Nonlinear Circuits and Systems with Memristors pp 271-316 | Cite as

# Pulse Programming of Memristor Circuits

- 114 Downloads

## Abstract

- (a)
we identify a wide class of memristor circuits, of any order and with any number of flux- or charge-controlled memristors, and introduce a systematic method for writing in an explicit way the SEs, both in the (

*φ*,*q*) and in the (*v*,*i*)-domain. The conditions for the existence of the SEs for such class are easily checkable (usually by inspection), since they are couched in topological terms. The techniques overcome drawbacks of the analogous technique described in Chap. 5, that was able in general only to yield the SE formulation in implicit form. - (b)
The obtained SEs have a relatively simple mathematical structure and, in the

*autonomous*case, under certain assumptions, a systematic method is introduced to identify and write analytically the invariant manifolds, to show the coexistence of different dynamics and to find the reduced-order dynamics on each invariant manifold.

## References

- 1.M. Itoh, L.O. Chua, Memristor oscillators. Int. J. Bifurc. Chaos
**18**(11), 3183–3206 (2008)MathSciNetCrossRefGoogle Scholar - 2.R. Riaza, C. Tischendorf, Semistate models of electrical circuits including memristors. Int. J. Circuit Theory Appl.
**39**(6), 607–627 (2011)CrossRefGoogle Scholar - 3.A. Ascoli, F. Corinto, R. Tetzlaff, Generalized boundary condition memristor model. Int. J. Circuit Theory Appl.
**44**(1), 60–84 (2016)CrossRefGoogle Scholar - 4.J. Ma, F. Wu, G. Ren, J. Tang, A class of initials-dependent dynamical systems. Appl. Math. Comput.
**298**, 65–76 (2017)MathSciNetzbMATHGoogle Scholar - 5.B. Bao, T. Jiang, Q. Xu, M. Chen, H. Wu, Y. Hu, Coexisting infinitely many attractors in active band-pass filter-based memristive circuit. Nonlinear Dyn.
**86**(3), 1711–1723 (2016)CrossRefGoogle Scholar - 6.A. Buscarino, C. Corradino, L. Fortuna, M. Frasca, L.O. Chua, Turing patterns in memristive cellular nonlinear networks. IEEE Trans. Circuits Syst. I Regul. Pap.
**63**(8), 1222–1230 (2016)MathSciNetCrossRefGoogle Scholar - 7.V.-T. Pham, S. Vaidyanathan, C.K. Volos, S. Jafari, N.V. Kuznetsov, T.M. Hoang, A novel memristive time-delay chaotic system without equilibrium points. Eur. Phys. J. Spec. Top.
**225**(1), 127–136 (2016)CrossRefGoogle Scholar - 8.R. Riaza, Manifolds of equilibria and bifurcations without parameters in memristive circuits. SIAM J. Appl. Math.
**72**(3), 877–896 (2012)MathSciNetCrossRefGoogle Scholar - 9.B. Bao, Z. Ma, J. Xu, Z. Liu, Q. Xu, A simple memristor chaotic circuit with complex dynamics. Int. J. Bifurc. Chaos
**21**(9), 2629–2645 (2011)CrossRefGoogle Scholar - 10.Q. Li, S. Hu, S. Tang, G. Zeng, Hyperchaos and horseshoe in a 4D memristive system with a line of equilibria and its implementation. Int. J. Circuit Theory Appl.
**42**(11), 1172–1188 (2014)CrossRefGoogle Scholar - 11.F. Corinto, A. Ascoli, M. Gilli, Analysis of current–voltage characteristics for memristive elements in pattern recognition systems. Int. J. Circuit Theory Appl.
**40**(12), 1277–1320 (2012)CrossRefGoogle Scholar - 12.L.O. Chua, Dynamic nonlinear networks: state-of-the-art. IEEE Trans. Circuits Syst.
**27**(11), 1059–1087 (1980)MathSciNetCrossRefGoogle Scholar - 13.H.C. So, On the hybrid description of a linear
*n*–port resulting from the extraction of arbitrarily specified elements. IEEE Trans. Circuit Theory**CT–12**(3), 381–387 (1965)Google Scholar - 14.F. Zhang,
*The Schur Complement and Its Applications*, vol. 4 (Springer, Berlin, 2006)Google Scholar - 15.F. Corinto, P.P. Civalleri, L.O. Chua, A theoretical approach to memristor devices. IEEE J. Emerg. Sel. Topics Circuits Syst.
**5**(2), 123–132 (2015)ADSCrossRefGoogle Scholar - 16.S. Kumar, J.P. Strachan, R. Stanley Williams, Chaotic dynamics in nanoscale NbO
_{2}Mott memristors for analogue computing. Nature**548**(7667), 318 (2017)Google Scholar - 17.M. Itoh , L.O. Chua, Star cellular neural networks for associative and dynamic memories. Int. J. Bifurc. Chaos
**14**(5), 1725–1772 (2004)MathSciNetCrossRefGoogle Scholar - 18.F. Corinto, M. Gilli, T. Roska, On full-connectivity properties of locally connected oscillatory networks. IEEE Trans. Circuits Syst. I: Regul. Pap.
**58**(5), 1063–1075 (2011)MathSciNetCrossRefGoogle Scholar