Delayed Dynamical Systems: Networks, Chimeras and Reservoir Computing

We present a systematic approach to reveal the correspondence between time delay dynamics and networks of coupled oscillators. After early demonstrations of the usefulness of spatio-temporal representations of time-delay system dynamics, extensive research on optoelectronic feedback loops has revealed their immense potential for realizing complex system dynamics such as chimeras in rings of coupled oscillators and applications to reservoir computing. Delayed dynamical systems have been enriched in recent years through the application of digital signal processing techniques. Very recently, we have showed that one can significantly extend the capabilities and implement networks with arbitrary topologies through the use of field programmable gate arrays (FPGAs). This architecture allows the design of appropriate filters and multiple time delays which greatly extend the possibilities for exploring synchronization patterns in arbitrary topological networks. This has enabled us to explore complex dynamics on networks with nodes that can be perfectly identical, introduce parameter heterogeneities and multiple time delays, as well as change network topologies to control the formation and evolution of patterns of synchrony

Synchronization of a class of fractional-order neural networks with multiple time delays by comparison principles

This paper studies the synchronization of fractional-order neural networks with multiple time delays. Based on an inequality of fractional-order and comparison principles of linear fractional equation with multiple time delays, some sufficient conditions for synchronization of master-slave systems are obtained. Example and related simulations are given to demonstrate the feasibility of the theoretical results

Separation of multiple time delays using new spectral estimation schemes

Includes bibliographical references.The problem of estimating multiple time delays in presence of colored noise is considered in this paper. This problem is first converted to a high-resolution frequency estimation problem. Then, the sample lagged covariance matrices of the resulting signal are computed and studied in terms of their eigenstructure. These matrices are shown to be as effective in extracting bases for the signal and noise subspaces as the standard autocorrelation matrix, which is normally used in MUSIC and the pencil-based methods. Frequency estimators are then derived using these subspaces. The effectiveness of the method is demonstrated on two examples: a standard frequency estimation problem in presence of colored noise and a real-world problem that involves separation of multiple specular components from the acoustic backscattered from an underwater target.This work was supported by the Office of Naval Research (ONR 321TS). The Technical Agent was Coastal Systems Station, Panama City, FL

Feedback control of chaos in impact oscillator with multiple time-delays

Peer reviewe

Robust controller design for ATM network with time - varying multiple time - delays

Makalenin ilk sayfası mevcuttur.For the congestion of the Asynchronous Transfer Mode (ATM) networks with time-varying multiple time-delays and changeful available bit-rate (ABR) bandwidth, an ABR flow controller is designed and the LMI-based delay-dependent stabilizability. criteria is proposed. The algorithm, which is independent of the derivative of varying delays, is less conservative and can be implemented easily. It also achieves two expectant goals, i.e. it satisfies a weighted fairness condition and ensures convergence of queue length to the desired steady-state value. Simulation results show that the control system is robust and rapid and the quality of service (QoS) is guaranteed

An optimal controller for time-varying stochastic systems with multiple time delays

A flexible controller for optimal control of linear time-varying stochastic systems with multiple time delays is developed. The plants to be controlled are represented using a multi-input multi-output controlled autoregressive moving average model. The delays are described using a diagonal matrix. Input and output filters in the form of linear time-varying moving average operators are introduced into a generalized minimum variance control cost functional in order to meet the needs of various applications. The controller is applicable to a large class of linear time-varying systems