IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i17p3696-d1226951.html
   My bibliography  Save this article

Dynamics of Optimal Cue Integration with Time-Varying Delay in the Insects’ Navigation System

Author

Listed:
  • Molan Li

    (School of Mathematics and Information Science, Guangxi University, Nanning 530004, China)

  • Da Li

    (School of Mathematics and Information Science, Guangxi University, Nanning 530004, China)

  • Junxing Zhang

    (School of Mathematics and Information Science, Guangxi University, Nanning 530004, China)

  • Xuanlu Xiang

    (School of Mathematics and Information Science, Guangxi University, Nanning 530004, China)

  • Di Zhao

    (School of Mathematics and Information Science, Guangxi University, Nanning 530004, China)

Abstract

Neural networks with a ring structure are considered biologically plausible and have the ability of enforcing unique and persistent heading representations, yielding realistic homing behaviors. Recent studies have found that insects optimally integrate sensory information from the environment for head direction by using ring attractor networks. Optimal cue integration as the basic component of a complex insect navigation system proves to consist of a ring attractor network that is coupled by some integration neurons and some uniform inhibition neurons. The dynamics of the coupled mechanisms between neurons in optimal cue integration determine whether the insects’ homing capability is affected by environmental noises. Furthermore, time delays caused by communication between different kinds of neurons may induce complex dynamical properties. These dynamical behaviors are essential for understanding the neural mechanisms of insect homing behaviors, but there is a lack of relevant research on the dynamics of optimal cue integration with time-varying delay in the insects’ navigation system. In this paper, we discuss the dynamical properties of optimal cue integration with time-varying delay and show that it is asymptotically stable and leads to a unique insect home direction. These results are critical in providing the theoretical basis for further research on insect homing behaviors and the establishment of autonomous robots that mimic insect navigation mechanisms in the future.

Suggested Citation

  • Molan Li & Da Li & Junxing Zhang & Xuanlu Xiang & Di Zhao, 2023. "Dynamics of Optimal Cue Integration with Time-Varying Delay in the Insects’ Navigation System," Mathematics, MDPI, vol. 11(17), pages 1-17, August.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:17:p:3696-:d:1226951
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/17/3696/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/17/3696/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Yang Hu & Guangping Hu, 2023. "Stabilization and Chaos Control of an Economic Model via a Time-Delayed Feedback Scheme," Mathematics, MDPI, vol. 11(13), pages 1-13, July.
    2. Ho Ko & Sonja B. Hofer & Bruno Pichler & Katherine A. Buchanan & P. Jesper Sjöström & Thomas D. Mrsic-Flogel, 2011. "Functional specificity of local synaptic connections in neocortical networks," Nature, Nature, vol. 473(7345), pages 87-91, May.
    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. Bettina Voelcker & Ravi Pancholi & Simon Peron, 2022. "Transformation of primary sensory cortical representations from layer 4 to layer 2," Nature Communications, Nature, vol. 13(1), pages 1-13, December.
    2. Matteo Farinella & Daniel T Ruedt & Padraig Gleeson & Frederic Lanore & R Angus Silver, 2014. "Glutamate-Bound NMDARs Arising from In Vivo-like Network Activity Extend Spatio-temporal Integration in a L5 Cortical Pyramidal Cell Model," PLOS Computational Biology, Public Library of Science, vol. 10(4), pages 1-21, April.
    3. Christopher Ebsch & Robert Rosenbaum, 2018. "Imbalanced amplification: A mechanism of amplification and suppression from local imbalance of excitation and inhibition in cortical circuits," PLOS Computational Biology, Public Library of Science, vol. 14(3), pages 1-28, March.
    4. Gabriel Koch Ocker & Ashok Litwin-Kumar & Brent Doiron, 2015. "Self-Organization of Microcircuits in Networks of Spiking Neurons with Plastic Synapses," PLOS Computational Biology, Public Library of Science, vol. 11(8), pages 1-40, August.
    5. Thaddeus R Cybulski & Edward S Boyden & George M Church & Keith E J Tyo & Konrad P Kording, 2017. "Nucleotide-time alignment for molecular recorders," PLOS Computational Biology, Public Library of Science, vol. 13(5), pages 1-22, May.
    6. Suchin S Gururangan & Alexander J Sadovsky & Jason N MacLean, 2014. "Analysis of Graph Invariants in Functional Neocortical Circuitry Reveals Generalized Features Common to Three Areas of Sensory Cortex," PLOS Computational Biology, Public Library of Science, vol. 10(7), pages 1-12, July.
    7. Takafumi Arakaki & G Barello & Yashar Ahmadian, 2019. "Inferring neural circuit structure from datasets of heterogeneous tuning curves," PLOS Computational Biology, Public Library of Science, vol. 15(4), pages 1-38, April.
    8. Dimitri Yatsenko & Krešimir Josić & Alexander S Ecker & Emmanouil Froudarakis & R James Cotton & Andreas S Tolias, 2015. "Improved Estimation and Interpretation of Correlations in Neural Circuits," PLOS Computational Biology, Public Library of Science, vol. 11(3), pages 1-28, March.
    9. Markus Helmer & Vladislav Kozyrev & Valeska Stephan & Stefan Treue & Theo Geisel & Demian Battaglia, 2016. "Model-Free Estimation of Tuning Curves and Their Attentional Modulation, Based on Sparse and Noisy Data," PLOS ONE, Public Library of Science, vol. 11(1), pages 1-33, January.
    10. Jeyadarshan Jeyabalaratnam & Vishal Bharmauria & Lyes Bachatene & Sarah Cattan & Annie Angers & Stéphane Molotchnikoff, 2013. "Adaptation Shifts Preferred Orientation of Tuning Curve in the Mouse Visual Cortex," PLOS ONE, Public Library of Science, vol. 8(5), pages 1-8, May.
    11. Pierre Yger & Kenneth D Harris, 2013. "The Convallis Rule for Unsupervised Learning in Cortical Networks," PLOS Computational Biology, Public Library of Science, vol. 9(10), pages 1-16, October.
    12. Bartul Mimica & Tuçe Tombaz & Claudia Battistin & Jingyi Guo Fuglstad & Benjamin A. Dunn & Jonathan R. Whitlock, 2023. "Behavioral decomposition reveals rich encoding structure employed across neocortex in rats," Nature Communications, Nature, vol. 14(1), pages 1-20, December.
    13. Ryan C Williamson & Benjamin R Cowley & Ashok Litwin-Kumar & Brent Doiron & Adam Kohn & Matthew A Smith & Byron M Yu, 2016. "Scaling Properties of Dimensionality Reduction for Neural Populations and Network Models," PLOS Computational Biology, Public Library of Science, vol. 12(12), pages 1-27, December.
    14. Sadra Sadeh & Stefan Rotter, 2015. "Orientation Selectivity in Inhibition-Dominated Networks of Spiking Neurons: Effect of Single Neuron Properties and Network Dynamics," PLOS Computational Biology, Public Library of Science, vol. 11(1), pages 1-17, January.

    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:gam:jmathe:v:11:y:2023:i:17:p:3696-:d:1226951. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.