Coupling Delay Research Articles

Delayed Impulsive Control for μ-Synchronization of Nonlinear Multi-Weighted Complex Networks with Uncertain Parameter Perturbation and Unbounded Delays

The global μ-synchronization problem for nonlinear multi-weighted complex dynamical networks with uncertain parameter perturbation and mixed time-varying delays is investigated in this paper. Unlike other existing works, all delays, including sampling and internal and coupling delays, are assumed to be unbounded, making the considered model more general and practical. Based on the generalized impulsive comparison principles, a time-varying impulsive controller with sampling delays is designed, and some new sufficient conditions are obtained to make drive–response multi-weighted networks reach μ-synchronization. In addition, the external coupling matrices do not need to meet the requirement of zero-row sum, and the limitation of time delay on pulse interval is weakened. The results obtained in this article can be seen as extensions of previous related research.

Dynamics of full-coupled chains of a great number of oscillators with a large delay in couplings

The subject of this work is the study of local dynamics of full-coupled chains of a great number of oscillators with a large delay in couplings. From a discrete model describing the dynamics of a great number of coupled oscillators, a transition has been made to a nonlinear integro-differential equation, continuously depending on time and space variable. A class of full-coupled systems has been considered. The main assumption is that the amount of delay in the couplings is large enough. This assumption opens the way to the use of special asymptotic methods of study. The parameters under which the critical case is realized in the problem of the equilibrium state stability have been distinguished. It is shown that they have infinite dimension. The analogues of normal forms — nonlinear boundary value problems of Ginzburg–Landau type have been constructed. In some cases, these boundary value problems contain integral components too. Their nonlocal dynamics describes the behavior of all solutions of the original equations in the balance state neighbourhood. Methods. As applied to the considered problems, methods of constructing quasinormal forms on central manifolds are developed. An algorithm for constructing the asymptotics of solutions based on the use of quasinormal forms for determining slowly varying amplitudes has been created. Results. Quasinormal forms that determine the dynamics of the original boundary value problem have been constructed. The dominant terms of asymptotic approximations for solutions of the considered chains have been obtained. On the basis of the given statements, a number of interesting dynamical effects have been revealed. For example, an infinite alternation of direct and reverse bifurcations when the delay coefficient increases. Their distinguishing feature is that they have two or three spatial variables.

Novel non-fragile extended dissipative synchronization of T-S fuzzy complex dynamical networks with interval hybrid coupling delays

<abstract><p>This paper presents the first investigation of extended dissipative synchronization in a specific type of Takagi-Sugeno (T-S) fuzzy complex dynamical networks with interval hybrid coupling delays. First, the decoupling method is employed to reorganize the multiple communication dynamical system, which comprises discrete-time, partial and distributed coupling delays. Second, the non-fragile control, which allows for uncertainty management within predefined norm bounds, has been applied to networks. Moreover, it becomes possible to derive a less conservative condition by utilizing multiple integral Lyapunov functionals, a decoupling strategy, Jensen's inequality, Wirtinger's inequality, and mathematical inequality techniques. This condition ensures that the T-S fuzzy complex dynamical networks, with interval hybrid coupling delays, can attain asymptotic synchronization with the assistance of a non-fragile feedback controller. Additionally, we extended this system to the extended dissipativity analysis, including passivity, $ L_2-L_\infty, H_{\infty} $ and dissipativity performance in a unified formulation. A set of strict linear matrix inequalities (LMIs) conditions is a sufficient criterion. Finally, two simulation examples are proposed to verify the merit of the obtained results.</p></abstract>

An ultra-narrow-band optical filter based on zero refractive index metamaterial

Owing to the photonic band gap effect and defect state effect, photonic metamaterials have received much attention in the design of narrow bandpass filters, which are the key devices of optical communication equipment such as wavelength division multiplexing devices. In this work, based on zero-index metamaterial (ZIM), a compact filter with both high peak transmission coefficient and ultra-narrow bandwidth is proposed. The photonic metamaterial with conical dispersion and Dirac-like point is achieved by optimizing the structure and material component parameters of dielectric rods with square lattice in air. It is demonstrated that a triply degenerate state can be realized at the Dirac-like point, which relates this metamaterial to a zero-index medium with effective permittivity and permeability equal to zero simultaneously. Electromagnetic (EM) wave can propagate without any phase delay at this frequency, and strong dispersion occurs in the adjacent frequency cone, leading to dramatic changes in optical properties. We introduce a ZIM into photonic metamaterial defect filter to compress the bandwidth to the realization of ultra-narrow bandpass filter. The ZIM is embedded into the resonant cavity of line defect filter, which is also composed of dielectric rods with square lattice in air. In order to increase the sensitivity of the phase change with frequency, the Dirac-like frequency is adjusted to match the resonant frequency of the filter. We study the transmission spectrum of the structure through the COMSOL Multiphysics simulation software, and find that the peak width at half-maximum of the filter decreases as the thickness of ZIM increases, and the peak transmittance is still high when bandwidth is greatly compressed. The zero phase delay inside the slab can be observed. Through field distribution analysis, the zero-phase delay and strong coupling characteristics of electromagnetic field are observed at peak frequency. The comparison with conventional photonic metamaterials filter is discussed. We believe that this work is helpful in investigating the realization of ultra-narrow bandpass filters.

Thermal energy storage thermal data processing for heating systems

In order to solve the problem that the traditional industrial control methods cannot control the heating flow and water temperature in a timely and effective manner due to the high delay and complex coupling characteristics of the urban central heating system, the authors propose deep learning-based data processing and management for thermal heating systems. The author analyzes the non-ideality of district heating system and its influence on the application of deep learning technology, and gives solutions, respectively, finally, a primary side regulation scheme of district heating system based on deep learning and automatic control technology is proposed as a whole. The experimental results show that, by comparing the water supply temperature predicted by the equipment model of the primary side heat station with its actual measured value, the mean square error of the prediction results using the model directly is 1.30%, and the mean square error after model correction is 0.094%. The secondary return water temperature was controlled by adjusting the opening of the primary side electric valve, the expected secondary return water temperature in the scheme was compared with the actual secondary return water temperature, and the mean square error was 0.102%. It is proved that the scheme can achieve good control effect in the actual system, and the data result proves that the scheme is feasible.

Adaptive Pinning Synchronization of Complex Networks with Partial Delay and Noise Coupling

Adaptive Pinning Synchronization of Complex Networks with Partial Delay and Noise Coupling

State Estimation-Based Hybrid-Triggered Controller Design for Synchronization of Repeated Scalar Nonlinear Complex Dynamical Networks

The goal of this work is to examine the issue of state estimation-based synchronization of nonlinear complex dynamical networks that are prone to external disturbances, repeated scalar nonlinearities and time-varying coupling delays. In a nutshell, hybrid-triggered communication transmission nonfragile control design with respect to the estimated states and extended dissipative theory is designed, which comprises of both the time and event-triggered mechanisms, and a hybrid generator is presented between the sensor and controller. More preciously, a stochastic variable satisfying the Bernoulli random binary distribution is utilized to represent the phenomenon of random transmission between the time and event-triggered mechanism. Furthermore, delay-dependent adequate conditions for ensuring the synchronization of the addressed system are developed in the form of linear matrix inequalities. And, the requisite gain matrices and hybrid-triggered parameters are evaluated with the help of solving these procured conditions. Lastly, a numerical example with an application to memristor-based Chua’s circuit model is demonstrated to ensure the effectiveness of established control technique.

Combination projection synchronization of fractional-order complex dynamic networks with time-varying delay couplings and disturbances

In this paper, the problem of combination projection synchronization of fractional-order complex dynamic networks with time-varying delay couplings and external interferences is studied. Firstly, the definition of combination projection synchronization of fractional-order complex dynamic networks is given, and the synchronization problem of the drive-response systems is transformed into the stability problem of the error system. In addition, time-varying delays and disturbances are taken into consideration to make the network synchronization more practical and universal. Then, based on Lyapunov stability theory and fractional inequality theory, the adaptive controller is formulated to make the drive and response systems synchronization by the scaling factors. The controller is easier to realize because there is no time-delay term in the controller. At last, the corresponding simulation examples demonstrate the effectiveness of the proposed scheme.

Biological Significance of the Coupling Delay in Synchronized Oscillations.

The significance of the coupling delay, which is the time required for interactions between coupled oscillators, in various oscillatory dynamics has been investigated mathematically for more than three decades, but its biological significance has been revealed only recently. In the segmentation clock, which regulates the periodic formation of somites in embryos, Hes7 expression oscillates synchronously between neighboring presomitic mesoderm (PSM) cells, and this synchronized oscillation is controlled by Notch signaling-mediated coupling between PSM cells. Recent studies have shown that inappropriate coupling delays dampen and desynchronize Hes7 oscillations, as simulated mathematically, leading to the severe fusion of somites and somite-derived tissues such as the vertebrae and ribs. These results indicate the biological significance of the coupling delay in synchronized Hes7 oscillations in the segmentation clock. The recent development of an in vitro PSM-like system will facilitate the detailed analysis of the coupling delay in synchronized oscillations.

Saturated and asymmetric saturated impulsive control synchronization of coupled delayed inertial neural networks with time-varying delays

This paper considers control systems with impulses that are saturated and asymmetrically saturated which are used to examine the synchronization of inertial neural networks (INNs) with time-varying delay and coupling delays. Under the theoretical discussions, mixed delays, such as transmission delay and coupling delay are presented for inertial neural networks. The addressed INNs are transformed into first order differential equations utilizing variable transformation on INNs and then certain adequate conditions are derived for the exponential synchronization of the addressed model by substituting saturation nonlinearity with a dead-zone function. In addition, an asymmetric saturated impulsive control approach is given to realize the exponential synchronization of addressed INNs in the leader-following synchronization pattern. Finally, simulation results are used to validate the theoretical research findings.

New Adaptive Finite-Time Cluster Synchronization of Neutral-Type Complex-Valued Coupled Neural Networks with Mixed Time Delays

The issue of adaptive finite-time cluster synchronization corresponding to neutral-type coupled complex-valued neural networks with mixed delays is examined in this research. A neutral-type coupled complex-valued neural network with mixed delays is more general than that of a traditional neural network, since it considers distributed delays, state delays and coupling delays. In this research, a new adaptive control technique is developed to synchronize neutral-type coupled complex-valued neural networks with mixed delays in finite time. To stabilize the resulting closed-loop system, the Lyapunov stability argument is leveraged to infer the necessary requirements on the control factors. The effectiveness of the proposed method is illustrated through simulation studies.

Kinematics of individual muscle units in natural contractions measured in vivo using ultrafast ultrasound

Objective. The study of human neuromechanical control at the motor unit (MU) level has predominantly focussed on electrical activity and force generation, whilst the link between these, i.e. the muscle deformation, has not been widely studied. To address this gap, we analysed the kinematics of muscle units in natural contractions. Approach. We combined high-density surface electromyography (HDsEMG) and ultrafast ultrasound (US) recordings, at 1000 frames per second, from the tibialis anterior muscle to measure the motion of the muscular tissue caused by individual MU contractions. The MU discharge times were identified online by decomposition of the HDsEMG and provided as biofeedback to 12 subjects who were instructed to keep the MU active at the minimum discharge rate (9.8 ± 4.7 pulses per second; force less than 10% of the maximum). The series of discharge times were used to identify the velocity maps associated with 51 single muscle unit movements with high spatio-temporal precision, by a novel processing method on the concurrently recorded US images. From the individual MU velocity maps, we estimated the region of movement, the duration of the motion, the contraction time, and the excitation–contraction (E–C) coupling delay. Main results. Individual muscle unit motions could be reliably identified from the velocity maps in 10 out of 12 subjects. The duration of the motion, total contraction time, and E–C coupling were 17.9 5.3 ms, 56.6 8.4 ms, and 3.8 3.0 ms (n = 390 across ten participants). The experimental measures also provided the first evidence of muscle unit twisting during voluntary contractions and MU territories with distinct split regions. Significance. The proposed method allows for the study of kinematics of individual MU twitches during natural contractions. The described measurements and characterisations open new avenues for the study of neuromechanics in healthy and pathological conditions.

Modeling and Signal Integrity Analysis of RRAM-Based Neuromorphic Chip Crossbar Array Using Partial Equivalent Element Circuit (PEEC) Method

This paper provides a comprehensive study of signal integrity issues in RRAM-based neuromorphic chip crossbar arrays due to interconnect parasitic. First, the parasitic parameters of the crossbar array are calculated by the partial equivalent element circuit (PEEC) method with an efficient unit-cell approach. Numerical experiments show that for a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$50\times 50$ </tex-math></inline-formula> array scale, this method consumes only 1.5% of the calculation time of the commercial software based 3D model, which translates to a calculation speed up of 72 times. Moreover, the PEEC circuit simulation results match well with those of the 3D model. Then, we investigate the effects of parasitic parameters such as capacitance and inductance, as well as the feature size of the crossbar array on signal integrity. All of them will lead to corresponding changes in parasitic effects, which in turn result in the most common signal integrity issues such as crosstalk, time delay and mutual capacitive coupling induced sneak path problem. Different from other studies, the excitation used in this paper is the neural spike signal generated by the Izhikevich neuron model, which is both rich in dynamic characteristics and high in computational efficiency. Finally, based on the study we propose a simple but effective design scheme for reduction of signal distortion, which can provide valuable design guidance for neuromorphic systems to achieve high performance and high computational accuracy.

Synchronization of Dynamical Networks With Heterogeneous Delays via Time-Varying Pinning

This work investigates the synchronization problem of a dynamical network composed of nonlinear nodes with directed couplings and suffering from heterogeneous delays. Specifically, a time-varying pinning control is adopted to achieve synchronization. The system’s dynamics are interpreted under a multiplex network framework, from which an indicator is designed to measure the synchronizability of the pinned network. Criteria are then derived to ensure exponential synchronization while the largest admissible coupling delay is also estimated. These criteria are based on the time average of the proposed indicator over some user-defined time intervals. Therefore, it possesses high versatility to support a wide range of scenarios with different intermittent control strategies. An interesting observation is that the proposed indicator is always upper bounded, manifesting that if the couplings between the nodes are too weak, pinning synchronization may fail no matter how large the pinning gain is. To further demonstrate the applicability of the theorem and the corollaries, numerical examples under different pinning configurations are presented.

Spatiotemporal pattern of periodic rhythms in delayed Van der Pol oscillators for the CPG-based locomotion of snake-like robot

This is the further research on the delayed half-center oscillator (DHCO) neural system presented in our previous paper (Song and Xu in Nonlinear Dyn 108:2595–2609, 2022. https://doi.org/10.1007/s11071-022-07222-y). The DHCO is used to construct a CPG (central pattern generator) neural system to control locomotion of a snake-like robot with pitch-yaw connecting configuration. To this end, we firstly give an improved model of the VDP (Van der Pol) oscillator. Employing mutually coupled delay, a pair of VDP oscillator is connected to produce an half-center oscillator (HCO) module with time delay that is called as a DHCO (delayed HCO) model. Based on the analysis of the Hopf bifurcation, periodic rhythm and their spatiotemporal patterns of the DHCO are illustrated in the different regions of parameters. The DHCO presents periodic rhythms with synchronous and anti-synchronous patterns, which is to control joint actuators combined in snake-like robot with pitch-yaw connecting configuration. To realize a backward propulsive wave to promote snake-like robotic locomotion, based on the DHCOs, we construct a chain type of the CPG neural system combined with a new unidirectional delay in which phase difference can be regulated. Numerical simulations are illustrated that the CPG neural system can control snake-like robot to move with serpentine, rectilinear, and side-winding patterns in the forward and backward directions. The results show that the snake-like robot can be controlled in expected locomotion patterns for a region but not a fixed value of the controlling parameters. Further, the corresponding regions of the parameters are obtained by using theoretical dynamical analysis but not a trial-and-error method. The snake-like robot gets smooth and stable gait transition with parameter changing.

Adaptive control for synchronization of semi‐linear complex spatio‐temporal networks with time‐invariant coupling delay and time‐variant coupling delay

SummaryThis article studies the adaptive control for synchronization of semi‐linear complex spatio‐temporal networks (CSNs). And the leader‐following and leaderless CSN with time‐invariant coupling delay and time‐variant coupling delay are developed separately from two aspects. The adaptive control strategies are proposed to reach the asymptotic convergence of synchronization error. Synchronization criteria and sufficient conditions are obtained for the leader‐following CSN error model and leaderless CSN error model by constructing the apposite Lyapunov–Krasovskii functions and applying Wirtinger's inequality. Finally, two experimental examples are given to verify the feasibility of the theories proposed in this article.

Function Projective Synchronization of Two Complex Networks with Unknown Sector Nonlinear Input and Multiple Time-Varying Delay Couplings

This paper deals with the function projective synchronization of two complex dynamic networks with unknown sector nonlinear input, multiple time-varying delay couplings, model uncertainty, and external interferences. Based on Lyapunov stability theory and inequality transformation method, the robust adaptive synchronization controller is designed, by which the drive and response systems can achieve synchronization according to the function scaling factor. Different from some existing studies on nonlinear system with sector nonlinear input, this paper studies the synchronization of two complex dynamic networks when the boundary of sector nonlinear input is unknown. The controller does not include the boundary value of the sector nonlinear input and the time delay term, so it is more practical and relatively easy to implement. The corresponding simulation examples demonstrate the effectiveness of the proposed scheme.

Identifying partial topology of complex networks with stochastic perturbations and time delay

In various practical scenarios, the topology of a complex network is generally unknown or unavailable. Based on the adaptive feedback control strategy and the pining mechanism, some controllers and observers are designed in this manuscript to identify the partial topology of the noise-contaminated networks with coupling delay. The approach can be extended to infer the whole topology of the networks. For large-scale complex networks, our approach greatly reduces the calculation compared with the previous methods. Numerical simulations are employed to illustrate the effectiveness of the proposed theoretical results.

Robust Asynchronous Filtering for Discrete-Time T–S Fuzzy Complex Dynamical Networks Against Deception Attacks

In this article, the robust asynchronous filtering problem is investigated for a class of discrete-time T–S fuzzy complex dynamical networks subjected to random coupling delays and deception attacks. Specifically, the deception attacks are considered in the filter, where the adversary attempts to inject some false information data in the measurement output to modify the transmitted signal in the communication networks. We introduce, respectively, two sets of stochastic variables satisfying the Bernoulli distribution to depict the probability of the data transmitted by the network being subjected to time-varying coupling delays and deception attacks. By using Lyapunov–Krasovskii stability theory and Abel lemma-based finite-sum inequality, a new set of sufficient conditions is established, which ensures the stochastic stability of the resulting error system with a prescribed mixed <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_\infty$</tex-math></inline-formula> and passivity performance index. The proposed filter parameters are obtained by solving linear matrix inequalities. Ultimately, both the effectiveness and advantages of the proposed asynchronous filter with deception attacks are verified by two numerical examples including a tunnel diode circuit model.

Impulse Response Characterization of a Commercial Multimode Fiber Using Superconducting Nanowire Single-Photon Detectors

Time-of-flight measurements are key to study distributed mode coupling and differential mode group delay (DMDG) in multimode fibers (MMFs). However, current approaches using regular photodetectors with limited sensitivity preclude the detection of weak modal interactions in such fibers masking interesting physical effects. Here we demonstrate the use of high-sensitivity superconducting nanowire single-photon detectors (SNSPDs) to measure the mode transfer matrix of a commercial graded-index multimode fiber. Two high performance 45-mode multi-plane light conversion (MPLC) devices served as the mode multiplexer/demultiplexer. Distributed mode coupling and DMDG among different mode groups are accurately quantified from the impulse response measurement. We also observed cladding modes of the MMF as a pedestal of the pulse in the measurement. This work paves way for applications such as quantum communications using many spatial modes of the fiber.