430
11 Nonlinear Dynamics of Circuits with Mem-Elements
and
M 22 ˙
z(t) = −H 21
F a (X(t)) − F a (X 0 )
Y(t) − Y 0
−H 22 z(t) + M 22 R 0
= −H 21
F a (X(t))
Y(t)
−H 22
z(t) − H
−1
22 H 21
F a (X 0 )
Y 0
−H
−1
22 M 22 R 0
= −H 21
F a (X(t))
Y(t)
− H 22 Z(t)
where we used (11.30). The corollary is proved by deriving z(t) from (11.30) and
substituting in (11.39).
References
1. A. Wu, Z. Zeng, X. Zhu, J. Zhang, Exponential synchronization of memristor-based recurrent
neural networks with time delays. Neurocomputing 74(17), 3043–3050 (2011)
2. A. Wu, S. Wen, Z. Zeng, Synchronization control of a class of memristor-based recurrent neural
networks. Inf. Sci. 183(1), 106–116 (2012)
3. H. Kim, M. Sah, C. Yang, T. Roska, L.O. Chua, Memristor bridge synapses. Proc. IEEE 100(6),
2061–2070 (2012)
4. Z. Guo, J. Wang, Z. Yan, Global exponential synchronization of two memristor-based recurrent
neural networks with time delays via static or dynamic coupling. IEEE Trans. Syst. Man
Cybern. Syst. 45(2), 235–249 (2015)
5. Q. Xiao, Z. Huang, Z. Zeng, Passivity analysis for memristor-based inertial neural networks
with discrete and distributed delays. IEEE Trans. Syst. Man Cybern. Syst. 49(2), 375–385
(2019)
6. Z. Guo, J. Wang, Z. Yan, Attractivity analysis of memristor-based cellular neural networks with
time-varying delays. IEEE Trans. Neural Netw. Learn. Syst. 25(4), 704–717 (2014)
7. Y. Wan, J. Cao, Periodicity and synchronization of coupled memristive neural networks with
supremums. Neurocomputing 159(1), 137–143 (2015)
8. Q. Xu, Y. Lin, B. Bao, M. Chen, Multiple attractors in a non-ideal active voltage-controlled
memristor based Chua’s circuit. Chaos, Solitons Fractals 83, 186–200 (2016)
9. X. Yang, D.W.C. Ho, Synchronization of delayed memristive neural networks: robust analysis
approach. IEEE Trans. Cybern. 46(12), 3377–3387 (2016)
10. S. Ding, Z. Wang, N. Rong, H. Zhang, Exponential stabilization of memristive neural networks
via saturating sampled-data control. IEEE Trans. Cybern. 47(10), 3027–3039 (2017)
11. H. Liu, Z. Wang, B. Shen, H. Dong, Delay-distribution-dependent H ∞ state estimation for
discrete-time memristive neural networks with mixed time-delays and fading measurements.
IEEE Trans. Cybern. 50(2):440-51 (2018)
11 Nonlinear Dynamics of Circuits with Mem-Elements
and
M 22 ˙
z(t) = −H 21
F a (X(t)) − F a (X 0 )
Y(t) − Y 0
−H 22 z(t) + M 22 R 0
= −H 21
F a (X(t))
Y(t)
−H 22
z(t) − H
−1
22 H 21
F a (X 0 )
Y 0
−H
−1
22 M 22 R 0
= −H 21
F a (X(t))
Y(t)
− H 22 Z(t)
where we used (11.30). The corollary is proved by deriving z(t) from (11.30) and
substituting in (11.39).
References
1. A. Wu, Z. Zeng, X. Zhu, J. Zhang, Exponential synchronization of memristor-based recurrent
neural networks with time delays. Neurocomputing 74(17), 3043–3050 (2011)
2. A. Wu, S. Wen, Z. Zeng, Synchronization control of a class of memristor-based recurrent neural
networks. Inf. Sci. 183(1), 106–116 (2012)
3. H. Kim, M. Sah, C. Yang, T. Roska, L.O. Chua, Memristor bridge synapses. Proc. IEEE 100(6),
2061–2070 (2012)
4. Z. Guo, J. Wang, Z. Yan, Global exponential synchronization of two memristor-based recurrent
neural networks with time delays via static or dynamic coupling. IEEE Trans. Syst. Man
Cybern. Syst. 45(2), 235–249 (2015)
5. Q. Xiao, Z. Huang, Z. Zeng, Passivity analysis for memristor-based inertial neural networks
with discrete and distributed delays. IEEE Trans. Syst. Man Cybern. Syst. 49(2), 375–385
(2019)
6. Z. Guo, J. Wang, Z. Yan, Attractivity analysis of memristor-based cellular neural networks with
time-varying delays. IEEE Trans. Neural Netw. Learn. Syst. 25(4), 704–717 (2014)
7. Y. Wan, J. Cao, Periodicity and synchronization of coupled memristive neural networks with
supremums. Neurocomputing 159(1), 137–143 (2015)
8. Q. Xu, Y. Lin, B. Bao, M. Chen, Multiple attractors in a non-ideal active voltage-controlled
memristor based Chua’s circuit. Chaos, Solitons Fractals 83, 186–200 (2016)
9. X. Yang, D.W.C. Ho, Synchronization of delayed memristive neural networks: robust analysis
approach. IEEE Trans. Cybern. 46(12), 3377–3387 (2016)
10. S. Ding, Z. Wang, N. Rong, H. Zhang, Exponential stabilization of memristive neural networks
via saturating sampled-data control. IEEE Trans. Cybern. 47(10), 3027–3039 (2017)
11. H. Liu, Z. Wang, B. Shen, H. Dong, Delay-distribution-dependent H ∞ state estimation for
discrete-time memristive neural networks with mixed time-delays and fading measurements.
IEEE Trans. Cybern. 50(2):440-51 (2018)