Time-delayed Coupling Research Articles

Comparison principle and synchronization analysis of fractional-order complex networks with parameter uncertainties and multiple time delays

<abstract><p>This paper investigates the global synchronization problems of fractional-order complex dynamical networks with uncertain inner coupling and multiple time delays. In particular, both internal time delays and coupling time delays are introduced into our model. To overcome the difficulties caused by various delays and uncertainties, a generalized delayed comparison principle with fractional-order and impulsive effects is established by using the Laplace transform. Based on the Lyapunov stability theory and mixed impulsive control technologies, some new synchronization criteria for concerned complex dynamical networks are derived. In addition, the synchronization criteria are related to the impulsive interval, network topology structure, fractional-order, and control gains. The theoretical results obtained in this paper can enhance the value of previous related works. Finally, numerical simulations are presented to show the correctness of our main results.</p></abstract>

Dynamic behaviors and bandwidth-enhanced time-delay signature suppression of mutually coupled spin-polarized vertical-cavity surface-emitting lasers

A novel symmetric model based on the mutually coupled spin-polarized vertical-cavity surface-emitting lasers (MCSP-VCSELs) subject to optically pumped is implemented and analyzed in this paper. Numerous nonlinear dynamic behaviors containing the state of steady, period, period-doubling, and chaos have been observed in the bifurcation diagram, revealing the period-doubling route to chaos. The characteristics of these dynamic behaviors are analyzed in detail along with clarifying the physical mechanism of their occurrence. The influences of laser parameters on the dynamic behaviors are investigated through mapping diagrams, and the results show that both the pump intensity and pump ellipticity are crucial to the complicated dynamic behaviors including chaos. Additionally, the increase of the coupling strength, coupling time delay, and frequency detuning have beneficial impacts to chaos while the spin relaxation rate has a harmful effect on the contrary. The comparison results on different parameter planes illustrate that the time-delay signature (TDS) suppression and bandwidth enhancement can be achieved simultaneously when coupling strength, frequency detuning and pump strength are relatively large. Therefore, the MCSP-VCSELs have an application prospect in chaos-based fields.

Control of noise-induced coherent oscillations in three-neuron motifs

The phenomenon of self-induced stochastic resonance (SISR) requires a nontrivial scaling limit between the deterministic and the stochastic timescales of an excitable system, leading to the emergence of coherent oscillations which are absent without noise. In this paper, we numerically investigate SISR and its control in single neurons and three-neuron motifs made up of the Morris–Lecar model. In single neurons, we compare the effects of electrical and chemical autapses on the degree of coherence of the oscillations due to SISR. In the motifs, we compare the effects of altering the synaptic time-delayed couplings and the topologies on the degree of SISR. Finally, we provide two enhancement strategies for a particularly poor degree of SISR in motifs with chemical synapses: (1) we show that a poor SISR can be significantly enhanced by attaching an electrical or an excitatory chemical autapse on one of the neurons, and (2) we show that by multiplexing the motif with a poor SISR to another motif (with a high SISR in isolation), the degree of SISR in the former motif can be significantly enhanced. We show that the efficiency of these enhancement strategies depends on the topology of the motifs and the nature of synaptic time-delayed couplings mediating the multiplexing connections.

Hopf bifurcations in a network of FitzHugh–Nagumo biological neurons

Abstract The paper is focused on the analysis of effect of coupling strength and time delay for a pair of connected neurons on the dynamics of the system. The FitzHugh–Nagumo model is used as a neuron model. The article contains analytical conditions for Hopf bifurcations in the system. A numerical verification of the results is given. Several examples of global bifurcation in the system were analyzed.

Modified Kuramoto model with inverse-square law coupling and spatial time delay

We propose a modified Kuramoto model to describe the hand-clapping synchronization observed in a large group of people. There are two different ingredients in our model: The finiteness of the sound speed leads to the time-delay effect across the system, and the large distance makes the sound intensity decrease significantly. These two different but related factors are expected to make the synchrony in a large audience hard to achieve. We numerically and analytically test which between the two factors can be crucial to explain the failure of hand-clapping synchronization in a large group of people. We conclude that the time-delay effect due to the finite sound speed is not as important as the effect of the decreasing sound intensity with distance as long as the audience size is not too big.

Intermittent delay stabilization of complex-valued stochastic complex network

In this paper, the stabilization issue for complex-valued stochastic Markovian switching complex network with time delay and time-varying coupling structure (CSMNDC) is investigated via intermittent delay feedback control. Different from intermittent control based on current state in previous work, a class of intermittent control on the basis of past state is designed for the first time, by combining with the advantages of aperiodically intermittent control and delay feedback control. Then, some sufficient conditions are derived to guarantee the exponential stability in mean square of CSMNDC based on Lyapunov method, graph theory as well as some techniques of inequalities. In particular, the stabilization of networks is studied on complex space directly without splitting their real and imaginary parts by using complex generalized Itô’s formula. Additionally, both delay feedback control and aperiodically intermittent control are employed to solve the stabilization issue for CSMNDC here. Whereafter, the stabilization issue of complex-valued stochastic Markovian switching Cohen-Grossberg neural network with time delay and time-varying coupling structure is researched as a practical application of our theoretical results. Ultimately, a numerical example is presented to verify the validity and effectiveness of the theoretical results.

Design of parallel reservoir computing by mutually-coupled semiconductor lasers with optoelectronic feedback

Via implementing parallel tasks including Santa-Fe time series prediction and nonlinear channel equalization, we studied the characteristics of reservoir computing (RC) using two mutually-coupled semiconductor lasers (MC-SLs) with optoelectronic feedback. The influence of system parameters (injection current, coupling strength, scaling factor and coupling time-delays) on RC performance have been investigated in detail. Results show that, the optimized performance is always achieved around the edge of bifurcation points; positive feedback is more preferred when the scaling factor exceeds a certain level; under optimized parameters, both of lower normalized mean squared error (NMSE) and symbol error rate (SER) can be achieved to perform parallel tasks, due to the richer dynamics and states of virtual nodes. The effect of system parameters on RC performance was also discussed. Our study would be helpful for the design and optimization of proposed parallel RC with optoelectronic feedback.

Extended state observer-based control of heartbeat described by heterogeneous coupled oscillator model

In this paper, a novel framework to investigate the effect of external electrical signals on cardiac rhythm dynamics using the extended state observer-based control (ESOBC) is proposed. Heterogeneous coupled oscillator model (HCOM) is adopted for the generation of P, Ta, QRS, and T waves, and the realistic synthetic electrocardiogram (ECG) due to its capacity for simulating cardiac muscles response. Sinoatrial (SA) and atrioventricular (AV) nodes and His–Purkinje system are described by modified Van der Pol-type (MVDP) equations connected with time-delay velocity coupling. The electrical responses resulted from depolarization (De) and repolarization (Re) of cardiac muscles are separately presented by modified FitzHugh–Nagumo (MFHN) model. The SA and HP pacemakers are coupled with atrial (AT) and ventricles (VT) muscles, respectively, through the stimulation currents. To satisfy the integral chain form of ESO, and deal with the complex structure of the model, including the large number of parameters, and the coupling between the oscillators and interdependent states, three steps are considered. Firstly, a coordinate transformation is proposed for AT and VT responses described by MFHN model to handle mismatched condition. Following this, the nonlinearity of MFHN and the coupling between cardiac muscles and pacemakers are considered as lumped disturbances. Lastly, an extended state observer is designed to compensate the nonlinearity and estimate the unmeasured system states and handle the lumped disturbances. The stability of the closed-loop system is proved, and the effectiveness of the proposed framework for suppressing well-known rhythm disorder, i.e., sinus tachycardia is demonstrated. The framework presented in this work can be easily extended for a wide range of arrhythmia, and serve as an approach to investigate the effect of external stimulation to the heart muscles.

Circuit Model of an Overhead Transmission Line Considering the TEM‐Mode Formation Delay

When lightning strikes a transmission tower or overhead line, the lightning current generates a spherically expanding electromagnetic field. The propagation mode of an expanding electromagnetic wave is different from that of a transverse electromagnetic (TEM) wave, which is applied to the modeling of transmission lines. This paper presents an equivalent circuit model of an overhead transmission line that considers the TEM‐mode formation delay. The TEM‐mode formation delay is approximately represented by the first‐order delay functions in surge impedances and time delays in the mutual coupling from one line to the others. The proposed circuit model of the overhead line is introduced to the Alternative Transients Program version of Electromagnetic Transients Program using the MODELS language through a formulation in the phase domain based on Dommel's method. The results of the proposed model are validated through a comparison with the results of a three‐dimensional numerical electromagnetic analysis. Furthermore, the effect of the delay of the TEM‐mode formation on the voltages across the insulator strings of a lightning‐struck tower is described by referencing a previous experimental study conducted using an actual 500 kV transmission tower. © 2021 Institute of Electrical Engineers of Japan. Published by Wiley Periodicals LLC.

Dynamics of Coupled Thermoacoustic Oscillators Under Asymmetric Forcing

Quenching of limit cycle oscillations (LCO), either through mutual coupling or external forcing, has attracted wide attention in several fields of science and engineering. However, the simultaneous utilization of these coupling schemes in quenching of LCO has rarely been studied despite its practical applicability. We study the dynamics of two thermoacoustic oscillators simultaneously subjected to mutual coupling and asymmetric external forcing through experiments and theoretical modeling. We investigate the forced response of both identical and non-identical thermoacoustic oscillators for two different amplitudes of LCO. Under mutual coupling alone, identical thermoacoustic oscillators display the occurrence of partial amplitude death and amplitude death, whereas under forcing alone, asynchronous quenching of LCO is observed at non-resonant conditions. When the oscillators are simultaneously subjected to mutual coupling and asymmetric forcing, we observe a larger parametric region of oscillation quenching than when the two mechanisms are utilized individually. This enhancement in the region of oscillation quenching is due to the complementary effect of amplitude death and asynchronous quenching. However, a forced response of coupled non-identical oscillators shows that the effect of forcing is insignificant on synchronization and quenching of oscillations in the oscillator which is not directly forced. Finally, we qualitatively capture the experimental results using a reduced-order theoretical model of two coupled Rijke tubes which are coupled through dissipative and time-delay coupling and asymmetrically forced. We believe that these findings offer fresh insights into the combined effects of mutual and forced synchronization in a system of coupled nonlinear oscillators.

Nonlinear Vibration of Manipulator Induced by Coupling Time Delay and Control Strategy

This article uses the theory of Hopf bifurcation to study the stability[1-2] of nonlinear manipulator system with time delay built by Spong. The period vibration, almost periodic vibration and chaos motion are stabilized by the controllers designed in the article, which is achieved by changed the polynomial u in the dynamic of manipulator. It is proved that the controllers in this article are useful by calculating the eigenvalues of the linear form of the dynamic of manipulator, which are expressed in the complex plane, according to the stability theory[2].

Detecting coexisting oscillatory patterns in delay coupled Lur'e systems.

This work addresses the problem of pattern analysis in networks consisting of delay-coupled identical Lur'e systems. We study a class of nonlinear systems, which, being isolated, are globally asymptotically stable. Assembling such systems into a network via time-delayed coupling may result in the change of network equilibrium stability under parameter variation in the coupling. In this work, we focus on cases where a Hopf bifurcation causes the change of stability of the network equilibrium and leads to the occurrence of oscillatory modes (patterns). Moreover, some of these patterns can co-exist for the same set of coupling parameters, which makes the analysis by means of common methods, such as the Lyapunov-Krasovskii method or the analysis of Poincaré maps, cumbersome. A numerically efficient algorithm, aiming at the computation of the oscillatory patterns occurring in such networks, is presented. Moreover, we show that our approach is able to deal with co-existing patterns, and both stable and unstable regimes can be simultaneously computed, which gives deep insight into the network dynamics. In order to illustrate the efficiency of the method, we present two examples in which the instability of the network equilibria is caused by a subcritical and a supercritical Hopf bifurcation. In addition, a bifurcation analysis of the subcritical case is performed in order to further explain the occurrence of the detected coexisting modes.

Modulated Time Delays, Synchronized Josephson Junctions in High-Temperature Superconductors and Chaotic Terahertz Waves

We make the first report on chaos synchronization between Josephson junctions governed by a central junction, when the coupling time between the driving junction and driven junctions is modulated. The results are compared with the case of constant coupling time delays between the junctions. We establish that synchronization is quite robust to the modulation of the coupling time delays, including chaotically modulated delay times. Synchronized Josephson junctions can serve as a terahertz wave generators with enough power for practical applications in diverse scientific fields.

Parity-time symmetric systems with memory

Classical open systems with balanced gain and loss, i.e. parity-time ($\mathcal{PT}$) symmetric systems, have attracted tremendous attention over the past decade. Their exotic properties arise from exceptional point (EP) degeneracies of non-Hermitian Hamiltonians that govern their dynamics. In recent years, increasingly sophisticated models of $\mathcal{PT}$-symmetric systems with time-periodic (Floquet) driving, time-periodic gain and loss, and time-delayed coupling have been investigated, and such systems have been realized across numerous platforms comprising optics, acoustics, mechanical oscillators, optomechanics, and electrical circuits. Here, we introduce a $\mathcal{PT}$-symmetric (balanced gain and loss) system with memory, and investigate its dynamics analytically and numerically. Our model consists of two coupled $LC$ oscillators with positive and negative resistance, respectively. We introduce memory by replacing either the resistor with a memristor, or the coupling inductor with a meminductor, and investigate the circuit energy dynamics as characterized by $\mathcal{PT}$-symmetric or $\mathcal{PT}$-symmetry broken phases. Due to the resulting nonlinearity, we find that energy dynamics depend on the sign and strength of initial voltages and currents, as well as the distribution of initial circuit energy across its different components. Surprisingly, at strong inputs, the system exhibits self-organized Floquet dynamics, including $\mathcal{PT}$-symmetry broken phase at vanishingly small dissipation strength. Our results indicate that $\mathcal{PT}$-symmetric systems with memory show a rich landscape.

Robust in-phase synchronization in repressor-based coupled gene oscillators

Abstract Inside living cells, proteins or mRNA can show oscillations even without a periodic driving force. Such genetic oscillations are precise timekeepers for cell-cycle regulations, pattern formation during embryonic development in higher animals, and daily cycle maintenance in most organisms. The synchronization between oscillations in adjacent cells happens via intercellular coupling, which is essential for periodic segmentation formation in vertebrates and other biological processes. While molecular mechanisms of generating sustained oscillations are quite well understood, how do simple intercellular coupling produces robust synchronizations are still poorly understood? To address this question, we investigate two models of coupled gene oscillators - activator-based coupled oscillators (ACO) and repressor-based coupled oscillators (RCO) models. In our study, a single autonomous oscillator (that operates in a single cell) is based on a negative feedback, which is delayed by intracellular dynamics of an intermediate species. For the ACO model (RCO), the repressor protein of one cell activates (represses) the production of another protein in the neighbouring cell after a intercellular time delay. We investigate the coupled models in the presence of intrinsic noise due to the inherent stochasticity of the biochemical reactions. We analyze the collective oscillations from stochastic trajectories in the presence and absence of explicit coupling delay and make careful comparison between two models. Our results show no clear synchronizations in the ACO model when the coupling time delay is zero. However, a non-zero coupling delay can lead to anti-phase synchronizations in ACO. Interestingly, the RCO model shows robust in-phase synchronizations in the presence and absence of the coupling time delay. Our results suggest that the naturally occurring intercellular couplings might be based on repression rather than activation where in-phase synchronization is crucial.

Synchronization of Chaotic Quantum Dot Light Emitting Diodes under Optical Feedback Effect

Chaos synchronization of delayed quantum dot light emitting diode has been studied theortetically which are coupled via the unidirectional and bidirectional. at synchronization of chaotic, The dynamics is identical with delayed optical feedback for those coupling methods. Depending on the coupling parameters and delay time the system exhibits complete synchronization, . Under proper conditions, the receiver quantum dot light emitting diode can be satisfactorily synchronized with the transmitter quantum dot light emitting diode due to the optical feedback effect.

Flexible multipoint-to-multipoint communication in semiconductor laser networks using one-way isolation.

We propose a type of semiconductor laser (SL) network that supports flexible chaos synchronization and multipoint-to-multipoint communications by using one-way isolation (OWI). The properties of chaos synchronization, influences of coupling strength and time delay mismatches on the quality of chaos synchronization, and the performance as well as the security of the SL network-based chaotic communications are systematically discussed. The numerical results demonstrate that, with the introduction of OWI, flexible chaos synchronization can be easily achieved in arbitrary-size SL clusters over wide parameter spaces of coupling strength and current factor. Based on the high-quality flexible chaos synchronization, satisfactory performance for Gb/s chaotic communications can be achieved in arbitrary-size clusters in the SL networks. Moreover, it is also indicated that in the SL networks, the security of intra-cluster communications can be guaranteed in three aspects. Firstly, the eavesdroppers cannot intercept any useful information by using a typical illegal attack. Secondly, due to the OWI, the chaotic carriers are only transmitted in the corresponding clusters, not transmitted among clusters, as such the security can be further improved. Thirdly, the high sensitivity of cross-correlation coefficient to the injection delay mismatches indicates that the injection delays of idle SLs to communicating SLs can be regarded as the keys of the communication clusters. The proposed scheme offers an alternative solution to flexible secure network-type communications.

A Multigap Multiaperture Pseudospark Switch and Its Performance Analysis for High-Voltage Applications

In this article, the development and switching characterization of a coaxial three-gap demountable multigap multiaperture pseudospark switch (MGMA-PSS) prototype is presented. The investigated MGMA-PSS geometry has three gaps which are separated by two cavity drift space regions. A high dielectric constant ferroelectricbased single plasma trigger unit, located within the hollow cathode of the first gap, is used for effective discharge initiation and subsequent synchronous breakdown of the three gaps of the MGMA-PSS. To guarantee long lifetime with high currents and high hold-off voltages and optimized plasma coupling, kidney-shaped ring slot electrodes with baffles are used. Each of the gaps is designed for a minimum voltage hold-off up to 30 kV, with a total voltage hold-off for the MGMA-PSS of approximately 70 kV. Studies of switching behavior are carried out at different operating conditions, such as operating voltages (5-40 kV), hydrogen gas pressures (10-40 Pa), various trigger configurations,and change of circuit parameters [charging capacitance (36, 200, and 380 nF), load resistance(2.7 and 8.3 Ω)]. The short time-scale analysis of the breakdown voltage waveform shows steps in the voltage fall at low gas pressure (<; 20 Pa) and low hold-off voltages (<; 15 kV), which indicates a too-long time delay in plasma formation and coupling within the drift regions. This effect could not be observed at higher voltages (≥15 kV) and gas pressure (≥20 Pa). The overall performance of the threegap prototype PSS has been analyzed in terms of hold-off voltage, fall time, current rise time, peak current, delay time, and related parameters.

Synchronization of chaotic network quantum dot light-emitting diodes under optical feedback

Chaos synchronization of delayed quantum dot light-emitting diodes has been studied theoretically, which are coupled via open and closed-loop networks. Dynamics are identical with delayed optical feedback for those coupling methods. Depending on the coupling parameters and delay time, the system exhibits complete synchronization. Under proper conditions, the quantum dot light-emitting diodes can be satisfactorily synchronized under the optical feedback effect of diodes.

Synchronization and multistability in the coupled neurons with propagation and processing delays

The dynamics of spiking and bursting activities have attracted interest from scientists due to their significance in the brain and neural systems. In this work, the effects of processing delay, specifically the time delay in coupling, on the dynamical behaviors of the coupled Hindmarsh–Rose neurons with resting state are investigated. The results reveal that the processing delay can induce rich spiking patterns, such as anti-phase synchronous spiking, in-phase synchronous periodic bursting, anti-phase synchronous periodic bursting and anti-phase synchronous chaotic bursting, and maintained the bistability and tristability of different spiking patterns. This emphasizes that the processing delay-induced spiking patterns might not be observed in the diffusively coupled neurons with resting state with and without propagation delay. The results can help deepen the knowledge on neural synchronization and information processing in the neuronal network and brain.