IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v132y2020ics0960077919305156.html
   My bibliography  Save this article

One dimensional map-based neuron model: A phase space interpretation

Author

Listed:
  • Zandi-Mehran, Nazanin
  • Panahi, Shirin
  • Hosseini, Zahra
  • Hashemi Golpayegani, Seyed Mohammad Reza
  • Jafari, Sajad

Abstract

Computational models play an essential role in studying and predicting the behavior of a bio-system. Discrete dynamical models, usually known as maps, are important, especially when it comes to the mathematical study of the behavior of the neurons and neural network. Map-based neural models are simple, yet powerful and computationally efficient tools to study complex dynamical systems. In this paper, a one-dimensional map-based neuron model is proposed for which various dynamical behaviors are investigated using phase-space interpretation. In order to reproduce the behaviors observed in the real neurons such as action potential (AP), spike, burst, chaotic burst and, myocardial AP, different multi-criteria functions are formulated. In our proposed model, all the mentioned dynamical behaviors can be obtained only by changing the respective parameter. Therefore, though being simple, in terms of both analytical solutions and numerical calculations, our model is perfectly capable of demonstrating complex behaviors. In this study, the response of the model to various stimuli (excitation current) is explored. The time series analysis, phase-space and cobweb plot are provided as well for each multi-criteria function. Also, the bifurcation analysis with respect to different parameters of the model is carried out.

Suggested Citation

  • Zandi-Mehran, Nazanin & Panahi, Shirin & Hosseini, Zahra & Hashemi Golpayegani, Seyed Mohammad Reza & Jafari, Sajad, 2020. "One dimensional map-based neuron model: A phase space interpretation," Chaos, Solitons & Fractals, Elsevier, vol. 132(C).
    • Handle: RePEc:eee:chsofr:v:132:y:2020:i:c:s0960077919305156
    DOI: 10.1016/j.chaos.2019.109558
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077919305156
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2019.109558?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. Hiroaki Kitano, 2002. "Computational systems biology," Nature, Nature, vol. 420(6912), pages 206-210, November.
    2. Mesbah, Samineh & Moghtadaei, Motahareh & Hashemi Golpayegani, Mohammad Reza & Towhidkhah, Farzad, 2014. "One-dimensional map-based neuron model: A logistic modification," Chaos, Solitons & Fractals, Elsevier, vol. 65(C), pages 20-29.
    3. Khaleghi, Leyla & Panahi, Shirin & Chowdhury, Sayantan Nag & Bogomolov, Sergey & Ghosh, Dibakar & Jafari, Sajad, 2019. "Chimera states in a ring of map-based neurons," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 536(C).
    4. Massimiliano Zanin & Francisco Del Pozo & Stefano Boccaletti, 2011. "Computation Emerges from Adaptive Synchronization of Networking Neurons," PLOS ONE, Public Library of Science, vol. 6(11), pages 1-6, November.
    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. Muni, Sishu Shankar & Rajagopal, Karthikeyan & Karthikeyan, Anitha & Arun, Sundaram, 2022. "Discrete hybrid Izhikevich neuron model: Nodal and network behaviours considering electromagnetic flux coupling," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    2. Samuel Bandara & Johannes P Schlöder & Roland Eils & Hans Georg Bock & Tobias Meyer, 2009. "Optimal Experimental Design for Parameter Estimation of a Cell Signaling Model," PLOS Computational Biology, Public Library of Science, vol. 5(11), pages 1-12, November.
    3. Mark Read & Paul S. Andrews & Jon Timmis & Vipin Kumar, 2011. "Techniques for grounding agent-based simulations in the real domain: a case study in experimental autoimmune encephalomyelitis," Mathematical and Computer Modelling of Dynamical Systems, Taylor & Francis Journals, vol. 18(1), pages 67-86, May.
    4. Chandra, Yanto & Wilkinson, Ian F., 2017. "Firm internationalization from a network-centric complex-systems perspective," Journal of World Business, Elsevier, vol. 52(5), pages 691-701.
    5. Jacobo Ayensa-Jiménez & Marina Pérez-Aliacar & Teodora Randelovic & José Antonio Sanz-Herrera & Mohamed H. Doweidar & Manuel Doblaré, 2020. "Analysis of the Parametric Correlation in Mathematical Modeling of In Vitro Glioblastoma Evolution Using Copulas," Mathematics, MDPI, vol. 9(1), pages 1-22, December.
    6. Qing-Ju Jiao & Yan-Kai Zhang & Lu-Ning Li & Hong-Bin Shen, 2011. "BinTree Seeking: A Novel Approach to Mine Both Bi-Sparse and Cohesive Modules in Protein Interaction Networks," PLOS ONE, Public Library of Science, vol. 6(11), pages 1-12, November.
    7. Tom C Freeman & Leon Goldovsky & Markus Brosch & Stijn van Dongen & Pierre Mazière & Russell J Grocock & Shiri Freilich & Janet Thornton & Anton J Enright, 2007. "Construction, Visualisation, and Clustering of Transcription Networks from Microarray Expression Data," PLOS Computational Biology, Public Library of Science, vol. 3(10), pages 1-11, October.
    8. Yuksel Bayraktar & Esme Isik & Ibrahim Isik & Ayfer Ozyilmaz & Metin Toprak & Fatma Kahraman Guloglu & Serdar Aydin, 2022. "Analyzing of Alzheimer’s Disease Based on Biomedical and Socio-Economic Approach Using Molecular Communication, Artificial Neural Network, and Random Forest Models," Sustainability, MDPI, vol. 14(13), pages 1-15, June.
    9. Yang, J. & Primo, E. & Aleja, D. & Criado, R. & Boccaletti, S. & Alfaro-Bittner, K., 2022. "Implementing and morphing Boolean gates with adaptive synchronization: The case of spiking neurons," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    10. Mika Gustafsson & Michael Hörnquist, 2010. "Gene Expression Prediction by Soft Integration and the Elastic Net—Best Performance of the DREAM3 Gene Expression Challenge," PLOS ONE, Public Library of Science, vol. 5(2), pages 1-8, February.
    11. Diego Fernández Slezak & Cecilia Suárez & Guillermo A Cecchi & Guillermo Marshall & Gustavo Stolovitzky, 2010. "When the Optimal Is Not the Best: Parameter Estimation in Complex Biological Models," PLOS ONE, Public Library of Science, vol. 5(10), pages 1-10, October.
    12. Matthew A Hibbs & Chad L Myers & Curtis Huttenhower & David C Hess & Kai Li & Amy A Caudy & Olga G Troyanskaya, 2009. "Directing Experimental Biology: A Case Study in Mitochondrial Biogenesis," PLOS Computational Biology, Public Library of Science, vol. 5(3), pages 1-12, March.
    13. Alan A Cohen & Emmanuel Milot & Qing Li & Patrick Bergeron & Roxane Poirier & Francis Dusseault-Bélanger & Tamàs Fülöp & Maxime Leroux & Véronique Legault & E Jeffrey Metter & Linda P Fried & Luigi Fe, 2015. "Detection of a Novel, Integrative Aging Process Suggests Complex Physiological Integration," PLOS ONE, Public Library of Science, vol. 10(3), pages 1-26, March.
    14. Niki Vermeulen, 2018. "The choreography of a new research field: Aggregation, circulation and oscillation," Environment and Planning A, , vol. 50(8), pages 1764-1784, November.
    15. Peng, Hongxin & Ji’e, Musha & Du, Xinyu & Duan, Shukai & Wang, Lidan, 2023. "Design of pseudorandom number generator based on a controllable multi-double-scroll chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    16. Armaghan W Naik & Joshua D Kangas & Christopher J Langmead & Robert F Murphy, 2013. "Efficient Modeling and Active Learning Discovery of Biological Responses," PLOS ONE, Public Library of Science, vol. 8(12), pages 1-1, December.
    17. Joep P J Schmitz & Jeroen A L Jeneson & Joep W M van Oorschot & Jeanine J Prompers & Klaas Nicolay & Peter A J Hilbers & Natal A W van Riel, 2012. "Prediction of Muscle Energy States at Low Metabolic Rates Requires Feedback Control of Mitochondrial Respiratory Chain Activity by Inorganic Phosphate," PLOS ONE, Public Library of Science, vol. 7(3), pages 1-14, March.
    18. Marco S Nobile & Paolo Cazzaniga & Daniela Besozzi & Dario Pescini & Giancarlo Mauri, 2014. "cuTauLeaping: A GPU-Powered Tau-Leaping Stochastic Simulator for Massive Parallel Analyses of Biological Systems," PLOS ONE, Public Library of Science, vol. 9(3), pages 1-20, March.
    19. Fabian Fröhlich & Barbara Kaltenbacher & Fabian J Theis & Jan Hasenauer, 2017. "Scalable Parameter Estimation for Genome-Scale Biochemical Reaction Networks," PLOS Computational Biology, Public Library of Science, vol. 13(1), pages 1-18, January.
    20. Markus J. Buehler & Theodor Ackbarow, 2008. "Nanomechanical strength mechanisms of hierarchical biological materials and tissues," Computer Methods in Biomechanics and Biomedical Engineering, Taylor & Francis Journals, vol. 11(6), pages 595-607.

    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:132:y:2020:i:c:s0960077919305156. 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.