020.110312 doi: 10.1016/j.chaos.2020.110312
[24]	A. Tutueva, L. Moysis, V. Rybin, A. Zubarev, C. Volos, D. Butusov, Adaptive symmetry control in secure communication systems, Chaos Soliton. Fract., 159 (2022), 112181. https://doi.org/10.1016/j.chaos.2022.112181 doi: 10.1016/j.chaos.2022.112181
[25]	V. Vafaei, A. J. Akbarfam, H. Kheiri, A new synchronisation method of fractional-order chaotic systems with distinct orders and dimensions and its application in secure communication, Int. J. Syst. Sci., 52 (2021), 3437–3450. https://doi.org/10.1080/00207721.2020.1836282 doi: 10.1080/00207721.2020.1836282
[26]	S. F. Wang, A 3D autonomous chaotic system: dynamics and synchronization, Indian J. Phys., 98 (2024), 4525–4533. https://doi.org/10.1007/s12648-024-03189-1 doi: 10.1007/s12648-024-03189-1
[27]	C. G. Wei, Y. He, X. C. Shangguan, Y. L. Fan, Master-slave synchronization for time-varying delay chaotic Lur'e systems based on the integral-term-related free-weighting-matrices technique, J. Franklin I., 359 (2022), 9079–9093. https://doi.org/10.1016/j.jfranklin.2022.08.027 doi: 10.1016/j.jfranklin.2022.08.027
[28]	T. Wu, J. H. Park, L. L. Xiong, X. Q. Xie, H. Y. Zhang, A novel approach to synchronization conditions for delayed chaotic Lur'e systems with state sampled-data quantized controller, J. Franklin I., 357 (2020), 9811–9833. https://doi.org/10.1016/j.jfranklin.2019.11.083 doi: 10.1016/j.jfranklin.2019.11.083
[29]	T. Yang, Z. Wang, X. Huang, J. W. Xia, Sampled-data exponential synchronization of Markovian with multiple time delays, Chaos Soliton. Fract., 160 (2022), 112252. https://doi.org/10.1016/j.chaos.2022.112252 doi: 10.1016/j.chaos.2022.112252
[30]	K. Yoshioka-Kobayashi, M. Matsumiya, Y. Niino, A. Isomura, H. Kori, A. Miyawaki, et al., Coupling delay controls synchronized oscillation in the segmentation clock, Nature, 580 (2020), 119–123. https://doi.org/10.1038/s41586-019-1882-z doi: 10.1038/s41586-019-1882-z
[31]	Z. Q. Yu, P. X. Liu, S. Ling, H. Q. Wang, Adaptive finite-time synchronisation of variable-order fractional chaotic systems for secure communication, Int. J. Syst. Sci., 55 (2024), 317–331. https://doi.org/10.1080/00207721.2023.2271621 doi: 10.1080/00207721.2023.2271621
[32]	J. D. Zha, C. B. Li, B. Song, W. Hu, Synchronisation control of composite chaotic systems, Int. J. Syst. Sci., 47 (2016), 3952–3959. https://doi.org/10.1080/00207721.2016.1157224 doi: 10.1080/00207721.2016.1157224
[33]	H. Y. Zhang, D. Y. Meng, J. Wang, G. D. Lu, Synchronization of uncertain chaotic systems via fuzzy-regulated adaptive optimal control approach, Int. J. Syst. Sci., 51 (2020), 473–487. https://doi.org/10.1080/00207721.2020.1716104 doi: 10.1080/00207721.2020.1716104
[34]	R. M. Zhang, D. Q. Zeng, S. M. Zhong, K. B. Shi, Memory feedback PID control for exponential synchronization of chaotic Lur'e systems, Int. J. Syst. Sci., 48 (2017), 2473–2484. https://doi.org/10.1080/00207721.2017.1322642 doi: 10.1080/00207721.2017.1322642
[35]	Z. Q. Zhang, J. D. Cao, Novel finite-time synchronization criteria for inertial neural networks with time delays via integral inequality method, IEEE T. Neur. Net. Lear., 30 (2019), 1476–1485. https://doi.org/10.1109/TNNLS.2018.2868800 doi: 10.1109/TNNLS.2018.2868800
[36]	Z. Q. Zhang, M. Chen, A. L. Li, Further study on finite-time synchronization for delayed inertial neural networks via inequality skills, Neurocomputing, 373 (2020), 15–23. https://doi.org/10.1016/j.neucom.2019.09.034 doi: 10.1016/j.neucom.2019.09.034
[37]	Z. Q. Zhang, J. D. Cao, Finite-time synchronization for fuzzy inertial neural networks by maximum-value approach, IEEE T. Fuzzy Syst., 30 (2022), 1436–1446. https://doi.org/10.1109/TFUZZ.2021.3059953 doi: 10.1109/TFUZZ.2021.3059953
[38]	D. Q. Zeng, K. T. Wu, Y. J. Liu, R. M. Zhang, S. M. Zhong, Event-triggered sampling control for exponential synchronization of chaotic Lur'e systems with time-varying communication delays, Nonlinear Dyn., 91 (2018), 905–921. https://doi.org/10.1007/s11071-017-3918-y doi: 10.1007/s11071-017-3918-y
[39]	S. Zheng, Synchronization analysis of time delay complex-variable chaotic systems with discontinuous coupling, J. Franklin I., 353 (2016), 1460–1477. https://doi.org/10.1016/j.jfranklin.2016.02.006 doi: 10.1016/j.jfranklin.2016.02.006

Reader Comments

Your name:*

Email:*
© 2024 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)