Journal of Shandong University(Engineering Science) ›› 2022, Vol. 52 ›› Issue (2): 74-79.doi: 10.6040/j.issn.1672-3961.0.2021.388

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A generalized Hamiltonian conservative chaotic system with multi-stable flows

JIA Hongyan, CHEN Zhonggao, SHI Wenxin, HAN Xiaoguang*   

  1. College of Electronic Information and Automation, Tianjin University of Science and Technology, Tianjin 300222, China
  • Published:2022-04-20

CLC Number: 

  • TP29
[1] HENON M, HELLES C. The applicability of the third integral of motion: some numerical experiments[J]. Astrophys Journal, 1964, 69(1): 73-79.
[2] SPROTT J C. Some simple chaotic flows[J]. Physical Review E, 1994, 50(2): 647-650.
[3] HOOVER W G. Remark on “some simple chaotic flows” [J]. Physical Review E, 1995, 51(1): 759-760.
[4] POSCH H A, HOOVER W G, VESELY F J. Canonical dynamics of the Nosé-oscillator: stability, order, and chaos[J]. Physical Review A, 1986, 33(6): 4253-4265.
[5] HOOVER W G. Canonical dynamics: equilibrium phase-space distributions[J]. Physical Review A, 1985, 31(3): 1695-1697.
[6] SPROTT J C. Some simple chaotic jerk functions[J]. American Journal of Physics, 1997, 65(6): 537-543.
[7] THOMAS R. Deterministic chaos seen in terms of feedback circuits: analysis, synthesis, “labyrnth chaos” [J]. International Journal of Bifurcation and Chaos, 1999, 9(10): 1889-1905.
[8] VAIDYANATHAN S, VOLOS C. Analysis and adaptive control of a novel 3-D conservative no-equilibrium chaotic system[J]. Archives of Control Sciences, 2015, 25(3): 333-353.
[9] MAHMOUD G M, AHMED M E. Analysis of chaotic and hyperchaotic conservative complex nonlinear systems[J]. Miscolc Mathematical Notes, 2017, 18(1): 315-326.
[10] SINGH J P, ROY B K. Five new 4-D autonomous conservative chaotic systems with various type of non-hyperbolic and lines of equilibria[J]. Chaos, Solitons and Fractals, 2018, 114: 81-91.
[11] VAIDYANATHAN S, PAKIRISWAMY S. A 3-D novel conservative chaotic system and its generalized projective synchronization via adaptive control[J]. Journal of Engineering Science & Technology, 2015, 8(2): 52-60.
[12] CANG S J, WU A G, WANG Z H. On a 3-D generalized Hamiltonian model with conservative and dissipative chaotic flows[J]. Chaos, Solitons and Fractals, 2017, 99: 45-51.
[13] GUGAPRIYA G, RAJAGOPAL K, KARTHIKEYAN A. A family of conservative chaotic systems with cyclic symmetry[J]. Pramana-Journal of Physics, 2019, 92(4): 48-54.
[14] CANG S J, LI Y, XUE W. Conservative chaos and invariant tori in the modified Sprott A system[J]. Nonlinear Dynamics, 2020, 99(2): 1699-1708.
[15] QI G Y, HU J B, WANG Z. Modeling of a Hamiltonian conservative chaotic system and its mechanism routes from periodic to quasiperiodic, chaos and strong chaos[J]. Applied Mathematical Modeling, 2020, 78: 350-365.
[16] QI G Y. Modelings and mechanism analysis underlying both the 4D Euler equations and Hamiltonian con-servative chaotic systems[J]. Nonlinear Dynamics, 2019, 95(3): 2063-2077.
[17] JIA H Y, SHI W X, WANG L. Analysis of Sprott-A system and generation of a new Hamiltonian conservative chaotic system with coexisting hidden attractors[J]. Chaos, Solitons and Fractals, 2020, 133: 109635.
[18] CANG S J, WU A G, ZHANG R Y. Conservative chaos in a class of non-conservative systems: theoretical analysis and numerical demonstrations[J]. International Journal of Bifurcation and Chaos, 2018, 28(7): 1850087.
[19] DONG E Z, YUAN M F, DU S Z. A new class of Hamiltonian conservative chaotic systems with multistability and design of pseudo-random number generator[J]. Applied Mathematical Modeling, 2019, 73: 40-71.
[20] XIAN Y J, XIA C, GUO T T. Dynamical analysis and FPGA implementation of a large range chaotic system with coexisting attractors[J]. Results in Physics, 2018, 11: 368-376.
[21] LI C B, SPROTT J C. Multistability in the Lorenz system: a broken butterfly[J]. International Journal of Bifurcation and Chaos, 2014, 24: 1450131.
[22] JIA H Y, SHI W X, QI G Y. Coexisting attractors, energy analysis and boundary of Lü system[J]. International Journal of Bifurcation and Chaos, 2020, 30(3): 2050048.
[23] WANG F P, WANG F Q. Multistability and coexisting transient chaos in a simple memcapacitive system[J]. Chinese Physics B, 2020, 29(5): 58502.
[24] ZHANG S, ZENG Y H, LI Z J. Generating one to four-wing hidden attractors in a novel 4D no-equilibrium chaotic system with extreme multistability[J]. Chaos, 2018, 28: 13113.
[25] LEONOV G, KUZNETSOV N, VAGAITSEV V. Localization of hidden Chua's attractors[J]. Physics Letters A, 2011, 375(23): 2230-2233.
[26] JAFARI S, SPROTT J. Simple chaotic flows with a line equilibrium[J]. Chaos, Solitons and Fractals, 2013, 57: 79-84.
[27] ZHENG G C, LIU C X, WANG Y. Dynamic analysis and finite time synchronization of a fractional-order chaotic system with hidden attractors[J]. Acta Physica Sinica, 2018, 67(5): 50502.
[28] BAO B, BAO H, WANG N. Hidden extreme multistability in memristive hyperchaotic system[J]. Chaos, Solitons and Fractals, 2017, 94: 102-111.
[29] CHEN M, SUN M, BAO B. Controlling extreme multistability of memristor emulator-based dynamical circuit in flux—charge domain[J]. Nonlinear Dynamic, 2018, 91(2): 1395-1412.
[30] JAFARI S, SPROTT J C, DEHGHAN S. Categories of conservative flows[J]. International Journal of Bifurcation and Chaos, 2019, 29(2): 1950021.
[31] SINGH J P, ROY B K. Five new 4-D autonomous conservative chaotic systems with various type of non-hyperbolic and lines of equilibria[J]. Chaos, Solitons and Fractals, 2018, 114: 81-91.
[32] LIANG X Y, QI G Y. Mechanical analysis of Chen chaotic system[J]. Chaos, Solitons and Fractals, 2017, 98: 173-177.
[33] JIA H Y, GUO Z Q, WANG S F. Mechanics analysis and hardware implementation of a new 3D chaotic system[J]. International Journal of Bifurcation and Chaos, 2018, 28(13): 1850161.
[34] ANTONELLO P, VINICIO P. A unified view of Kolmogorov and Lorenz systems[J]. Physics Letters A, 2000, 275(5/6): 435-446.
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