References
341
in the chapter demonstrate the effectiveness of FCAM to study in the (ϕ, q)domain the global nonlinear dynamics and collective behavior of large arrays of
interconnected cells.
References
1. L.O. Chua (Ed.), Special issue on nonlinear waves, patterns and spatio-temporal chaos in
dynamic arrays. IEEE Trans. Circuits Syst. I Fundam. Theory Appl. 42(10), 557–823 (1995)
2. S. Kumar, J.P. Strachan, R. Stanley Williams, Chaotic dynamics in nanoscale NbO 2 Mott
memristors for analogue computing. Nature 548(7667), 318 (2017)
3. A. Pikovsky, M. Rosenblum, J. Kurths, Synchronization: A Universal Concept in Nonlinear
Sciences, vol. 12 (Cambridge University Press, Cambridge, 2003)
4. A.-L. Barabási, Linked: The New Science of Networks (American Association of Physics
Teachers, College Park, 2003)
5. G.V. Osipov, V.D. Shalfeev, The evolution of spatio-temporal disorder in a chain of
unidirectionally-coupled Chua’s circuits. IEEE Trans. Circ. Syst. I Fund. Theory Appl. 42(10),
687–692 (1995)
6. M.J. Ogorzalek, Z. Galias, A.M. Dabrowski, W.R. Dabrowski, Chaotic waves and spatiotemporal patterns in large arrays of doubly-coupled Chua’s circuits. IEEE Trans. Circ. Syst.
I Fund. Theory Appl. 42(10), 706–714 (1995)
7. F. Kavaslar, C. Guzelis, A computer-assisted investigation of a 2-D array of Chua’s circuits.
IEEE Trans. Circ. Syst. I Fund. Theory Appl. 42(10), 721–735 (1995)
8. E. Sánchez, M.A. Matías, V. Pérez-Muñuzuri, Chaotic synchronization in small assemblies of
driven Chua’s circuits. IEEE Trans. Circ. Syst. I Fund. Theory Appl. 47(5), 644–654 (2000)
9. M. de Magistris, M. di Bernardo, E. Di Tucci, S. Manfredi, Synchronization of networks of
non-identical Chua’s circuits: analysis and experiments. IEEE Trans. Circ. Syst. I Regul. Pap.
59(5), 1029–1041 (2012)
10. A. Bogojeska, M. Mirchev, I. Mishkovski, L. Kocarev, Synchronization and consensus in statedependent networks. IEEE Trans. Circ. Syst. I Regul. Pap. 61(2), 522–529 (2014)
11. H. Liu, M. Cao, C.W. Wu, Coupling strength allocation for synchronization in complex
networks using spectral graph theory. IEEE Trans. Circ. Syst. I Regul. Pap. 61(5), 1520–1530
(2014)
12. W.K. Wong, W. Zhang, Y. Tang, X. Wu, Stochastic synchronization of complex networks with
mixed impulses. IEEE Trans. Circ. Syst. I Regul. Pap. 60(10), 2657–2667 (2013)
13. D. Kim, M. Jin, P.H. Chang, Control and synchronization of the generalized Lorenz system
with mismatched uncertainties using backstepping technique and time-delay estimation. Int. J.
Circuit Theory Appl. (2017). https://doi.org/10.1002/cta.2353
14. L.O. Chua, Memristor-The missing circuit element. IEEE Trans. Circuit Theory 18(5), 507–
519 (1971)
15. A. Ascoli, V. Lanza, F. Corinto, R. Tetzlaff, Synchronization conditions in simple memristor
neural networks. J. Franklin Inst. 352(8), 3196–3220 (2015)
16. V. Erokhin, T. Berzina, P. Camorani, A. Smerieri, D. Vavoulis, J. Feng, M.P. Fontana, Material
memristive device circuits with synaptic plasticity: learning and memory. BioNanoScience
1(1–2), 24–30 (2011)
17. Z. Wang, S. Ambrogio, S. Balatti, D. Ielmini, A 2-transistor/1-resistor artificial synapse capable
of communication and stochastic learning in neuromorphic systems. Front. Neurosci. 8, (2014)
18. 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)
19. L.V. Gambuzza, A. Buscarino, L. Fortuna, M. Frasca, Memristor-based adaptive coupling for
consensus and synchronization. IEEE Trans. Circ. Syst. I Regul. Pap. 62(4), 1175–1184 (2015)
341
in the chapter demonstrate the effectiveness of FCAM to study in the (ϕ, q)domain the global nonlinear dynamics and collective behavior of large arrays of
interconnected cells.
References
1. L.O. Chua (Ed.), Special issue on nonlinear waves, patterns and spatio-temporal chaos in
dynamic arrays. IEEE Trans. Circuits Syst. I Fundam. Theory Appl. 42(10), 557–823 (1995)
2. S. Kumar, J.P. Strachan, R. Stanley Williams, Chaotic dynamics in nanoscale NbO 2 Mott
memristors for analogue computing. Nature 548(7667), 318 (2017)
3. A. Pikovsky, M. Rosenblum, J. Kurths, Synchronization: A Universal Concept in Nonlinear
Sciences, vol. 12 (Cambridge University Press, Cambridge, 2003)
4. A.-L. Barabási, Linked: The New Science of Networks (American Association of Physics
Teachers, College Park, 2003)
5. G.V. Osipov, V.D. Shalfeev, The evolution of spatio-temporal disorder in a chain of
unidirectionally-coupled Chua’s circuits. IEEE Trans. Circ. Syst. I Fund. Theory Appl. 42(10),
687–692 (1995)
6. M.J. Ogorzalek, Z. Galias, A.M. Dabrowski, W.R. Dabrowski, Chaotic waves and spatiotemporal patterns in large arrays of doubly-coupled Chua’s circuits. IEEE Trans. Circ. Syst.
I Fund. Theory Appl. 42(10), 706–714 (1995)
7. F. Kavaslar, C. Guzelis, A computer-assisted investigation of a 2-D array of Chua’s circuits.
IEEE Trans. Circ. Syst. I Fund. Theory Appl. 42(10), 721–735 (1995)
8. E. Sánchez, M.A. Matías, V. Pérez-Muñuzuri, Chaotic synchronization in small assemblies of
driven Chua’s circuits. IEEE Trans. Circ. Syst. I Fund. Theory Appl. 47(5), 644–654 (2000)
9. M. de Magistris, M. di Bernardo, E. Di Tucci, S. Manfredi, Synchronization of networks of
non-identical Chua’s circuits: analysis and experiments. IEEE Trans. Circ. Syst. I Regul. Pap.
59(5), 1029–1041 (2012)
10. A. Bogojeska, M. Mirchev, I. Mishkovski, L. Kocarev, Synchronization and consensus in statedependent networks. IEEE Trans. Circ. Syst. I Regul. Pap. 61(2), 522–529 (2014)
11. H. Liu, M. Cao, C.W. Wu, Coupling strength allocation for synchronization in complex
networks using spectral graph theory. IEEE Trans. Circ. Syst. I Regul. Pap. 61(5), 1520–1530
(2014)
12. W.K. Wong, W. Zhang, Y. Tang, X. Wu, Stochastic synchronization of complex networks with
mixed impulses. IEEE Trans. Circ. Syst. I Regul. Pap. 60(10), 2657–2667 (2013)
13. D. Kim, M. Jin, P.H. Chang, Control and synchronization of the generalized Lorenz system
with mismatched uncertainties using backstepping technique and time-delay estimation. Int. J.
Circuit Theory Appl. (2017). https://doi.org/10.1002/cta.2353
14. L.O. Chua, Memristor-The missing circuit element. IEEE Trans. Circuit Theory 18(5), 507–
519 (1971)
15. A. Ascoli, V. Lanza, F. Corinto, R. Tetzlaff, Synchronization conditions in simple memristor
neural networks. J. Franklin Inst. 352(8), 3196–3220 (2015)
16. V. Erokhin, T. Berzina, P. Camorani, A. Smerieri, D. Vavoulis, J. Feng, M.P. Fontana, Material
memristive device circuits with synaptic plasticity: learning and memory. BioNanoScience
1(1–2), 24–30 (2011)
17. Z. Wang, S. Ambrogio, S. Balatti, D. Ielmini, A 2-transistor/1-resistor artificial synapse capable
of communication and stochastic learning in neuromorphic systems. Front. Neurosci. 8, (2014)
18. 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)
19. L.V. Gambuzza, A. Buscarino, L. Fortuna, M. Frasca, Memristor-based adaptive coupling for
consensus and synchronization. IEEE Trans. Circ. Syst. I Regul. Pap. 62(4), 1175–1184 (2015)