IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v158y2022ics0960077922002739.html
   My bibliography  Save this article

Stability and dynamics of complex order fractional difference equations

Author

Listed:
  • Bhalekar, Sachin
  • Gade, Prashant M.
  • Joshi, Divya

Abstract

We extend the definition of n-dimensional difference equations to complex order. We investigate the stability of linear systems defined by an n-dimensional matrix and derive the conditions for the stability of zero solution of linear systems. For the one-dimensional case, we find that the stability region, if any is enclosed by a boundary curve and we obtain a parametric equation for the same. Furthermore, we find that there is no stable region if this parametric curve is self-intersecting. Even for the real eigenvalues, the solutions can be complex and dynamics in one-dimension is richer than the case for real order. These results can be extended to n-dimensions. For nonlinear systems, we observe that the stability of the linearized system determines the stability of the equilibrium point.

Suggested Citation

  • Bhalekar, Sachin & Gade, Prashant M. & Joshi, Divya, 2022. "Stability and dynamics of complex order fractional difference equations," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
    • Handle: RePEc:eee:chsofr:v:158:y:2022:i:c:s0960077922002739
    DOI: 10.1016/j.chaos.2022.112063
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077922002739
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2022.112063?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. Pakhare, Sumit S. & Daftardar-Gejji, Varsha & Badwaik, Dilip S. & Deshpande, Amey & Gade, Prashant M., 2020. "Emergence of order in dynamical phases in coupled fractional gauss map," Chaos, Solitons & Fractals, Elsevier, vol. 135(C).
    2. Plastino, A.R & Giordano, C & Plastino, A & Casas, M, 2004. "Liouville equation and the q-statistical formalism," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 336(3), pages 376-390.
    3. Prashant M. Gade & Sachin Bhalekar, 2021. "On Fractional Order Maps And Their Synchronization," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 29(06), pages 1-9, September.
    Full references (including those not matched with items on IDEAS)

    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. Yan, Yanjun & Chen, Kai & Zhao, Yijiu & Wang, Houjun & Xu, Bo & Wang, Yifan, 2024. "An innovative orthogonal matrix based on nonlinear chaotic system for compressive sensing," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).
    2. Sabe, Naval R. & Pakhare, Sumit S. & Gade, Prashant M., 2024. "Synchronization transitions in coupled q-deformed logistic maps," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).
    3. Pakhare, Sumit S. & Bhalekar, Sachin & Gade, Prashant M., 2022. "Synchronization in coupled integer and fractional-order maps," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).

    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:158:y:2022:i:c:s0960077922002739. 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.