scholarly journals Nonlinear dynamics of delay systems: an overview

2019 ◽  
Vol 377 (2153) ◽  
pp. 20180389 ◽  
Author(s):  
A. Otto ◽  
W. Just ◽  
G. Radons
Keyword(s):  
Nonlinear Dynamics ◽  
Nonlinear Effects ◽  
Signal Propagation ◽  
Delay System ◽  
Delay Systems ◽  
Climate Modelling ◽  
Theme Issue ◽  
Time Varying Delay ◽  
Interdisciplinary Field ◽  
Laser Systems

Time delays play an important role in many fields such as engineering, physics or biology. Delays occur due to finite velocities of signal propagation or processing delays leading to memory effects and, in general, infinite-dimensional systems. Time delay systems can be described by delay differential equations and often include non-negligible nonlinear effects. This overview article introduces the theme issue ‘Nonlinear dynamics of delay systems’, which contains new fundamental results in this interdisciplinary field as well as recent developments in applications. Fundamentally, new results were obtained especially for systems with time-varying delay and state-dependent delay and for delay system with noise, which do often appear in real systems in engineering and nature. The applications range from climate modelling over network dynamics and laser systems with feedback to human balancing and machine tool chatter. This article is part of the theme issue ‘Nonlinear dynamics of delay systems’.

scholarly journals Delay-induced switched states in a slow–fast system

2019 ◽  
Vol 377 (2153) ◽  
pp. 20180118 ◽  
Author(s):  
Stefan Ruschel ◽  
Serhiy Yanchuk
Keyword(s):  
Nonlinear Dynamics ◽  
Positive Feedback ◽  
Delay Time ◽  
Delay System ◽  
Delay Systems ◽  
Round Trip ◽  
Theme Issue ◽  
Feedback Function ◽  
Fast System ◽  
Two Component

We consider the two-component delay system εx ′( t ) = −  x ( t ) −  y ( t ) +  f ( x ( t  − 1)), y ′( t ) =  ηx ( t ) with small para- meters ε , η and positive feedback function f . Previously, such systems have been reported to model switching in optoelectronic experiments, where each switching induces another one after approximately one delay time, related to one round trip of the signal. In this paper, we study these delay-induced switched states. We provide conditions for their existence and show how the formal limits ε  → 0 and/or η  → 0 facilitate our understanding of this phenomenon. This article is part of the theme issue ‘Nonlinear dynamics of delay systems’.

scholarly journals Complex partial synchronization patterns in networks of delay-coupled neurons

2019 ◽  
Vol 377 (2153) ◽  
pp. 20180128 ◽  
Author(s):  
D. Nikitin ◽  
I. Omelchenko ◽  
A. Zakharova ◽  
M. Avetyan ◽  
A. L. Fradkov ◽  
...  
Keyword(s):  
Nonlinear Dynamics ◽  
Temporal Dynamics ◽  
Delay Systems ◽  
Theme Issue ◽  
Partial Synchronization ◽  
Multiplex Network ◽  
Control Scheme ◽  
Non Local ◽  
Spatio Temporal ◽  
Fast Oscillations

We study the spatio-temporal dynamics of a multiplex network of delay-coupled FitzHugh–Nagumo oscillators with non-local and fractal connectivities. Apart from chimera states, a new regime of coexistence of slow and fast oscillations is found. An analytical explanation for the emergence of such coexisting partial synchronization patterns is given. Furthermore, we propose a control scheme for the number of fast and slow neurons in each layer. This article is part of the theme issue ‘Nonlinear dynamics of delay systems’.

Exponential Delay Dependent Stabilization for Time-Varying Delay Systems With Saturating Actuator

2010 ◽  
Vol 133 (1) ◽  
Author(s):  
Pin-Lin Liu
Keyword(s):  
Time Delay ◽  
Design Method ◽  
Delay System ◽  
Rate Of Change ◽  
Delay Systems ◽  
Linear Matrix ◽  
Time Varying ◽  
Time Varying Delay ◽  
Delay Dependent ◽  
Varying Delay

This paper deals with the stabilization criteria for a class of time-varying delay systems with saturating actuator. Based on the Lyapunov–Krasovskii functional combining with linear matrix inequality techniques and Leibniz–Newton formula, delay-dependent stabilization criteria are derived using a state feedback controller. We also consider efficient convex optimization algorithms to the time-varying delay system with saturating actuator case: the maximal bound on the time delay such that the prescribed level of operation range and imposed exponential stability requirements are still preserved. The value of the time-delay as well as its rate of change are taken into account in the design method presented and further permit us to reduce the conservativeness of the approach. The results have been illustrated by given numerical examples. These results are shown to be less conservative than those reported in the literature.

Conservativeness Judgement of Controller for Systems with Time-Varying Delay

2012 ◽  
Vol 249-250 ◽  
pp. 1173-1179
Author(s):  
Jiu Ying Deng ◽  
Hui Fei Deng ◽  
Jian Bin Xiong ◽  
Qin Ruo Wang
Keyword(s):  
Delay System ◽  
Delay Systems ◽  
Descriptor System ◽  
Linear Matrix ◽  
Stability Conditions ◽  
Optimization Approach ◽  
Time Varying ◽  
Time Varying Delay ◽  
Delay Dependent ◽  
Varying Delay

The conservatism of asymptotic stability conditions is considered in terms of linear matrix inequalities for time-varying delay systems. The conservative index is defined to evaluate the conservativeness for both delay-dependent and delay-independent stability conditions. The general results on performance analysis are presented based on descriptor system approach. The conservativeness index is defined for time-varying delay system. The optimization approach is given to obtain the upper delay and rational performances for the state-feedback controller of time-delay systems. Experimental results verify the effectiveness of the new method.

Stabilizing Gain Regions of PID Controller for Time Delay Systems

2013 ◽  
Vol 313-314 ◽  
pp. 432-437
Author(s):  
Fu Min Peng ◽  
Bin Fang
Keyword(s):  
Stability Analysis ◽  
Time Delay ◽  
Pid Controller ◽  
Delay System ◽  
Nyquist Plot ◽  
Delay Systems ◽  
Time Delay Systems ◽  
Frequency Range ◽  
Time Delay System ◽  
Key Points

Based on the inverse Nyquist plot, this paper proposes a method to determine stabilizing gain regions of PID controller for time delay systems. According to the frequency characteristic of the inverse Nyquist plot, it is confirmed that the frequency range is used for stability analysis, and the abscissas of two kind key points are obtained in this range. PID gain is divided into several regions by abscissas of key points. Using an inference and two theorems presented in the paper, the stabilizing PID gain regions are determined by the number of intersections of the inverse Nyquist plot and the vertical line in the frequency range. This method is simple and convenient. It can solve the problem of getting the stabilizing gain regions of PID controller for time delay system.

Dynamic Anti-Saturation Integral Controller Used in Time-Varying Delay System

2011 ◽  
Vol 467-469 ◽  
pp. 766-769
Author(s):  
Gui You Pu ◽  
Ge Wen Kang
Keyword(s):  
Variable Structure ◽  
Delay System ◽  
Time Varying ◽  
Control Methods ◽  
Simulation Studies ◽  
Motor Speed ◽  
Intelligent Controller ◽  
Time Varying Delay ◽  
Integral Controller ◽  
Varying Delay

Systems with large variable delay, traditional control methods can’t performance well. In this paper, a controller combined with the human-simulated intelligent controller (HSIC) and newly dynamic anti-saturation integral controller, is used in the time-varying delay motor speed control. Simulation studies show, there is no chatter in this controller which is always in norm variable structure controller and this method reaches good performance in the time-varying delay system.

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