Synchronisation of the ensemble of nonidentical FitzHugh-Nagumo oscillators with memristive couplings

E. V. Navrotskaya ; A. V. Kurbako ; V. I. Ponomarenko ; M. D. Prokhorov

Izvestiya VUZ. Applied Nonlinear Dynamics, Tome 32 (2024) no. 1, pp. 96-110.

Résumé

The aim of the study is to investigate the features of synchronization in ensembles of nonidentical neuron-like FitzHugh-Nagumo oscillators interacting via memristor-based coupling. Methods. The collective dynamics in a ring of FitzHugh-Nagumo oscillators connected via memristive coupling was studied numerically and experimentally. The nonidentity of oscillators was achieved by detuning them by the threshold parameter responsible for the excitation of oscillator, or by detuning them by the parameter characterizing the ratio of time scales, the value of which determines the natural frequency of oscillator. We investigated the synchronization of memristively coupled FitzHugh-Nagumo oscillators as a function of the magnitude of the coupling coefficient, the initial conditions of all variables, and the number of oscillators in the ensemble. As a measure of synchronization, we used a coefficient characterizing the closeness of oscillator trajectories. Results. It is shown that with memristive coupling of FitzHugh-Nagumo oscillators, their synchronization depends not only on the magnitude of the coupling coefficient, but also on the initial states of both the oscillators themselves and the variables responsible for the memristive coupling. We compared the synchronization features of nonidentical FitzHugh-Nagumo oscillators with memristive and diffusive couplings. It is shown that, in contrast to the case of diffusive coupling of oscillators, in the case of meristive coupling, with increasing coupling strength of the oscillators, the destruction of the regime of completely synchronous in-phase oscillations can be observed, instead of which a regime of out-of-phase oscillations appears. Conclusion. The obtained results can be used when solving the problems of synchronization control in ensembles of neuronlike oscillators, in particular, for achieving or destroying the regime of in-phase synchronization of oscillations in an ensemble of coupled oscillators.

Détail

Keywords: FitzHugh-Nagumo model, neuronlike oscillators, memristive coupling, radio physical experiment

Bibliographie

[1] Yamazaki K., Vo-Ho V.-K., Bulsara D., Le N., “Spiking neural networks and their applications: A review”, Brain Sciences, 12:7 (2022), 863 | DOI

[2] Quiroga R. Q., Panzeri S., Principles of Neural Coding, CRC Press, Boca Raton, 2013, 664 pp.

[3] Kasabov N., Evolving Connectionist Systems: The Knowledge Engineering Approach, Springer, London, 2007, 451 pp. | DOI | Zbl

[4] Lobov S., Mironov V., Kastalskiy I., Kazantsev V., “A spiking neural network in sEMG fea-ture extraction”, Sensors, 15:11 (2015), 27894–27904 | DOI

[5] Lobov S.A., Chernyshov A.V., Krilova N.P., Shamshin M.O., Kazantsev V.B., “Competitive learning in a spiking neural network: Towards an intelligent pattern classifier”, Sensors, 20:2 (2000), 500 | DOI

[6] Virgilio G. C. D., Sossa A. J. H., Antelis J. M., Falcón L. E., “Spiking Neural Networks applied to the classification of motor tasks in EEG signals”, Neural Netw, 122 (2020), 130–143 | DOI

[7] Andreev A. V., Ivanchenko M. V., Pisarchik A. N., Hramov A. E., “Stimulus classification using chimera-like states in a spiking neural network”, Chaos, Solitons Fractals, 139 (2020), 110061 | DOI | MR | Zbl

[8] Navrotskaya E. V., Kulminskii D. D., Ponomarenko V. I., Prokhorov M. D., “Otsenka parametrov impulsnogo vozdeistviya s pomoschyu seti neiropodobnykh ostsillyatorov”, Izvestiya vuzov. PND, 30:4 (2022), 495–512 | DOI | MR

[9] Hossain M. S., Muhammad G., “Emotion recognition using deep learning approach from audio–visual emotional big data”, Information Fusion, 49 (2019), 69–78 | DOI

[10] Yu D., Deng L., Automatic Speech Recognition: A Deep Learning Approach, Springer, London, 2015, 321 pp. | DOI | Zbl

[11] Bing Z., Meschede C., Röhrbein F., Huang K., Knoll A. C., “A survey of robotics control based on learning-inspired spiking neural networks”, Frontiers in Neurorobotics, 12 (2018), 35 | DOI

[12] Wang X., Hou Z.-G., Lv F., Tan M., Wang Y., “Mobile robots' modular navigation controller using spiking neural networks”, Neurocomputing, 134 (2014), 230–238 | DOI

[13] Chou T.-S., Bucci L. D., Krichmar J. L., “Learning touch preferences with a tactile robot using dopamine modulated STDP in a model of insular cortex”, Frontiers in Neurorobotics, 9 (2015), 6 | DOI

[14] Lobov S. A., Mikhaylov A. N., Shamshin M., Makarov V. A., Kazantsev V. B., “Spatial properties of STDP in a self-learning spiking neural network enable controlling a mobile robot”, Frontiers in Neuroscience, 14 (2020), 88 | DOI

[15] Yi Z., Lian J., Liu Q., Zhu H., Liang D., Liu J., “Learning rules in spiking neural networks: A survey”, Neurocomputing, 531 (2023), 163–179 | DOI

[16] Dmitrichev A. S., Kasatkin D. V., Klinshov V. V., Kirillov S. Yu., Maslennikov O. V., Schapin D. S., Nekorkin V. I., “Nelineinye dinamicheskie modeli neironov: obzor”, Izvestiya vuzov. PND, 26:4 (2018) | DOI

[17] Shepelev I. A., Slepnev A. V., Vadivasova T. E., “Different synchronization characteristics of distinct types of traveling waves in a model of active medium with periodic boundary conditions”, Communications in Nonlinear Science and Numerical Simulation, 38 (2016), 206–217 | DOI | MR | Zbl

[18] Shepelev I. A., Vadivasova T. E., Bukh A. V., Strelkova G. I., Anishchenko V. S., “New type of chimera structures in a ring of bistable FitzHugh–Nagumo oscillators with nonlocal interaction”, Physics Letters A, 381:16 (2017), 1398–1404 | DOI | MR

[19] Shepelev I. A., Shamshin D. V., Strelkova G. I., Vadivasova T. E., “Bifurcations of spatiotemporal structures in a medium of FitzHugh–Nagumo neurons with diffusive coupling”, Chaos, Solitons Fractals, 104 (2017), 153–160 | DOI | MR | Zbl

[20] Plotnikov S. A., Fradkov A. L., “On synchronization in heterogeneous FitzHugh–Nagumo networks”, Chaos, Solitons Fractals, 121 (2019), 85–91 | DOI | MR | Zbl

[21] Kulminskiy D. D., Ponomarenko V. I., Prokhorov M. D., Hramov A. E., “Synchronization in ensembles of delay-coupled nonidentical neuronlike oscillators”, Nonlinear Dynamics, 98:1 (2019), 735–748 | DOI

[22] Plotnikov S. A., Lehnert J., Fradkov A. L., Schöll E., “Adaptive control of synchronization in delay-coupled heterogeneous networks of FitzHugh–Nagumo nodes”, Int. J. Bifurc. Chaos, 26:4 (2016), 1650058 | DOI | Zbl

[23] Kurbako A. V., Ponomarenko V. I., Prokhorov M. D., “Adaptivnoe upravlenie nesinkhronnymi kolebaniyami v seti identichnykh elektronnykh neiropodobnykh generatorov”, Pisma v ZhTF, 48:19 (2022), 43–46 | DOI

[24] Korneev I. A., Slepnev A. V., Semenov V. V., Vadivasova T. E., “Volnovye protsessy v koltse memristivno svyazannykh avtogeneratorov”, Izvestiya vuzov. PND, 28:3 (2020), 324–340 | DOI | MR

[25] Wang C., Lv M., Alsaedi A., Ma J., “Synchronization stability and pattern selection in a memristive neuronal network”, Chaos, 27:11 (2017), 113108 | DOI | MR

[26] Xu F., Zhang J., Jin M., Huang S., Fang T., “Chimera states and synchronization behavior in multilayer memristive neural networks”, Nonlinear Dynamics, 94:2 (2018), 775–783 | DOI

[27] Usha K., Subha P. A., “Collective dynamics and energy aspects of star-coupled Hindmarsh–Rose neuron model with electrical, chemical and field couplings”, Nonlinear Dynamics, 96:3 (2019), 2115–2124 | DOI | MR | Zbl

[28] Bao H., Zhang Y., Liu W., Bao B., “Memristor synapse-coupled memristive neuron network: synchronization transition and occurrence of chimera”, Nonlinear Dynamics, 100:1 (2020), 937–950 | DOI | Zbl

[29] Korneev I. A., Semenov V. V., Slepnev A. V., Vadivasova T. E., “The impact of memristive coupling initial states on travelling waves in an ensemble of the FitzHugh–Nagumo oscillators”, Chaos, Solitons Fractals, 147 (2021), 110923 | DOI | Zbl

[30] Xu Y., Jia Y., Ma J., Alsaedi A., Ahmad B., “Synchronization between neurons coupled by memristor”, Chaos, Solitons Fractals, 104 (2017), 435–442 | DOI

[31] Gerasimova S. A., Mikhailov A. N., Belov A. I., Korolev D. S., Gorshkov O. N., Kazantsev V. B., “Imitatsiya sinapticheskoi svyazi neironopodobnykh generatorov s pomoschyu memristivnogo ustroistva”, ZhTF, 87:8 (2017), 1248–1254 | DOI

[32] Chua L., “Memristor-The missing circuit element”, IEEE Transactions on Circuit Theory, 18:5 (1971), 507–519 | DOI

[33] Chua L. O., Kang S. M., “Memristive devices and systems”, Proceedings of the IEEE, 64:2 (1976), 209–223 | DOI

[34] Strukov D. B., Snider G. S., Stewart D. R., Williams R. S., “The missing memristor found”, Nature, 453:7191 (2008), 80–83 | DOI

[35] Patterson G. A., Fierens P. I., García A. A., Grosz D. F., “Numerical and experimental study of stochastic resistive switching”, Phys. Rev. E, 87:1 (2013), 012128 | DOI