Synchronization of chaotic systems.

By L. Pecora, T. Carroll. Chaos, 2015

2,820 citations recorded by the source corpus.

We review some of the history and early work in the area of synchronization in chaotic systems. We start with our own discovery of the phenomenon, but go on to establish the historical timeline of this topic back to the earliest known paper. The topic of synchronization of chaotic systems has always been intriguing, since chaotic systems are known to resist synchronization because of their positive Lyapunov exponents. The convergence of the two systems to identical trajectories is a surprise. We show how people originally thought about this process and how the concept of synchronization changed over the years to a more geometric view using synchronization manifolds. We also show that building synchronizing systems leads naturally to engineering more complex systems whose constituents are chaotic, but which can be tuned to output various chaotic signals. We finally end up at a topic that is still in very active exploration today and that is synchronization of dynamical systems in networks of oscillators.

Subfields: Computer Networks and Communications, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/385f6e7897be71cc79375679c9acf374b4c6e3cc

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In Statistical and Nonlinear Physics

Citations in the corpus

Stochastic Synchronization of Markovian Jump Neural Networks With Time-Varying Delay Using Sampled Data (2013, methodology): “Based on the Lyapunov stability theory and master–slave synchronization concept [20], the synchronization problem of continuous-time chaotic neural networks with time delay has been investigated in [3], [30], and [32], where some controllers have been derived to achieve synchronization of the consid”
Complex photonics: Dynamics and applications of delay-coupled semiconductors lasers (2013, methodology): “The seminal papers of Pecora and Carroll (1990) and Winful and Rahman (1990) created strong interest in the study of the synchronization of chaotic dynamical systems.”
Wireless Chaos-Based Communication Systems: A Comprehensive Survey (2016, background): “It was shown in [59] that the chaotic synchronization occurs when the output of at least one of the coupled differential equations of the”
Synchronization via Pinning Control on General Complex Networks (2013, background): “Since the pioneering work of Pecora and Carroll [24], chaos synchronization [2] has received a great deal of attention due to its potential applications in secure communications, biological neural networks [47], genetic regulatory networks [57], parameter estimation, and so on.”
Explosive transitions in complex networks’ structure and dynamics: Percolation and synchronization (2016, methodology): “When the chaotic oscillators have a well defined center of rotation, as it is the case of phase coherent systems, the instantaneous phase can be reliably calculated by means of few mathematical techniques [5].”
Coupling functions:universal insights into dynamical interaction mechanisms (2017, background): “…be applied, and we encounter three possible scenarios: i) The coupling function does not damp instabilities and the system never synchronizes (Boccaletti et al., 2002; Pecora and Carroll, 1998). ii) The coupling function damps out instabilities only for a finite range of coupling…”
Chaotic Local Search-Based Differential Evolution Algorithms for Optimization (2021, background): “Chaos has been implemented in many applications along with the development of nonlinear dynamic systems [27].”
Synchronization in complex networks of phase oscillators: A survey (2014, methodology): “Additionally, synchronization phenomena can also occur among chaotic and aperiodic oscillators (Pecora and Carroll, 1990), whose analysis is thus far mainly restricted to numerical linearization via the Master Stability Function approach (Pecora and Carroll, 1998; Boccaletti et al.”
Random walks and diffusion on networks (2016, methodology): “In particular, methods to estimate the 696 relaxation time via the spectral gap of L are useful for understanding relaxation 697 properties of RWs [54, 226, 227].”
The structure and dynamics of multilayer networks (2014, background): “In the past years, the emergence of synchronized states [367] has been extensively reported and studied for the case of mono-layer networks, with the emphasis focusing on how the complexity of the layer topology influences the propensity of the coupled units to synchronize [368–371].”
Synchronization and desynchronization in epilepsy: controversies and hypotheses (2012, background): “Synchrony implies that two systems, x(t) and y(t), will asymptotically converge so that their trajectories become identical, x(t) = y(t) (Brown & Rulkov 1997), and that such dynamics are structurally stable (Pecora & Carroll 1990).”
A Memristor-Based Hyperchaotic System with Hidden Attractors: Dynamics, Synchronization and Circuital Emulating (2015, background): “Such circuits are main parts in diverse chaos-based applications such as image encryption scheme, path planning generator for autonomous mobile robots, or random bit generator [74-80].”