References:
[1] Skarda, C. A., Freeman W.J. , "Chaos and the New Science of the Brain", Concepts in Neuroscience, 1(2), pp. 275-285 (1990).
[2] Kim, J. H., & Stringer, J., "Applied Chaos". New York, NY: John Wiley and Sons, Inc., (1992).
[3] Hodgkin, A. L., & Huxley, A. F., "Quantitative Description of Membrane Current and Its Application to Conduction and Excitation in Nerve", J. Physiol, 117(4), pp. 500-544 (1952).
[4] Ma, J., & Tang, J., "A review for dynamics of collective behaviors of network of neurons", Sci. China Technol, 58, pp. 2038-2045 (2015).
[5] Hindmarsh, J. L., & Rose, R. M., "A model of neuronal bursting using three coupled first order differential equations", Proc. Roy. Soc. London B, 221, pp. 87-102 (1984).
[6] Bao, B., Zhu, Y., Ma, J., et al., "Memristive neuron model with an adapting synapse and its hardware experiments", Science China Technological Sciences, pp. 1-11 (2021).
[7] Xu, Y., Ma, J., Zhan, X., et al., "Temperature effect on memristive ion channels", Cognitive neurodynamics, 13(6), pp. 601-611 (2019).
[8] Xu, Y., Guo, Y., Ren, G., et al., "Dynamics and stochastic resonance in a thermosensitive neuron", Applied Mathematics and Computation, 385, 125427 (2020).
[9] Liu, Y., Xu, W.j., Ma, J., et al., "A new photosensitive neuron model and its dynamics", Frontiers of Information Technology & Electronic Engineering, 21, pp. 1387-1396 (2020).
[10] Xu, Y., Liu, M., Zhu, Z., et al., "Dynamics and coherence resonance in a thermosensitive neuron driven by photocurrent", Chinese Physics B, 29(9), 098704 (2020).
[11] Zhou, P., Yao, Z., Ma, J., et al., "A piezoelectric sensing neuron and resonance synchronization between auditory neurons under stimulus", Chaos, Solitons & Fractals, 145, 110751 (2021).
[12] Wang, Y., Ma, J., Xu, Y., et al., "The Electrical Activity of Neurons Subject to Electromagnetic Induction and Gaussian White Noise", International Journal of Bifurcation and Chaos, 27(2), pp. 1750030-1750042 (2017).
[13] FitzHugh, R., "Impulses and Physiological States in Theoretical Models of Nerve Membrane", Biophys. J., 1(6), pp. 445-466 (1961).
[14] Nagumo, J., Arimoto, S., and Yoshizawa, S., "An Active Pulse Transmission Line Simulating Nerve Axon", Proc. of the IRE, 50(10), pp. 2061-2070 (1962).
[15] Pouryahya, S., "Nonlinear dynamics, synchronisation and chaos in coupled FHN cardiac and neural cells," Ph.D., National University of Ireland Maynooth, 2013.
[16] Guckenheimer, J., & Kuehn, C., "Homoclinic orbits of the FitzHugh–Nagumo equation: Bifurcations in the full system", SIAM J. Appl. Dynam. Syst., 9(1), pp. 138-153 (2010).
[17] Hoff, A., dos Santos, J. V., Manchein, C., et al., "Numerical bifurcation analysis of two coupled FitzHugh–Nagumo oscillators", Eur. Phys. J. B 87(7), pp. 1-9 (2014).
[18] Pal, K., Ghosh, D. and Gangopadhyay, G., "Synchronization and metabolic energy consumption in stochastic Hodgkin-Huxley neurons: Patch size and drug blockers", Neurocomputing, 422, pp. 222-234 (2021).
[19] Doss-Bachelet, C., Françoise, J. P., & Piquet, C., "Bursting oscillations in two coupled FitzHugh–Nagumo systems", ComPlexUs, 1(3), pp. 101-111 (2003).
[20] Majhi, S. and Ghosh, D., "Alternating chimeras in networks of ephaptically coupled bursting neurons", Chaos: An Interdisciplinary Journal of Nonlinear Science, 28(8), 083113 (2018).
[21] Bera, B. K., Rakshit, S., Ghosh, D., et al., "Spike chimera states and firing regularities in neuronal hypernetworks", Chaos: An Interdisciplinary Journal of Nonlinear Science, 29(5), 053115 (2019).
[22] Makarov, V. V., Kundu, S., Kirsanov, D. V., et al., "Multiscale interaction promotes chimera states in complex networks", Communications in Nonlinear Science and Numerical Simulation, 71, pp. 118-129 (2019).
[23] Ciszak, M., Euzzor, S., Arecchi, F. T., et al., "Experimental study of firing death in a network of chaotic FitzHugh–Nagumo neurons", Phys. Rev. E 87(2), 022919(022911-022917) (2013).
[24] Gray, C. M., & McCormick, D. A., "Chattering cells: superficial pyramidal neurons contributing to the generation of synchronous oscillations in the visual vortex", Science, 274(5284), pp. 109-113 (1996).
[25] Kudryashov, N. A., "Asymptotic and Exact Solutions of the FitzHugh – Nagumo Model", Regular and Chaotic Dynamics, 23(2), pp. 152-160 (2018).
[26] Tehrani, N. F., & Razvan, M., "Bifurcation structure of two coupled FHN neurons with delay", Mathematical Biosciences 270, pp. 41-56 (2015).
[27] Zemlyanukhin, A. I., & Bochkarev, A. V., "Analytical Properties and Solutions of the FitzHugh – Rinzel Model", Russian Journal of Nonlinear Dynamics, 15(1), pp. 3-12 (2019).
[28] Wojcik, J., & Shilnikov, A., "Voltage Interval Mappings for an Elliptic Bursting Model", 12: Springer, Cham, (2015).
[29] Belykh, V. N., & Pankratova, E. V., "Chaotic Synchronization in Ensembles of Coupled Neurons Modeled by the FitzHugh – Rinzel System", Radiophys. Quantum El., 49(11), pp. 910-921 (2006).
[30] Shima, S. I., & Kuramoto, Y., "Rotating spiral waves with phase-randomized core in nonlocally coupled oscillators", Phys. Rev. E 69, 036213 (2004).
[31] Kuramoto, Y., & Shima, S. I., "Rotating spirals without Phase singularity in Reaction-Diffusion systems", Progr. Theor. Phys. Suppl, 150, 115 (2003).
[32] Kuramoto, Y., Shima, S. I., Battogtokh, D., et al., "Mean-Field Theory Revives in self-oscillatory field with Non-Local coupling", Prog. Theor. Phys. Suppl, 161, 127 (2006).
[33] Brooks, H. A., & Bressloff, P. C., "Quasicycles in the stochastic hybrid Morris-Lecar neural model", Physical Review E, 92, 012704 (2015).
[34] Hou, Z., & Xin, H., "Noise-sustained spiral waves: effect of spatial and temporal memory", Phys Rev Lett 89, 280601 (2002).
[35] Mondal, A., Sharma, S.K., Upadhyay, R.K. et al, "Firing activities of a fractional-order FitzHugh-Rinzel bursting neuron model and its coupled dynamics", Sci Rep 9, 15721 (2019).
[36] Rinzel, J., "A Formal Classification of Bursting Mechanisms in Excitable Systems, in Mathematical Topics in Population Biology", Morphogenesis and Neurosciences, Lecture Notes in Biomathematics, 71, pp. 267-281 (1987).
[37] Rinzel, J., & Troy, W. C., "Bursting phenomena in a simplified Oregonator flow system model", J Chem Phys 76, pp. 1775-1789 (1982).
[38] Lv, M., Wang, C., Ren, G., et al., "Model of electrical activity in a neuron under magnetic flow effect", Nonlinear Dyn., 85, pp. 1479-1490 (2016).
[39] Wolf, A., Swift, J. B., Swinney, H. L., e al., "Determining Lyapunov exponents from a time series", Physica D: Nonlinear Phenomena, 16(3), pp. 285-317 (1985).
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