Synchronisation of chaos and its applications

Eroğlu, Deniz; Lamb, Jeroen S. W.; Pereira, Tiago

doi:10.1080/00107514.2017.1345844

Cited by 90 publications

(57 citation statements)

References 137 publications

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“…This approach was generalized for undirected networks of diffusively coupled systems merging numerical computations of Lyapunov exponents and transverse instabilities of the synchronous states. See also [DB14,ELP17] for a review. These results have been generalized to weighted and directed graphs via dichotomy estimates [PERV14].…”

Section: Appendix C Transfer Operatormentioning

confidence: 99%

Heterogeneously coupled maps: hub dynamics and emergence across connectivity layers

2020

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The aim of this paper is to rigorously study dynamics of Heterogeneously Coupled Maps (HCM). Such systems are determined by a network with heterogeneous degrees. Some nodes, called hubs, are very well connected while most nodes interact with few others. The local dynamics on each node is chaotic, coupled with other nodes according to the network structure. Such high-dimensional systems are hard to understand in full, nevertheless we are able to describe the system over exponentially large time scales. In particular, we show that the dynamics of hub nodes can be very well approximated by a low-dimensional system. This allows us to establish the emergence of macroscopic behaviour such as coherence of dynamics among hubs of the same connectivity layer (i.e. with the same number of connections), and chaotic behaviour of the poorly connected nodes. The HCM we study provide a paradigm to explain why and how the dynamics of the network can change across layers.

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Section: Appendix C Transfer Operatormentioning

confidence: 99%

Heterogeneously coupled maps: hub dynamics and emergence across connectivity layers

2020

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“…Our three assumptions are the following. (a) The local dynamics are close to some unknown ergodic and chaotic map F (that is, kF − F i k ≤ δ, which is often the case in applications [25,26]). (b) The network connectivity is heterogeneous, which means that the number of incoming connections at a node i (given by its degree k i ¼ P j A ij ) varies widely across the network.…”

Section: B Main Assumptionsmentioning

confidence: 99%

Revealing Dynamics, Communities, and Criticality from Data

et al. 2020

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Complex systems such as ecological communities and neuron networks are essential parts of our everyday lives. These systems are composed of units which interact through intricate networks. The ability to predict sudden changes in the dynamics of these networks, known as critical transitions, from data is important to avert disastrous consequences of major disruptions. Predicting such changes is a major challenge as it requires forecasting the behavior for parameter ranges for which no data on the system are available. We address this issue for networks with weak individual interactions and chaotic local dynamics. We do this by building a model network, termed an effective network, consisting of the underlying local dynamics and a statistical description of their interactions. We show that behavior of such networks can be decomposed in terms of an emergent deterministic component and a fluctuation term. Traditionally, such fluctuations are filtered out. However, as we show, they are key to accessing the interaction structure. We illustrate this approach on synthetic time series of realistic neuronal interaction networks of the cat cerebral cortex and on experimental multivariate data of optoelectronic oscillators. We reconstruct the community structure by analyzing the stochastic fluctuations generated by the network and predict critical transitions for coupling parameters outside the observed range.

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“…Synchronization is a process of controlling the output of the response system (slave system) to force its behavior to follow that of the corresponding drive system (master system) asymptotically. Since the pioneering study of Pecora and Carroll [1], various control schemes have been introduced to synchronize dynamical systems due to its applications in image processing, cryptography, ecological system, combinatorial optimization, lasers technology, and secure communications [2].…”

Section: Introductionmentioning

confidence: 99%