Abstract
Neurons can exhibit abundant electrical activities in response to various externally applied stimuli, which can lay the groundwork for widening their use in neuron-based engineering applications. This paper presents the dynamical behaviors and analogy circuit-based confirmations in a bipolar pulse (BP) current-forced two-dimensional (2D) Wilson neuron model. Due to the existence of BP current, the proposed 2D neuron model has periodically switchable equilibrium states. The BP current-associated dynamical behaviors, including subthreshold oscillation (STO), periodic limit cycle, chaos, and antimonotonicity phenomenon, are numerically revealed by common dynamical analyses. Note that the electrical activity behaves a close dependence on the frequency of the externally applied BP current. Thereafter, an analog circuit is optimally synthesized to implement the 2D Wilson neuron model by utilizing the off-the-shelf discrete components, upon which the Multisim 12.0-based circuit simulations and hardware experiments are executed. It is revealed that the circuit-simulated and experimentally captured results well confirm the numerically simulated ones.
Similar content being viewed by others
References
A.L. Hodgkin, A.F. Huxley, J. Physiol. 117, 500 (1952)
J. Nagumo, S. Arimoto, S. Yoshizawa, Proc. IRE 50, 2061 (1962)
R. FitzHugh, J. Appl. Physiol. 25, 628 (1968)
C. Morris, H. Lecar, Biophys. J. 35, 193 (1981)
T.R. Chay, Physica D 16, 233 (1985)
H.R. Wilson, J. Theor. Biol. 200, 375 (1999)
R. FitzHugh, Biophys. J. 1, 445 (1961)
J.L. Hindmarsh, R.M. Rose, Nature 296, 162 (1982)
S. Zhang, J.H. Zheng, X.P. Wang, Z.G. Zeng, Chaos 31, 011101 (2021)
X.L. Song, H.T. Wang, Y. Chen, Nonlinear Dyn. 96, 2341 (2019)
M.Y. Ge, Y. Jia, Y. Xu, L. Yang, Nonliear Dyn. 91, 515 (2018)
X.Y. Hu, C.X. Liu, L. Liu, J. Ni, S. Li, Nonlinear Dyn. 84, 2317 (2016)
G.D. Ren, P. Zhou, J. Ma, A. Alsaedi, B. Ahmad, Int. J. Bifurc. Chaos 27, 1750187 (2017)
S. Mostaghimi, F. Nazarimehr, S. Jafari, J. Ma, Appl. Math. Comput. 348, 42 (2019)
H. Bao, W.B. Liu, M. Chen, Nonlinear Dyn. 96, 1879 (2019)
F.Q. Wu, J. Ma, G. Zhang, Appl. Math. Comput. 347, 590 (2019)
B.C. Bao, A.H. Hu, Q. Xu, H. Bao, H.G. Wu, M. Chen, Nonlinear Dyn. 92, 1695 (2018)
J. Wu, S.J. Ma, Nonlinear Dyn. 96, 1895 (2019)
X.L. Song, H.T. Wang, Y. Chen, Nonlinear Dyn. 94, 141 (2018)
R.K. Upadhyay, C. Paul, A. Mondal, G.K. Vishwakarma, Appl. Math. Comput. 329, 364 (2018)
Z.Q. Yang, Q.S. Lu, H.G. Gu, W. Ren, Int. J. Bifurc. Chaos 14, 4143 (2004)
Y.G. Yao, J. Ma Cogn. Neurodyn. 12, 343 (2018)
L.L. Lu, Y. Jia, W.H. Liu, L.J. Yang, Complexcity 2017, 7628537 (2017)
M. Bordet, S. Morfu, Chaos Solitons Fractals 54, 82 (2013)
S.K. Thottil, R.P. Ignatius, Nonlinear Dyn. 95, 239 (2018)
H. Bao, A.H. Hu, W.B. Liu, Int. J. Bifurc. Chaos 29, 1950006 (2019)
Y. Qi, A.L. Watts, J.W. Kim, P.A. Robinson, Biol. Cybern. 107, 15 (2013)
Z. Zhao, J.W. Kim, P.A. Robinson, C.J. Rennie, J. Comput. Neurosci. 36, 81 (2013)
Y. Liu, J. Ma, Y. Xu, Y. Jia, Int. J. Bifurc. Chaos 29, 1950156 (2009)
D.A. Steyn-Ross, M.L. Steyn-Ross, M.T. Wilson, J.W. Sleigh, Phys. Rev. E 74, 051920 (2006)
M.L. Steyn-Ross, D.A. Steyn-Ross, Phys. Rev. E 93, 022402 (2016)
A. Mondal, R.K. Upadhyay, J. Ma, B.K. Yadav, S.K. Sharma, A. Mondal, Cogn. Neurodyn. 13, 393407 (2019)
M.A. Imani, A. Ahmadi, M.R. Malekshahi, S. Haghiri, IEEE Trans. Biomed. Circ. Syst. 12, 1431 (2018)
M. Nouri, M. Hayati, T.S. Gotarredona, D. Abbott, IEEE Trans. Circ. Syst. II: Express Briefs 66, 136 (2019)
S. Zhang, J.H. Zheng, X.P. Wang, Z.G. Zeng, S.B. He, Nonlinear Dyn. 102, 2821 (2020)
K. Rajagopal, J.M. Munoz-Pacheco, V.T. Pham, D.V. Hoang, F.E. Alsaadi, F.E. Alsaadi, Eur. Phys. J. Special Topics 227, 811 (2018)
Y.N. Jiang, P. Huang, D.B. Zhu, Z. Zhou, R.Z. Han, L.F. Liu, X.Y. Liu, J.F. Kang, IEEE Trans. Circ. Syst. I: Regular Papers 65, 2726 (2018)
X.Y. Hu, C.X. Liu, Nonlinear Dyn. 97, 1721 (2019)
G. Wainrib, M. Thieullen, K. Pakdaman, J. Comput. Neurosci. 32, 327 (2012)
Y. Xu, J. Ma, X. Zhan, L.J. Yang, Y. Jia, Cogn. Neurodyn. 13, 601 (2019)
A. Wolf, J.B. Swift, H.L. Swinney, J.A. Vastano, Physica D 16, 285 (1985)
S.P. Dawson, C. Grebogi, J.A. Yorke, I. Kan, H. Kocak, Phys. Lett. A 162, 249 (1992)
L. Zhou, C.H. Wang, X. Zhang, W. Yao, Int. J. Bifurc. Chaos 28, 1850050 (2018)
J. Kengne, A.N. Negou, D. Tchiotsop, Nonlinear Dyn. 88, 2589 (2017)
I. Manimehan, P. Philominathan, Chaos Solitons Fractals 45, 1501 (2012)
B.C. Bao, H. Bao, N. Wang, M. Chen, Q. Xu, Chaos Solitons Fractals 94, 102 (2017)
S. Zhang, Y.C. Zeng, Z.J. Li, M.J. Wang, L. Xiong, Chaos 28, 013113 (2018)
H.R. Lin, C.H. Wang, Y.C. Sun, W. Yao, Nonlinear Dyn. 100, 3667 (2020)
Q. Xu, Y. Lin, B.C. Bao, M. Chen, Chaos Solitons Fractals 83, 186 (2016)
Acknowledgements
This work was supported by the grants from the National Natural Science Foundations of China under Grant Nos. 61801054 and 51777016, the Natural Science Foundations of Jiangsu Province, China under Grant Nos. BK20160282 and BK20191451, and the Postgraduate Research and Practice Innovation Program of Jiangsu Province, China under Grant No. KYCX20_2547.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Xu, Q., Ju, Z., Feng, C. et al. Analogy circuit synthesis and dynamics confirmation of a bipolar pulse current-forced 2D Wilson neuron model. Eur. Phys. J. Spec. Top. 230, 1989–1997 (2021). https://doi.org/10.1140/epjs/s11734-021-00183-0
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1140/epjs/s11734-021-00183-0