Chapter 8
Complex Dynamics and Synchronization
Phenomena in Arrays of Memristor
Oscillators
8.1 Introduction
A great deal of efforts have been traditionally devoted in circuit theory to analyze
nonstationary steady-state behaviors in networks obtained by locally coupled arrays
of simple dynamic circuits (also named cells, oscillators, units, etc.) [1]. These
arrays can be thought of as a bio-inspired circuit model of complex nonlinear
phenomena observable in nature with potential applications in signal processing
and computing systems. In fact, on one hand, they are a mean for reproducing,
analyzing, and understanding spatiotemporal nonlinear phenomena displayed by
spatially extended networks found in such diverse fields as electrical engineering,
computer science, biology, and physics. On the other hand, complex spatiotemporal
dynamics including chaos are potentially useful for developing future analogue
computing systems. Recent studies have shown for instance that chaos can play
a crucial role in searching for the global solution of combinatorial optimization
problems and chaotic relaxation oscillators with memristors have been used to boot
efficiency and accuracy of Hopfield-like computing networks [2].
One of the most relevant aspects concerns bifurcations and synchronization
phenomena [3, 4], i.e., a scenario where all the oscillators adjust their dynamic
behavior so that the whole array acts in unison and spatiotemporal patterns emerge.
Synchronization phenomena in one-dimensional (1D) and bi-dimensional (2D)
dynamic arrays using Chua’s oscillators as building block, with various types
of uni-directional, bi-directional, static, and dynamic diffusive interactions, have
been considered and analyzed by numerical simulations and analytic tools [5–
7]. The influence of the network topology properties and their link with complex
dynamic periodic/chaotic attractors in large biological and artificial systems have
been studied in detail in several works [8–13].
Memristors provide an accurate and power efficient emulator of neural synapses
and biological neural codes [14–16]. Recent works have shown the use of memristors as adaptive couplings for connecting simple Chua’s oscillators in a crossbar
© Springer Nature Switzerland AG 2021
F. Corinto et al., Nonlinear Circuits and Systems with Memristors,
https://doi.org/10.1007/978-3-030-55651-8_8
319
Complex Dynamics and Synchronization
Phenomena in Arrays of Memristor
Oscillators
8.1 Introduction
A great deal of efforts have been traditionally devoted in circuit theory to analyze
nonstationary steady-state behaviors in networks obtained by locally coupled arrays
of simple dynamic circuits (also named cells, oscillators, units, etc.) [1]. These
arrays can be thought of as a bio-inspired circuit model of complex nonlinear
phenomena observable in nature with potential applications in signal processing
and computing systems. In fact, on one hand, they are a mean for reproducing,
analyzing, and understanding spatiotemporal nonlinear phenomena displayed by
spatially extended networks found in such diverse fields as electrical engineering,
computer science, biology, and physics. On the other hand, complex spatiotemporal
dynamics including chaos are potentially useful for developing future analogue
computing systems. Recent studies have shown for instance that chaos can play
a crucial role in searching for the global solution of combinatorial optimization
problems and chaotic relaxation oscillators with memristors have been used to boot
efficiency and accuracy of Hopfield-like computing networks [2].
One of the most relevant aspects concerns bifurcations and synchronization
phenomena [3, 4], i.e., a scenario where all the oscillators adjust their dynamic
behavior so that the whole array acts in unison and spatiotemporal patterns emerge.
Synchronization phenomena in one-dimensional (1D) and bi-dimensional (2D)
dynamic arrays using Chua’s oscillators as building block, with various types
of uni-directional, bi-directional, static, and dynamic diffusive interactions, have
been considered and analyzed by numerical simulations and analytic tools [5–
7]. The influence of the network topology properties and their link with complex
dynamic periodic/chaotic attractors in large biological and artificial systems have
been studied in detail in several works [8–13].
Memristors provide an accurate and power efficient emulator of neural synapses
and biological neural codes [14–16]. Recent works have shown the use of memristors as adaptive couplings for connecting simple Chua’s oscillators in a crossbar
© Springer Nature Switzerland AG 2021
F. Corinto et al., Nonlinear Circuits and Systems with Memristors,
https://doi.org/10.1007/978-3-030-55651-8_8
319