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How can the networks with various topologies change the occurrence of bifurcation points in a period-doubling route to chaos: a case study of neural networks in the presence and absence of disturbance

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Abstract

Several mathematical models, such as Hodgkin–Huxley, FitzHugh–Nagumo, Morris–Lecar, Hindmarsh–Rose, and Leech, have been proposed to explain neural behaviors. Changing the parameters of neural models reveals the various neural dynamics. To make these models as realistic as possible, they should be studied in the networks, where there are interactions between the neurons. Hence, investigating neural models in the networks can be helpful. This study examines the attention-deficit disorder model's bifurcation points in both regular and irregular networks. The networks are analyzed in two cases. In the first case, networks are studied where perturbations enter one node. Calculating the recovery time of the disturbed neuron can investigate the bifurcation points. Results show that recovery time reveals the dynamical variation of the disturbed node. The second case examines networks with different coupling strengths and nodes' degrees. Results indicate that as coupling strengths and nodes' degree increase, bifurcations occur in the smaller parameters in the period-doubling route to chaos. A general trend cannot be seen in the inverse route of period doubling.

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Data availability statement

This manuscript has associated data in a data repository. [Authors’ comment: Data generated during the current study will be made available at reasonable request.]

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Funding

This work is partially funded by the Centre for Nonlinear Systems, Chennai Institute of Technology, India, vide funding number CIT/CNS/2022/RD/006.

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Authors and Affiliations

  1. Department of Biomedical Engineering, Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran

    Nastaran Navid Moghadam, Fahimeh Nazarimehr & Sajad Jafari

  2. Centre for Artificial Intelligence, Chennai Institute of Technology, Chennai, India

    Ramesh Ramamoorthy

  3. Centre for Nonlinear Systems, Chennai Institute of Technology, Chennai, India

    Karthikeyan Rajagopal

  4. Department of Electronics and Communications Engineering, University Centre for Research and Development, Chandigarh University, Punjab, India

    Karthikeyan Rajagopal

  5. Health Technology Research Institute, Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran

    Sajad Jafari

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  1. Nastaran Navid Moghadam
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Correspondence to Fahimeh Nazarimehr.

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Navid Moghadam, N., Ramamoorthy, R., Nazarimehr, F. et al. How can the networks with various topologies change the occurrence of bifurcation points in a period-doubling route to chaos: a case study of neural networks in the presence and absence of disturbance. Eur. Phys. J. Plus 138, 362 (2023). https://doi.org/10.1140/epjp/s13360-023-03939-w

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