Analysis and implementation of new fractional-order multi-scroll hidden attractors

doi:10.1088/1674-1056/abbbe4

Abstract To improve the complexity of chaotic signals, in this paper we first put forward a new three-dimensional quadratic fractional-order multi-scroll hidden chaotic system, then we use the Adomian decomposition algorithm to solve the proposed fractional-order chaotic system and obtain the chaotic phase diagrams of different orders, as well as the Lyaponov exponent spectrum, bifurcation diagram, and SE complexity of the 0.99-order system. In the process of analyzing the system, we find that the system possesses the dynamic behaviors of hidden attractors and hidden bifurcations. Next, we also propose a method of using the Lyapunov exponents to describe the basins of attraction of the chaotic system in the matlab environment for the first time, and obtain the basins of attraction under different order conditions. Finally, we construct an analog circuit system of the fractional-order chaotic system by using an equivalent circuit module of the fractional-order integral operators, thus realizing the 0.9-order multi-scroll hidden chaotic attractors.

Keywords: fractional order hidden attractor hidden bifurcation basins of attraction circuit implementation

Received: 12 August 2020
Revised: 11 September 2020
Accepted manuscript online: 28 September 2020

PACS:	05.45-a
	05.45.Ac	(Low-dimensional chaos)
	05.30.Pr	(Fractional statistics systems)
	05.45.Df	(Fractals)

Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 61561022 and 61672226).

Corresponding Authors: ^†Corresponding author. E-mail: licui@hnust.edu.cn

Cite this article:

Li Cui(崔力), Wen-Hui Luo(雒文辉), and Qing-Li Ou(欧青立) Analysis and implementation of new fractional-order multi-scroll hidden attractors 2021 Chin. Phys. B 30 020501

1 Yu F, Liu L, Shen H, Zhang Z N,Huang Y Y, Shi C Q, Cai S, Wu X M, Du S C and Wan Q Z 2020 Complexity 2020 5904607
2 Yu F, Liu L, Shen H, Zhang Z, Huang Y, Cai S, Deng Z and Wan Q 2020 Mathematical Problems in Engineering Article 2020 7530976
3 Yu F, Liu L, Qian S, Li L, Huang Y, Shi C, Cai S, Wu X, Du S and Wan Q 2020 Complexity 2020 8034196
4 Yu F, Shen H, Liu L, Zhang Z, Huang Y, He B, Cai S, Song Y, Yin B, Du S and Xu Q 2020 Complexity 2020 5212601
5 Yu F, Liu L, He B, Huang Y, Shi C, Cai S, Song Y, Du S and Wan Q 2019 Complexity 2019 4047957
6 Wang X Y and Guan N N2020 Optics and Laser Technology 131 106366
7 Wu T, Li Q L, Bao X B and Hu M 2020 Opt. Commun. 475 126042
8 Garc\'ía-Guerrero E E, Inzunza-Gonz\'alez E, Lòpez-Bonilla O R, C\'ardenas-Valdez J R and Tlelo-Cuautle E 2020 Chaos, Solitons and Fractals 133 109646
9 Lin H R, Wang C H, Yao W and Tan Y M 2020 Commun. Nonlinear Sci. Numer. Simul. 90 105390
10 Chen T, Wang L D and Duan S K 2020 Neurocomputing 380 36
11 Wang B, Chen B W, Wang Q Q, Li R, Wen J M, Lu C, Tian R F and Deng J 2020 Annals of Nuclear Energy 148 107711
12 Ye X L, Wang X Y, Gao S, Mou J and Wang Z S 2020 Opt. Lasers Eng. 127 105905
13 Mathale D, Doungmo Goufo Emile F and Khumalo M 2020 Chaos, Solitons and Fractals 139 110021
14 Cui L, Lu M, Ou Q L, Duan H and Luo W H 2020 Chaos, Solitons and Fractals 138 109894
15 Leonov G A, Kuznetsov N V and Vagaitsev V I 2012 Physica D 241 1482
16 Leonov G A, Kuznetsov N V and Vagaitsev V I 2011 Phys. Lett. A 375 2230
17 Munmuangsaen B and Srisuchinwong B 2018 Chaos, Solitons and Fractals 107 61
18 Peng X N and Zeng Y Z 2020 Chaos, Solitons and Fractals 139 110044
19 Yang L B, Yang Q G and Chen G R 2020 Commun. Nonlinear Sci. Numer. Simul. 90 105362
20 Wang N,Zhang G S, Kuznetsov N V and Bao H2021 Commun. Nonlinear Sci. Numer. Simul. 92 105494
21 Yu Y G, Li H X, Wang S, Yu J Z 2009 Chaos, Solitons and Fractals 42 1181
22 Echenaus\'ía-Monroy J L, Gilardi-Vel\'azquez H E, Jaimes-Re\'ategui R, Aboites V and Huerta-Cuellar G 2020 Commun. Nonlinear Sci. Numer. Simul. 90 105413
23 Zhu H, Zhou S B and Zhang J 2009 Chaos, Solitons and Fractals 39 1595
24 Chen L P, Pan W, Wu R C, Wang K P and He Y G 2016 Chaos, Solitons and Fractals 85 22
25 Chen L P, Pan W, Tenreiro Machado J A, Lopes A M, Wu R C and He Y G 2017 Eur. Phys. J. Special Topics 226 3775
26 Chen L P, Pan W, Wang K P, Wu R C, Tenreiro Machado J A and Lopes A M 2017 Chaos, Solitons and Fractals 105 244
27 Chen L P, Pan W, Wu R C, Tenreiro Machado J A and Lopes A M 2016 Chaos 26 084303
28 Goufo E F D 2019 Chaos, Solitons and Fractals 127 24
29 Bi H Y, Qi G Y, Hu J B, Faradja P and Chen G R 2020 Chaos, Solitons and Fractals 138 109815
30 Yang L B, Yang Q G and Chen G R 2020 Commun. Nonlinear Sci. Numer. Simul. 90 105362
31 Jahanshahi H, Yousefpour A, Munoz-Pacheco J M, Moroz I and Wei Z C 2019 Appl. Soft Computing
32 Folifack Signing V R, Kengne J and Mboupda Pone J R 2019 Chaos, Solitons and Fractals 118 187
33 Zhang X and Li Z J 2019 Int. J. Non-Linear Mech. 111 14
34 Faradja P and Qi G Y 2020 Chaos, Solitons and Fractals 132 109606
35 He S B, Sun K H and Wang H H2014 Acta Phys. Sin. 63 030502 (in Chinese)
36 Zheng J D, Pan H Y, Liu Q Y and Ding K Q 2020 Physica A 545 123641
37 Mateos D M, Zozor S and Olivares F 2020 Physics A 554 124640
38 Sadeghian H, Merat K, Salarieh H, Alasty A 2011 Appl. Math. Model. 35 1016
39 Jia H Y, Guo Z Q, Qi G Y and Chen Z Q 2018 Optik 155 233
40 Camargo S, Viana R L and Anteneodo C 2012 Phys. Rev. E 85 036207
41 Chaudhuri U, Prasad A 2014 Phys. Lett. A 378 713
42 Wontchui T T, Effa J Y, Ekobena Fouda H P, Ujjwal S R and Ramaswamy R 2017 Phys. Rev. E 96 062203
43 Wang G Y, Yuan F, Chen G R and Zhang Y 2018 Chaos 28 013125
44 Chen C J, Chen J Q, Bao H, Chen M and Bao B C Nonlinear Dyn. 95 3385
45 Zhang R X and Yang S P2009 Acta Phys. Sin. 58 2957 (in Chinese)

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Analysis and implementation of new fractional-order multi-scroll hidden attractors

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