Abstract
Memristor has been investigated in dynamical systems. Due to the ionic transportation from extracellular and intracellular, the induction current is excitable in neuron with ion-channels based on the electromagnetic effect. A neural memristor system is reconstructed when the induction current is considered. Furthermore, the dynamical behaviors are calculated by the mathematical approaches, including the bifurcation diagram, time series, and equilibrium point analysis. It is found that the neural memristor system has the infinite equilibrium and no-equilibrium when a bifurcation parameter varies. For the neural model with memristor, its dynamical behaviors can transit from multi-period attractor into strange attractor with varying the bifurcation parameter. It is important to point out that the memory interplay between membrane potential and induction current depends on the initial magnetic flux.
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References
L. Chua, IEEE Trans. Circuit Theory 18, 507 (1971)
D.B. Strukov, G.S. Snider, D.R. Stewart, R.S. Williams, Nature 453, 80 (2008)
M. Itoh, L.O. Chua, Int. J. Bifurcat. Chaos 18, 3183 (2008)
J.J. Yang, D.B. Strukov, D.R. Stewart, Nat. Nanotechnol. 8, 13 (2013)
Y.N. Joglekar, S.J. Wolf, Eur. J. Phys. 30, 661 (2009)
K.H. Kim, S. Gaba, D. Wheeler, J.M. Cruz-Albrecht, T. Hussain, N. Srinivasa, W. Lu, Nano Lett. 12, 389 (2011)
B. Muthuswamy, P.P. Kokate, IETE Tech. Rev. 26, 417 (2009)
A. Buscarino, L. Fortuna, M. Frasca, L. Valentina Gambuzza, Chaos 22, 023136 (2012)
B. Muthuswamy, L.O. Chua, Int. J. Bifurc. Chaos 20, 1567 (2010)
J. Ma, F. Wu, G. Ren, J. Tang, Appl. Math. Comput. 298, 65 (2017)
B. Bao, T. Jiang, G. Wang, P. Jin, H. Bao, M. Chen, Nonlinear Dyn. 89, 1157 (2017)
H. Bao, N. Wang, B. Bao, M. Chen, P. Jin, G. Wang, Commun. Nonlinear Sci. Numer. Simul. 57, 264 (2018)
Z. Wang, A. Akgul, V.T. Pham, S. Jafari, Nonlinear Dyn. 89, 1877 (2017)
X. Wang, S. Vaidyanathan, C. Volos, V.T. Pham, T. Kapitaniak, Nonlinear Dyn. 89, 1673 (2017)
F. Wu, P. Zhou, A. Alsaedi, T. Hayat, J. Ma, Chaos, Solitons Fractals 110, 124 (2018)
G. Zhang, J. Ma, A. Alsaedi, B. Ahmad, F. Alzahrani, Appl. Math. Comput. 321, 290 (2018)
G. Zhang, F. Wu, T. Hayat, J. Ma, Commun. Nonlinear Sci. Numer. Simul. 65, 79 (2018)
Q. Jia, Phys. Lett. A 366, 217 (2007)
C. Munteanu, V. Brişan, D. Chiroiu, R.Ioan Dumitriu, Nonlinear Dyn. 78, 1877 (2014)
R. Barboza, Int. J. Bifurc. Chaos 28, 1850018 (2018)
J. Liu, S. Liu, J.C. Sprott, Nonlinear Dyn. 83, 1109 (2016)
C. Li, J.C. Sprott, Phys. Lett. A 378, 178 (2014)
S.H. Jo, T. Chang, I. Ebong, B.B. Bhadviya, P. Mazumder, W. Lu, Nano Lett. 10, 1297 (2010)
Y.V. Pershin, M. Di Ventra, Adv. Phys. 602, 145 (2011)
D. Kuzum, R.G.D. Jeyasingh, B. Lee, H.S.P. Wong, Nano Lett. 12, 2179 (2011)
M. Lv, C. Wang, G. Ren, J. Ma, X. Song, Nonlinear Dyn. 85, 1479 (2016)
M. Lv, J. Ma, Neurocomputing 205, 375 (2016)
M. Ge, Y. Jia, Y. Xu, L. Yang, Nonlinear Dyn. 91, 515 (2018)
F. Wu, C. Wang, W. Jin, J. Ma, Physica A 469, 81 (2017)
L. Duan, Q. Cao, Z. Wang, J. Su, Nonlinear Dyn. 94, 1961 (2018)
J. Wu, Y. Xu, J. Ma, PLoS One 12, e0174330 (2017)
G. Ren, Y. Xu, C. Wang, Nonlinear Dyn. 88, 893 (2017)
F. Wu, C. Wang, Y. Xu, J. Ma, Sci. Rep. 6, 28 (2016)
J. Ma, F. Wu, T. Hayat, P. Zhou, J. Tang, Physica A 486, 508 (2017)
A. Mvogo, C.N. Takembo, H.P.E. Fouda, T.C. Kofané, Phys. Lett. A 381, 2264 (2017)
J. Ma, J. Tang, Sci. China Technol. Sci. 58, 2038 (2015)
J. Ma, L. Mi, P. Zhou, Y. Xu, T. Hayat, Appl. Math. Comput. 307, 321 (2017)
Y. Xu, Y. Jia, J. Ma, T. Hayat, A. Alsaedi, Sci Rep. 8, 1349 (2018)
F. Wu, J. Ma, G. Zhang, Appl. Math. Comput. 347, 590 (2019)
G.A. Leonov, N.V. Kuznetsov, O.A. Kuznetsova, S.M. Seledzhi, V.I. Vagaitsev, WSEAS Trans. Syst. Control 6, 54 (2011)
N.V. Stankevich, N.V. Kuznetsov, G.A. Leonov, L.O. Chua, Int. J. Bifurc. Chaos 27, 1730038 (2017)
J. Ma, F. Wu, W. Jin, P. Zhou, T. Hayat, Chaos 27, 053108 (2017)
A. Moujahid, A. D’Anjou, F.J. Torrealdea, F. Torrealdea, Phys. Rev. E. 83, 031912 (2011)
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Wu, F., Zhang, G. & Ma, J. A neural memristor system with infinite or without equilibrium. Eur. Phys. J. Spec. Top. 228, 1527–1534 (2019). https://doi.org/10.1140/epjst/e2019-800233-6
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DOI: https://doi.org/10.1140/epjst/e2019-800233-6