IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v104y2017icp228-237.html
   My bibliography  Save this article

Lyapunov analysis of the spatially discrete-continuous system dynamics

Author

Listed:
  • Maximenko, Vladimir A.
  • Hramov, Alexander E.
  • Koronovskii, Alexey A.
  • Makarov, Vladimir V.
  • Postnov, Dmitry E.
  • Balanov, Alexander G.

Abstract

The spatially discrete-continuous dynamical systems, that are composed of a spatially extended medium coupled with a set of lumped elements, are frequently met in different fields, ranging from electronics to multicellular structures in living systems. Due to the natural heterogeneity of such systems, the calculation of Lyapunov exponents for them appears to be a challenging task, since the conventional techniques in this case often become unreliable and inaccurate. The paper suggests an effective approach to calculate Lyapunov exponents for discrete-continuous dynamical systems, which we test in stability analysis of two representative models from different fields. Namely, we consider a mathematical model of a 1D transferred electron device coupled with a lumped resonant circuit, and a phenomenological neuronal model of spreading depolarization, which involves 2D diffusive medium. We demonstrate that the method proposed is able reliably recognize regular, chaotic and hyperchaotic dynamics in the systems under study.

Suggested Citation

  • Maximenko, Vladimir A. & Hramov, Alexander E. & Koronovskii, Alexey A. & Makarov, Vladimir V. & Postnov, Dmitry E. & Balanov, Alexander G., 2017. "Lyapunov analysis of the spatially discrete-continuous system dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 228-237.
    • Handle: RePEc:eee:chsofr:v:104:y:2017:i:c:p:228-237
    DOI: 10.1016/j.chaos.2017.08.021
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077917303508
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2017.08.021?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. Upadhyay, Ranjit Kumar & Mondal, Argha, 2017. "Synchronization of bursting neurons with a slowly varying d. c. current," Chaos, Solitons & Fractals, Elsevier, vol. 99(C), pages 195-208.
    2. Zhou, Leilei & Chen, Zengqiang & Wang, Zhonglin & Wang, Jiezhi, 2016. "On the analysis of local bifurcation and topological horseshoe of a new 4D hyper-chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 148-156.
    3. Soltanov, Kamal N. & Prykarpatski, Anatolij K. & Blackmore, Denis, 2017. "Long-time behavior of solutions and chaos in reaction-diffusion equations," Chaos, Solitons & Fractals, Elsevier, vol. 99(C), pages 91-100.
    4. Singh, Jay Prakash & Roy, B.K., 2016. "The nature of Lyapunov exponents is (+, +, −, −). Is it a hyperchaotic system?," Chaos, Solitons & Fractals, Elsevier, vol. 92(C), pages 73-85.
    5. T. M. Fromhold & A. Patanè & S. Bujkiewicz & P. B. Wilkinson & D. Fowler & D. Sherwood & S. P. Stapleton & A. A. Krokhin & L. Eaves & M. Henini & N. S. Sankeshwar & F. W. Sheard, 2004. "Chaotic electron diffusion through stochastic webs enhances current flow in superlattices," Nature, Nature, vol. 428(6984), pages 726-730, April.
    6. Gomez, Ignacio S., 2017. "Lyapunov exponents and poles in a non Hermitian dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 99(C), pages 155-161.
    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. Shoreh, A.A.-H. & Kuznetsov, N.V. & Mokaev, T.N., 2022. "New adaptive synchronization algorithm for a general class of complex hyperchaotic systems with unknown parameters and its application to secure communication," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 586(C).
    2. Signing, V.R. Folifack & Kengne, J. & Pone, J.R. Mboupda, 2019. "Antimonotonicity, chaos, quasi-periodicity and coexistence of hidden attractors in a new simple 4-D chaotic system with hyperbolic cosine nonlinearity," Chaos, Solitons & Fractals, Elsevier, vol. 118(C), pages 187-198.
    3. Lin, Y. & Liu, W.B. & Bao, H. & Shen, Q., 2020. "Bifurcation mechanism of periodic bursting in a simple three-element-based memristive circuit with fast-slow effect," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    4. Upadhyay, Ranjit Kumar & Paul, Chinmoy & Mondal, Argha & Vishwakarma, Gajendra K., 2018. "Estimation of biophysical parameters in a neuron model under random fluctuations," Applied Mathematics and Computation, Elsevier, vol. 329(C), pages 364-373.
    5. Du Mingjing & Yulan Wang, 2019. "Some Novel Complex Dynamic Behaviors of a Class of Four-Dimensional Chaotic or Hyperchaotic Systems Based on a Meshless Collocation Method," Complexity, Hindawi, vol. 2019, pages 1-15, October.
    6. Ma, Xujiong & Mou, Jun & Xiong, Li & Banerjee, Santo & Cao, Yinghong & Wang, Jieyang, 2021. "A novel chaotic circuit with coexistence of multiple attractors and state transition based on two memristors," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    7. Dávila-Fernández, Marwil J. & Sordi, Serena, 2019. "Path dependence, distributive cycles and export capacity in a BoPC growth model," Structural Change and Economic Dynamics, Elsevier, vol. 50(C), pages 258-272.
    8. Njimah, Ouzerou Mouncherou & Ramadoss, Janarthanan & Telem, Adelaide Nicole Kengnou & Kengne, Jacques & Rajagopal, Karthikeyan, 2023. "Coexisting oscillations and four-scroll chaotic attractors in a pair of coupled memristor-based Duffing oscillators: Theoretical analysis and circuit simulation," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
    9. Sahoo, Shilalipi & Roy, Binoy Krishna, 2022. "Design of multi-wing chaotic systems with higher largest Lyapunov exponent," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    10. Escot, Lorenzo & Sandubete, Julio E., 2023. "Estimating Lyapunov exponents on a noisy environment by global and local Jacobian indirect algorithms," Applied Mathematics and Computation, Elsevier, vol. 436(C).
    11. Ren, Hai-Peng & Tian, Kun & Grebogi, Celso, 2020. "Topological horseshoe in a single-scroll Chen system with time delay," Chaos, Solitons & Fractals, Elsevier, vol. 132(C).
    12. Gomez, Ignacio S., 2018. "KS–entropy and logarithmic time scale in quantum mixing systems," Chaos, Solitons & Fractals, Elsevier, vol. 106(C), pages 317-322.
    13. Singh, Jay Prakash & Roy, Binoy Krishna & Jafari, Sajad, 2018. "New family of 4-D hyperchaotic and chaotic systems with quadric surfaces of equilibria," Chaos, Solitons & Fractals, Elsevier, vol. 106(C), pages 243-257.
    14. Yadav, Vijay K. & Shukla, Vijay K. & Das, Subir, 2019. "Difference synchronization among three chaotic systems with exponential term and its chaos control," Chaos, Solitons & Fractals, Elsevier, vol. 124(C), pages 36-51.
    15. Luo, Chuanwen & Wang, Chuncheng & Wei, Junjie, 2009. "A new characteristic index of chaos," Chaos, Solitons & Fractals, Elsevier, vol. 39(4), pages 1831-1838.
    16. Lin, Hairong & Wang, Chunhua, 2020. "Influences of electromagnetic radiation distribution on chaotic dynamics of a neural network," Applied Mathematics and Computation, Elsevier, vol. 369(C).
    17. Xiaoyu Hu & Chongxin Liu, 2019. "Bursting and Synchronization of Coupled Neurons under Electromagnetic Radiation," Complexity, Hindawi, vol. 2019, pages 1-10, December.

    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:104:y:2017:i:c:p:228-237. 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.