IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v106y2018icp5-15.html
   My bibliography  Save this article

A novel hyperchaotic system with infinitely many heteroclinic orbits coined

Author

Listed:
  • Wang, Haijun
  • Li, Xianyi

Abstract

Based on the famous Shimizu–Morioka system, this paper proposes a novel five-dimensional Shimizu–Morioka-type hyperchaotic system that has an infinite set of heteroclinic orbits. Of particular interest are the following observed properties of the system: (i) the existence of both ellipse-parabola-type and hyperbola-parabola-type of equilibria; (ii) the strange attractor coexisting either non-isolated equilibria or two pairs of symmetrical equilibria; (iii) the existence of the proposed strange attractors and hyperchaotic attractors bifurcated from the corresponding singularly degenerate heteroclinic cycles; (iv) the existence of an infinite set of both ellipse-parabola-type and hyperbola-parabola-type heteroclinic orbits.

Suggested Citation

  • Wang, Haijun & Li, Xianyi, 2018. "A novel hyperchaotic system with infinitely many heteroclinic orbits coined," Chaos, Solitons & Fractals, Elsevier, vol. 106(C), pages 5-15.
    • Handle: RePEc:eee:chsofr:v:106:y:2018:i:c:p:5-15
    DOI: 10.1016/j.chaos.2017.10.029
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077917304459
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2017.10.029?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Chen, Yuming & Yang, Qigui, 2015. "A new Lorenz-type hyperchaotic system with a curve of equilibria," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 112(C), pages 40-55.
    2. LeBaron, Blake & Arthur, W. Brian & Palmer, Richard, 1999. "Time series properties of an artificial stock market," Journal of Economic Dynamics and Control, Elsevier, vol. 23(9-10), pages 1487-1516, September.
    3. Pan, Indranil & Das, Saptarshi, 2015. "When Darwin meets Lorenz: Evolving new chaotic attractors through genetic programming," Chaos, Solitons & Fractals, Elsevier, vol. 76(C), pages 141-155.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Wang, Haijun & Dong, Guili, 2019. "New dynamics coined in a 4-D quadratic autonomous hyper-chaotic system," Applied Mathematics and Computation, Elsevier, vol. 346(C), pages 272-286.
    2. Haijun Wang & Guiyao Ke & Jun Pan & Feiyu Hu & Hongdan Fan & Qifang Su, 2023. "Two pairs of heteroclinic orbits coined in a new sub-quadratic Lorenz-like system," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 96(3), pages 1-9, March.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Pham, Viet–Thanh & Jafari, Sajad & Volos, Christos & Kapitaniak, Tomasz, 2016. "A gallery of chaotic systems with an infinite number of equilibrium points," Chaos, Solitons & Fractals, Elsevier, vol. 93(C), pages 58-63.
    2. Kamaladdin Fataliyev & Aneesh Chivukula & Mukesh Prasad & Wei Liu, 2021. "Stock Market Analysis with Text Data: A Review," Papers 2106.12985, arXiv.org, revised Jul 2021.
    3. Siddiqi, Hammad, 2007. "Rational Interacting Agents and Volatility Clustering: A New Approach," MPRA Paper 2984, University Library of Munich, Germany.
    4. Bohm, Volker & Wenzelburger, Jan, 2005. "On the performance of efficient portfolios," Journal of Economic Dynamics and Control, Elsevier, vol. 29(4), pages 721-740, April.
    5. Hommes, Cars & Huang, Hai & Wang, Duo, 2005. "A robust rational route to randomness in a simple asset pricing model," Journal of Economic Dynamics and Control, Elsevier, vol. 29(6), pages 1043-1072, June.
    6. Brock, William A. & Hommes, Cars H. & Wagener, Florian O. O., 2005. "Evolutionary dynamics in markets with many trader types," Journal of Mathematical Economics, Elsevier, vol. 41(1-2), pages 7-42, February.
    7. E. Samanidou & E. Zschischang & D. Stauffer & T. Lux, 2001. "Microscopic Models of Financial Markets," Papers cond-mat/0110354, arXiv.org.
    8. Gaunersdorfer, A. & Hommes, C.H. & Wagener, F.O.O., 2000. "Bifurcation Routes to Volatility Clustering," CeNDEF Working Papers 00-04, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
    9. Yamamoto, Ryuichi, 2019. "Dynamic Predictor Selection And Order Splitting In A Limit Order Market," Macroeconomic Dynamics, Cambridge University Press, vol. 23(5), pages 1757-1792, July.
    10. Chueh-Yung Tsao & Ya-Chi Huang, 2018. "Revisiting the issue of survivability and market efficiency with the Santa Fe Artificial Stock Market," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 13(3), pages 537-560, October.
    11. Frijns, Bart & Lehnert, Thorsten & Zwinkels, Remco C.J., 2010. "Behavioral heterogeneity in the option market," Journal of Economic Dynamics and Control, Elsevier, vol. 34(11), pages 2273-2287, November.
    12. Marco Raberto & Silvano Cincotti & Sergio Focardi & Michele Marchesi, 2003. "Traders' Long-Run Wealth in an Artificial Financial Market," Computational Economics, Springer;Society for Computational Economics, vol. 22(2), pages 255-272, October.
    13. Amilon, Henrik, 2008. "Estimation of an adaptive stock market model with heterogeneous agents," Journal of Empirical Finance, Elsevier, vol. 15(2), pages 342-362, March.
    14. LeBaron, Blake, 2000. "Agent-based computational finance: Suggested readings and early research," Journal of Economic Dynamics and Control, Elsevier, vol. 24(5-7), pages 679-702, June.
    15. Xintong Wang & Christopher Hoang & Yevgeniy Vorobeychik & Michael P. Wellman, 2021. "Spoofing the Limit Order Book: A Strategic Agent-Based Analysis," Games, MDPI, vol. 12(2), pages 1-43, May.
    16. Flaminio Squazzoni, 2010. "The impact of agent-based models in the social sciences after 15 years of incursions," History of Economic Ideas, Fabrizio Serra Editore, Pisa - Roma, vol. 18(2), pages 197-234.
    17. Lijian Wei & Xiong Xiong & Wei Zhang & Xue-Zhong He & Yongjie Zhang, 2017. "The effect of genetic algorithm learning with a classifier system in limit order markets," Published Paper Series 2017-3, Finance Discipline Group, UTS Business School, University of Technology, Sydney.
    18. Dutta, Srimonti & Ghosh, Dipak & Samanta, Shukla, 2014. "Multifractal detrended cross-correlation analysis of gold price and SENSEX," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 413(C), pages 195-204.
    19. Hommes, Cars H., 2006. "Heterogeneous Agent Models in Economics and Finance," Handbook of Computational Economics, in: Leigh Tesfatsion & Kenneth L. Judd (ed.), Handbook of Computational Economics, edition 1, volume 2, chapter 23, pages 1109-1186, Elsevier.
    20. Noemi Schmitt & Frank Westerhoff, 2017. "Heterogeneity, spontaneous coordination and extreme events within large-scale and small-scale agent-based financial market models," Journal of Evolutionary Economics, Springer, vol. 27(5), pages 1041-1070, November.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:106:y:2018:i:c:p:5-15. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.