Complex compound-combination multi switching anti-synchronization of fractional-order complex chaotic systems and integer-order complex chaotic systems

International Journal of Dynamics and Control - Tập 10 Số 2 - Trang 525-542 - 2022
Xiaoqing Zhang1, Jian Xiao2
1Department of Science, Taiyuan Institute of Technology, Taiyuan, 030008, Shanxi, People's Republic of China
2College of Mathematics and Statistics, Chongqing University, Chongqing, 401331, People’s Republic of China

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Tài liệu tham khảo

Ott E, Grebogi C, Yorke JA (1990) Controlling chaos. Phys Rev Lett 64(11):1196–1199

Pecora LM, Carrroll TL (1990) Synchronization in chaotic systems. Phys Rev Lett 64(8):821–824

Si GQ, Sun ZY, Zhang YB, Chen WQ (2012) Projective synchronization of different fractional-order chaotic systems with non-identical orders. Nonlinear Anal Real 13(4):1761–1771

Agrawal SK, Das S (2015) Projective synchronization between different fractional-order hyperchaotic systems with uncertain parameters using proposed modified adaptive projective synchronization technique. Math Method Appl Sci 37(14):2164–2176

Niu Y, Wang X (2012) Adaptive projective synchronization of different chaotic systems with nonlinearity inputs. Chin Phys B 26(11):821–827

Ouannas A, Odibat Z (2015) Generalized synchronization of different dimensional chaotic dynamical systems in discrete time. Nonlinear Dyn 81(1–2):765–771

Zhang G, Liu Z, Ma Z (2007) Generalized synchronization of different dimensional chaotic dynamical systems. Chaos Solitons Fractals 32(2):773–779

Terry JR, Vanwiggeren GD (2001) Chaotic communication using generalized synchronization. Chaos Solitons Fractals 12(1):45–152

Vaidyanathan S, Sampath S, Azar AT (2015) Global chaos synchronization of identical chaotic systems via novel sliding mode control method and its application to Zhu system. Int J Model Identif Control 23(1):92–100

Chen D, Zhang R, Ma X, Liu S (2011) Chaotic synchronization and anti-synchronization for a novel class of multiple chaotic systems via a sliding mode control scheme. Nonlinear Dyn 69(1–2):35–55

Liu J, Liu ST, Sprott JC (2015) Adaptive complex modified hybrid function projective synchronization of different dimensional complex chaos with uncertain complex parameters. Nonlinear Dyn 83(2016):1109–1121

Liu ST, Liu P (2011) Adaptive anti-synchronization of chaotic complex nonlinear systems with unknown parameters. Nonlinear Anal Real 12(6):3046–3055

Liu J, Liu ST, Yuan C (2015) Adaptive complex modified projective synchronization of complex chaotic (hyperchaotic) systems with uncerta in complex parameters. Nonlinear Dyn 2:1035–1047

Liu P, Liu ST, Li X (2012) Adaptive modified function projective synchronization of general uncertain chaotic complex systems. Phys Scr 85(3):438–445

Zheng S, Dong GG, Bi QS (2010) Adaptive modified function projective synchronization of hyperchaotic systems with unknown parameters. Commun Nonlinear Sci 15(11):3547–3556

Xu Y, Wang H, Li Y, Pei B (2014) Image encryption based on synchronization of fractional chaotic systems. Commun Nonlinear Sci 19(10):3735–3744

Minati L, Chiesa P, Tabarelli D, Incerti L, Jovicich J (2015) Synchronization, non-linear dynamics and low-frequency fluctuations: analogy between spontaneous brain activity and networked single-transistor chaotic oscillators. Chaos 25(3):15775–16171

Luo RZ, Wang YL, Deng SC (2011) Combination synchronization of three classic chaotic systems using active backstepping design. Chaos 21(4):1–6

Sun JW, Shen Y, Zhang G, Xu C, Cui G (2013) Combination–combination synchronization among four identical or different chaotic systems. Nonlinear Dyn 73(3):1211–1222

Mahmoud GM, Abed-Elhameed TM, Ahmed ME (2016) Generalization of combination–combination synchronization of chaotic-dimensional fractional-order dynamical systems. Nonlinear Dyn 83(4):1885–1893

Zhou X, Xiong L, Cai X (2014) Combination-combination synchronization of four nonlinear complex chaotic systems. Abstr Appl Anal 2(3):1–14

Sun JW, Wang Y, Wang YF, Cui G, Shen Y (2016) Compound-combination synchronization of five chaotic systems via nonlinear control. Optik 127(8):4136–4143

Ojo KS, Njah AN, Olusola OI (2015) Compound-combination synchronization of chaos in identical and different orders chaotic systems. Arch Control Sci 25(4):463–490

Ibraheem A (2020) Dual compound–compound synchronization of twelve n-dimensional dynamical systems. Arab J Sci Eng 45(2020):6835–6848

Singh AK, Yadav VK, Das S (2017) Dual combination synchronization of the fractional order complex chaotic cystems. J Comput Nonlin Dyn 12(1):011017

Sun JW, Jiang SX, Cui GZ, Wang Y (2016) Dual combination synchronization of six chaotic systems. J Bacteriol 14(1):47–53

Yadav VK, Prasad G, Srivastava M, Das S (2019) Combination–combination phase synchronization among non-identical fractional order complex chaotic systems via nonlinear control. Int J Control 7(2):330–340

Ucar A, Lonngren KE, Bai EW (2008) Multi-switching synchronization of chaotic systems with active controllers. Chaos Solitons Fractals 38(1):254–262

Vincent UE, Saseyi AO, Mcclintock PVE (2015) Multi-switching combination synchronization of chaotic systems. Nonlinear Dyn 80(1–2):845–854

Shahzad M (2020) Multi-switching synchronization of different orders: a generalization of increased/reduced order synchronization. Iran J Technol Trans Sci 44(1):167–176

Khan A, Khattar D, Prajapati N (2017) Multiswitching combination-combination synchronization of chaotic systems. Pramana J Phys 88(3):47

Khan A, Khattar D, Prajapati N (2017) Dual combination combination multi switching synchronization of eight chaotic systems. Chin J Phys 55(4):1209–1218

Ibraheem A, Khan A (2019) Multi-switching compound-compound anti-synchronization of non-identical hyperchaotic systems. Int J Simul Model 1(2019):1–15

Fowler AC, Gibbon JD, Mcguinness MJ (1982) The complex Lorenz equations. Physica D 4(2):139–163

Dabiri A, Moghaddam BP (2018) Machado JAT (2018) Optimal variable-order fractional PID controllers for dynamical systems. J Comput Appl Math 339:40–48

Moghaddam BP, Machado JAT (2017) Extended algorithms for approximating variable order fractional derivatives with applications. J Sci Comput 71(3):1351–1374

Guy J (2001) Fractional master equation: non-standard analysis and Liouville–Riemann derivative. Chaos Solitons Fractals 12(13):2577–2587

Kilbas AA, Marzan SA (2005) Nonlinear differential equations with the Caputo fractional derivative in the space of continuously differentiable functions. Differ Equ 41(1):84–89

Luo C, Wang X (2018) Chaos in the fractional-order complex Lorenz system and its synchronization. Nonlinear Dyn 71(1):241–257

Luo C, Wang X (2013) Chaos generated from the fractional-order complex Chen system and its application to digital secure communication. Int J Mod Phys C 24(04):1350025

Liu XJ, Hong L, Yang LX (2013) Fractional-order complex T system: bifurcations, chaos control, and synchronization. Nonlinear Dyn 75(3):589–602

Liu J, Liu ST (2017) Complex modified function projective synchronization of complex chaotic systems with known and unknown complex parameters. Appl Math Model 48(2017):440–450

Gamal MM, Emad EM (2013) Complex modified projective synchronization of two chaotic complex nonlinear systems. Nonlinear Dyn 73(4):2231–2240

Mahmoud GM, Ahmed ME, Mahmoud EE (2008) Analysis of hyperchaotic complex Lorenz systems. Int J Mod Phys C 19(10):1477–1494

Luo C, Wang X (2013) Hybrid modified function projective synchronization of two different dimensional complex nonlinear systems with parameters identification. J Frankl I 350(9):2646–2663