Yin, Chuntao; Zhao, Yufei; Li, Xianghong; Shen, Yongjun Analysis and synchronization of the Chen system with fractional derivative. (English) Zbl 1546.34143 Int. J. Bifurcation Chaos Appl. Sci. Eng. 34, No. 7, Article ID 2450088, 14 p. (2024). MSC: 34H05 34A08 34D06 26A33 × Cite Format Result Cite Review PDF Full Text: DOI
Hashemi, M. S.; Haji-Badali, A.; Alizadeh, F.; Inc, Mustafa Classical and non-classical Lie symmetry analysis, conservation laws and exact solutions of the time-fractional Chen-Lee-Liu equation. (English) Zbl 1524.22025 Comput. Appl. Math. 42, No. 2, Paper No. 73, 21 p. (2023). MSC: 22E70 76M60 35L65 70S10 × Cite Format Result Cite Review PDF Full Text: DOI
Vijayalakshmi, Palanisamy; Jiang, Zhiheng; Wang, Xiong Lagrangian formulation of Lorenz and Chen systems. (English) Zbl 1464.37057 Int. J. Bifurcation Chaos Appl. Sci. Eng. 31, No. 4, Article ID 2150055, 7 p. (2021). MSC: 37J06 34A08 26A33 × Cite Format Result Cite Review PDF Full Text: DOI
Yin, Chuntao Chaos detection of the Chen system with Caputo-Hadamard fractional derivative. (English) Zbl 1464.34065 Int. J. Bifurcation Chaos Appl. Sci. Eng. 31, No. 1, Article ID 2150016, 14 p. (2021). MSC: 34C28 34A34 34A08 34D08 37D45 × Cite Format Result Cite Review PDF Full Text: DOI
Zeng, Caibin; Lin, Xiaofang; Huang, Jianhua; Yang, Qigui Pathwise solution to rough stochastic lattice dynamical system driven by fractional noise. (English) Zbl 1440.60057 Commun. Pure Appl. Anal. 19, No. 2, 811-834 (2020). Reviewer: Xiaohu Wang (Chengdu) MSC: 60H15 37H10 37K60 60G22 × Cite Format Result Cite Review PDF Full Text: DOI
Čermák, Jan; Nechvátal, Luděk Stability and chaos in the fractional Chen system. (English) Zbl 1448.34087 Chaos Solitons Fractals 125, 24-33 (2019). MSC: 34C28 34A08 34C60 37G10 37G35 37M05 37D45 × Cite Format Result Cite Review PDF Full Text: DOI
Seferi, Ylldrita; Markoski, Gjorgji; Gjurchinovski, Aleksandar Comparison of different numerical methods for fractional differential equations. (English) Zbl 1467.65071 Mat. Bilt. 42, No. 2, 61-74 (2018). MSC: 65L06 34A08 × Cite Format Result Cite Review PDF Full Text: Link
Lei, Tengfei Dynamics analysis and circuit implementation of fractional-order Chen chaotic system with time-delay. (Chinese. English summary) Zbl 1424.37054 J. Qufu Norm. Univ., Nat. Sci. 44, No. 3, 59-65 (2018). MSC: 37N99 94C05 26A33 34K37 37D45 × Cite Format Result Cite Review PDF
Doungmo Goufo, Emile Franc Mathematical analysis of peculiar behavior by chaotic, fractional and strange multiwing attractors. (English) Zbl 1401.34008 Int. J. Bifurcation Chaos Appl. Sci. Eng. 28, No. 10, Article ID 1850125, 14 p. (2018). MSC: 34A08 34A34 34C28 37D45 65L05 × Cite Format Result Cite Review PDF Full Text: DOI
Yang, Zhihong; Zhang, Caixia; Qu, Shuanghui; Wang, Li The dynamic properties of the heterogeneous fractional order Chen system and its plural circuit implementation. (Chinese. English summary) Zbl 1389.37060 J. Jiangxi Norm. Univ., Nat. Sci. Ed. 41, No. 2, 133-139 (2017). MSC: 37N99 37D45 94C05 34A08 × Cite Format Result Cite Review PDF Full Text: DOI
Das, Saptarshi; Pan, Indranil; Das, Shantanu Effect of random parameter switching on commensurate fractional order chaotic systems. (English) Zbl 1372.34113 Chaos Solitons Fractals 91, 157-173 (2016). MSC: 34K23 34K37 37H10 65P20 × Cite Format Result Cite Review PDF Full Text: DOI arXiv Link
Oumate, A. A.; Zourmba, K.; Gambo, B.; Mohamadou, A. Synchronization of the fractional-order Chen system and its circuit implementation. (English) Zbl 1365.34018 Far East J. Dyn. Syst. 28, No. 3, 205-220 (2016). MSC: 34A08 34C28 34D06 93C40 94C05 34A34 34H10 × Cite Format Result Cite Review PDF Full Text: DOI Link
Xu, Fei A class of integer order and fractional order hyperchaotic systems via the Chen system. (English) Zbl 1343.34103 Int. J. Bifurcation Chaos Appl. Sci. Eng. 26, No. 6, Article ID 1650109, 32 p. (2016). MSC: 34C28 34A34 34A08 × Cite Format Result Cite Review PDF Full Text: DOI
Feng, Yingling; Wang, Jianhong; Zhou, Zhi; Lv, Xiaoguo A predictor-corrector approach with controller for the fractional order used in Chen chaotic system. (Chinese. English summary) Zbl 1349.37025 Math. Pract. Theory 45, No. 23, 255-259 (2015). MSC: 37D45 34A08 34H10 × Cite Format Result Cite Review PDF
Alomari, A. K. A novel solution for fractional chaotic Chen system. (English) Zbl 1326.65101 J. Nonlinear Sci. Appl. 8, No. 5, 478-488 (2015). MSC: 65L99 34A08 34H10 × Cite Format Result Cite Review PDF Full Text: DOI Link
Matouk, A. E.; Elsadany, A. A. Achieving synchronization between the fractional-order hyperchaotic novel and Chen systems via a new nonlinear control technique. (English) Zbl 1315.34013 Appl. Math. Lett. 29, 30-35 (2014). MSC: 34A08 34D06 34A34 34C28 34D20 93C10 × Cite Format Result Cite Review PDF Full Text: DOI
Nasrollahi, A.; Bigdeli, N. Extended Chen: a new class of chaotic fractional-order systems. (English) Zbl 1300.26004 Int. J. Gen. Syst. 43, No. 7-8, 880-896 (2014). MSC: 26A33 × Cite Format Result Cite Review PDF Full Text: DOI
Xu, Fei Integer and fractional order multiwing chaotic attractors via the Chen system and the Lü system with switching controls. (English) Zbl 1296.34116 Int. J. Bifurcation Chaos Appl. Sci. Eng. 24, No. 3, Article ID 1450029, 22 p. (2014). MSC: 34C28 34D45 37D45 34A08 34A34 34H05 × Cite Format Result Cite Review PDF Full Text: DOI
Dong, Pengzhen; Shang, Gang; Liu, Jie Anticipating synchronization of integer order and fractional order hyper-chaotic Chen system. (English) Zbl 1260.34079 Int. J. Mod. Phys. B 26, No. 32, Article ID 1250211, 15 p. (2012). MSC: 34C28 34D06 34B45 34A08 34D08 × Cite Format Result Cite Review PDF Full Text: DOI
Wei, Zhouchao Synchronization of coupled nonidentical fractional-order hyperchaotic systems. (English) Zbl 1235.93059 Discrete Dyn. Nat. Soc. 2011, Article ID 430724, 9 p. (2011). MSC: 93B12 37D45 × Cite Format Result Cite Review PDF Full Text: DOI
Hegazi, A. S.; Matouk, A. E. Dynamical behaviors and synchronization in the fractional order hyperchaotic Chen system. (English) Zbl 1234.34036 Appl. Math. Lett. 24, No. 11, 1938-1944 (2011). MSC: 34D06 26A33 34C28 37D45 37N35 × Cite Format Result Cite Review PDF Full Text: DOI
Alomari, A. K. A new analytic solution for fractional chaotic dynamical systems using the differential transform method. (English) Zbl 1221.65191 Comput. Math. Appl. 61, No. 9, 2528-2534 (2011). MSC: 65L99 34A08 37D45 45J05 × Cite Format Result Cite Review PDF Full Text: DOI
Chang, Ching-Ming; Chen, Hsien-Keng Chaos and hybrid projective synchronization of commensurate and incommensurate fractional-order Chen-Lee systems. (English) Zbl 1215.37024 Nonlinear Dyn. 62, No. 4, 851-858 (2010). MSC: 37D45 34A08 34D20 × Cite Format Result Cite Review PDF Full Text: DOI
Cafagna, Donato; Grassi, Giuseppe An effective method for detecting chaos in fractional-order systems. (English) Zbl 1193.34086 Int. J. Bifurcation Chaos Appl. Sci. Eng. 20, No. 3, 669-678 (2010). MSC: 34C28 34A08 37D45 × Cite Format Result Cite Review PDF Full Text: DOI
Zhang, Ruoxun; Yang, Shiping Chaos in the fractional-order conjugate Chen system and its circuit emulation. (Chinese. English summary) Zbl 1212.37057 Acta Phys. Sin. 58, No. 5, 2957-2962 (2009). MSC: 37D45 94C05 × Cite Format Result Cite Review PDF
Wu, Xiangjun; Lu, Yang Generalized projective synchronization of the fractional-order Chen hyperchaotic system. (English) Zbl 1176.70029 Nonlinear Dyn. 57, No. 1-2, 25-35 (2009). MSC: 70K55 26A33 × Cite Format Result Cite Review PDF Full Text: DOI
Tavazoei, Mohammad Saleh; Haeri, Mohammad; Bolouki, Sadegh; Siami, Milad Using fractional-order integrator to control chaos in single-input chaotic systems. (English) Zbl 1220.70025 Nonlinear Dyn. 55, No. 1-2, 179-190 (2009). MSC: 70Q05 70K55 26A33 × Cite Format Result Cite Review PDF Full Text: DOI
Chen, Xiangrong; Liu, Chongxin; Li, Yongxun Generalized synchronization of fractional order hyperchaotic Chen system with improved observer. (Chinese. English summary) Zbl 1174.37311 J. Xi’an Jiaotong Univ. 42, No. 2, 238-242 (2008). MSC: 37D45 93B07 × Cite Format Result Cite Review PDF
Cafagna, Donato; Grassi, Giuseppe Bifurcation and chaos in the fractional-order Chen system via a time-domain approach. (English) Zbl 1158.34300 Int. J. Bifurcation Chaos Appl. Sci. Eng. 18, No. 7, 1845-1863 (2008). MSC: 34-01 34C23 34C28 34A34 37Gxx 26A33 × Cite Format Result Cite Review PDF Full Text: DOI
Tavazoei, Mohammad Saleh; Haeri, Mohammad A necessary condition for double scroll attractor existence in fractional-order systems. (English) Zbl 1209.37037 Phys. Lett., A 367, No. 1-2, 102-113 (2007). MSC: 37D45 34A08 × Cite Format Result Cite Review PDF Full Text: DOI
Shao, Shiquan; Gao, Xin; Liu, Xingwen Controlling projective synchronization in coupled fractional order chaotic Chen system. (Chinese. English summary) Zbl 1150.93397 Acta Phys. Sin. 56, No. 12, 6815-6819 (2007). MSC: 93B52 37D45 × Cite Format Result Cite Review PDF
El-Khazali, Reyad; Ahmad, Wajdi; Al-Assaf, Yousef Sliding mode control of generalized fractional chaotic systems. (English) Zbl 1139.93009 Int. J. Bifurcation Chaos Appl. Sci. Eng. 16, No. 10, 3113-3125 (2006). MSC: 93B12 37D45 93D21 26A33 × Cite Format Result Cite Review PDF Full Text: DOI
Zhang, Hongbin; Li, Chunguang; Chen, Guanrong; Gao, Xing Hyperchaos in the fractional-order nonautonomous Chen’s system and its synchronization. (English) Zbl 1103.37304 Int. J. Mod. Phys. C 16, No. 5, 815-826 (2005). MSC: 37D45 × Cite Format Result Cite Review PDF Full Text: DOI
Deng, Weihua; Li, Changpin Synchronization of chaotic fractional Chen system. (English) Zbl 1080.34537 J. Phys. Soc. Japan 74, No. 6, 1645-1648 (2005). Reviewer: Sergiy Yanchuk (Berlin) MSC: 34D05 34C15 26A33 × Cite Format Result Cite Review PDF Full Text: DOI
Li, Chunguang; Chen, Guanrong Chaos in the fractional order Chen system and its control. (English) Zbl 1069.37025 Chaos Solitons Fractals 22, No. 3, 549-554 (2004). MSC: 37D45 26A33 93B52 × Cite Format Result Cite Review PDF Full Text: DOI
Li, Changpin; Peng, Guojun Chaos in Chen’s system with a fractional order. (English) Zbl 1060.37026 Chaos Solitons Fractals 22, No. 2, 443-450 (2004). MSC: 37D45 28A80 × Cite Format Result Cite Review PDF Full Text: DOI