Time-delayed Coupling Research Articles

A heterogeneous coupled oscillator model for simulation of ECG signals

We present a novel model of cardiac conduction system including main pacemakers and heart muscles. Sinoatrial node, atrioventricular node and His–Purkinje system are represented by modified van der Pol-type oscillators connected with time-delay velocity coupling. For description of atrial and ventricular muscles, where depolarization and repolarization processes are considered as separate waves, we use modified FitzHugh–Nagumo model. In this work, we obtained synthetic ECG as a combined signal of atrial and ventricular muscles and reproduced several normal and pathological rhythms. Inclusion of cardiac muscle response allows to investigate interactions between pacemakers and resulting global heartbeat dynamics by means of clinically comparable realistic ECG signals. This feature distinguishes our model from existing cardiac oscillator models. To solve the system of differential equations describing the proposed heterogeneous coupled oscillator model we developed a software in MATLAB environment utilizing special DDE23 function.

Rapid and tunable post-translational coupling of genetic circuits

One promise of synthetic biology is the creation of genetic circuitry that enables the execution of logical programming in living cells. Such “wet programming” is positioned to transform a wide and diverse swath of biotechnology ranging from therapeutics and diagnostics to water treatment strategies. While progress in the development of a library of genetic modules continues apace1–4, a major challenge for their integration into larger circuits is the generation of sufficiently fast and precise communication between modules5,6. An attractive approach is to integrate engineered circuits with host processes that facilitate robust cellular signaling7. In this context, recent studies have demonstrated that bacterial protein degradation can trigger a precise response to stress by overloading a limited supply of intracellular proteases8–10. Here, we use protease competition to engineer rapid and tunable coupling of genetic circuits across multiple spatial and temporal scales. We characterize coupling delay times that are more than an order of magnitude faster than standard transcription-factor based coupling methods (less than one minute compared with ~20–40 minutes) and demonstrate tunability through manipulation of the linker between the protein and its degradation tag. We use this mechanism as a platform to couple genetic clocks at the intracellular and colony level, then synchronize the multi-colony dynamics to reduce variability in both clocks. We show how the coupled clock network can be used to encode independent environmental inputs into a single time series output, thus enabling the possibility of frequency multiplexing in a genetic circuit context. Our results establish a general framework for the rapid and tunable coupling of genetic circuits through the use of native queueing processes such as protein degradation.

Robust synchronization of an array of neural networks with hybrid coupling and mixed time delays

This paper is concerned with the global exponential synchronization for an array of hybrid coupled neural networks with leakage delay, time-varying discrete and distributed delays. By employing a novel augmented Lyapunov–Krasovskii functional (LKF), applying the theory of Kronecker product of matrices, Barbalat׳s Lemma and the technique of linear matrix inequality (LMI), delay-dependent sufficient conditions are obtained for the global exponential synchronization of the system. As an extension, robust synchronization criteria are derived for the corresponding system with parameter uncertainties. Some examples are given to show the effectiveness of the obtained theoretical results.

Loop structure and cluster synchronization of dynamical networks with time-delayed couplings

Loop structure and cluster synchronization of dynamical networks with time-delayed couplings

Strong and weak chaos in networks with time-delayed couplings

Strong and weak chaos in networks with time-delayed couplings

Consensus of the second-order multi-agent systems with an active leader and coupling time delay

This article investigates the consensus problem of the second-order multi-agent systems with an active leader and coupling time delay in direct graph. One decentralized state control rule is constructed for each agent to track the active leader and it is proved that the proposed control scheme enables the consensus to be obtained when the adjacency topology is fixed/switched. Simulation results show effectiveness of the proposed theoretical analysis.

Synchronization of general complex networks via adaptive control schemes

In this paper, the synchronization problem of general complex networks is investigated by using adaptive control schemes. Time-delay coupling, derivative coupling, nonlinear coupling etc. exist universally in real-world complex networks. The adaptive synchronization scheme is designed for the complex network with multiple class of coupling terms. A criterion guaranteeing synchronization of such complex networks is established by employing the Lyapunov stability theorem and adaptive control schemes. Finally, an illustrative example with numerical simulation is given to show the feasibility and efficiency of theoretical results.

Pinning synchronization of unilateral coupling neuron network with stochastic noise

In this paper, pinning synchronization of unilateral coupling time delay neuron network with stochastic noise is investigated. Based on Lyapunov stability theory, by designing appropriate controller and particular Lyapunov function, pinning synchronization of unilateral coupling Hindmarsh–Rose network with stochastic noise is obtained. This method needs only one single controller. Simulation results are given to verify the effectiveness of the proposed scheme. From the simulations, the relation between the time needed to achieve pinning synchronization of unilateral coupling neuron network with stochastic noise and the number of nodes, the noise intensity, the coupling intensity is illustrated.

The role of coupling strength and internal delay between compartments in shaping the bursting behavior of cortical neuron

Bursting is a typical firing behavior intrinsically existing in neurons from many brain regions, which has been thought to have functional roles in neuronal reliable signaling and synaptic plasticity. Meanwhile, many factors have been put forward to participate in the modulation of bursting behavior during the past decades. Here, in this research, the modulation of bursting behaviors was numerically investigated in a two-compartment model of cortical pyramidal neuron using the coupling strength and time delay between compartments as control parameters. By means of computer simulations, we showed that, for larger coupling strengths and smaller delays between the two compartments, a wide range of regular bursting can be observed, while too large coupling strengths and time delays would cause the model neuron to be quiescent. In addition, the dynamical firing range of regular spiking can be also obtained, which has two parts: one part corresponds to small coupling strengths irrespective of the values of time delay, while another part corresponds to larger coupling strengths and delays. These results suggested that coupling strength and internal time delay between the inner compartments possess potential roles in modulating the dynamical bursting behavior of neurons.

Synchronization Control of Time-Varying Complex Dynamic Network with Nonidentical Nodes and Coupling Time-Delay

This paper addresses the synchronization problem for a class of complex networks with time-varying topology as well as nonidentical nodes and coupling time-delay and presents two efficient control schemes to synchronize the network onto any given smooth goal dynamics. The time-varying network is supposed to be bounded within a certain range, which cannot be controlled. Through the adoption of hybrid control with linear static feedback control and adaptive feedback control, two control schemes are derived to guarantee such complex networks to reach the global synchronization. Finally, a set of numerical simulation experiments are carried out and the results demonstrate the effectiveness of the suggested control solutions.

Pinning Stabilization of Complex Networks Coupled with Time Delay and Disturbed with Stochastic Noise

A pinning stabilization problem of complex networks with time-delay coupling is studied under stochastic noisy circumstances in this paper. Only one controller is used to stabilize the network to the equilibrium point when the network is connected and the minimal number of controllers is used when the network is unconnected, where the structure of complex network is fully used. Some criteria are achieved to control the complex network under stochastic noise in the form of linear matrix inequalities. Several examples are given to show the validity of the proposed control criteria.

The Application of GA-RBF Neural Network Generalized Predictive Control Strategy in Circulating Fluidized Bed Unit

Circulating fluidized bed boiler, with heat storage capacity, nonlinear, large time delay, multi-variable and strong coupling characteristics, is a complex quantity control system. It is difficult to establish accurate model when the parameters of control object is uncertainty because of all disturbances. This article uses one way to identify model based on genetic algorithm and RBF network combined with generalized predictive control strategy, through online rolling optimization and feedback correction, to achieve predictive control. The results of the simulation show that it has strong robustness when the load condition changes, the parameter changes or lag affects.

D-FNN Based Modeling and BP Neural Network Decoupling Control of PVC Stripping Process

PVC stripping process is a kind of complicated industrial process with characteristics of highly nonlinear and time varying. Aiming at the problem of establishing the accurate mathematics model due to the multivariable coupling and big time delay, the dynamic fuzzy neural network (D-FNN) is adopted to establish the PVC stripping process model based on the actual process operation datum. Then, the PVC stripping process is decoupled by the distributed neural network decoupling module to obtain two single-input-single-output (SISO) subsystems (slurry flow to top tower temperature and steam flow to bottom tower temperature). Finally, the PID controller based on BP neural networks is used to control the decoupled PVC stripper system. Simulation results show the effectiveness of the proposed integrated intelligent control method.

SYNCHRONIZATION IN A RING OF UNIDIRECTIONALLY COUPLED FITZHUGH–NAGUMO NEURONS

Synchronization behavior of an ensemble of unidirectionally coupled neurons with a constant input is investigated. Chemical synapses are considered for coupling. Each neuron is also considered to be exposed to a self-delayed feedback. The synchronization phenomenon is analyzed by the error dynamics of the response trajectories of the system. The effect of various model parameters e.g. coupling strength, feedback gain and time delay, on synchronization is also investigated and a measure of synchrony is computed in each cases. It is shown that the synchronization is not only achieved by increasing the coupling strength, the system also required to have a suitable feedback gain and time delay for synchrony. Robustness of the parameters for synchrony is verified for larger systems.

Two pulse-coupled non-identical, frequency-different BZ oscillators with time delay

Two non-identical, frequency-different pulse-coupled oscillators with time delay have been systematically studied using four-variable model of the Belousov-Zhabotinsky (BZ) reaction at mutual inhibitory, mutual excitatory, and mixed excitatory-inhibitory types of coupling. Different resonances like 1 : 2, 2 : 3, 1 : 3, etc., as well as complex rhythms and abrupt changes between them occur depending on the coupling strengths, time delay, and frequency ratio. Analogously to in-phase and anti-phase oscillations for 1 : 1 resonance, a similar phase locking exists for 1 : 2 resonance in the case of inhibitory coupling. For excitatory coupling, a bursting regime is found. The number of spikes in a single burst can be tuned by both the frequency ratio and time delay. For excitatory-inhibitory coupling, a region where one oscillator is suppressed (OS zone) has been found. Boundary of the OS zone depends on the frequency ratio. For weakly coupled oscillators, Farey sequence has been found for excitatory-inhibitory and mutual excitatory coupling.

Projective Synchronization Analysis of Drive-Response Coupled Dynamical Network with Multiple Time-Varying Delays via Impulsive Control

The problem of projective synchronization of drive-response coupled dynamical network with delayed system nodes and multiple coupling time-varying delays is investigated. Some sufficient conditions are derived to ensure projective synchronization of drive-response coupled network under the impulsive controller by utilizing the stability analysis of the impulsive functional differential equation and comparison theory. Numerical simulations on coupled time delay Lorenz chaotic systems are exploited finally to illustrate the effectiveness of the obtained results.

Clustering in delay-coupled smooth and relaxational chemical oscillators

We investigate cluster synchronization in networks of nonlinear systems with time-delayed coupling. Using a generic model for a system close to the Hopf bifurcation, we predict the order of appearance of different cluster states and their corresponding common frequencies depending upon coupling delay. We may tune the delay time in order to ensure the existence and stability of a specific cluster state. We qualitatively and quantitatively confirm these results in experiments with chemical oscillators. The experiments also exhibit strongly nonlinear relaxation oscillations as we increase the voltage, i.e., go further away from the Hopf bifurcation. In this regime, we find secondary cluster states with delay-dependent phase lags. These cluster states appear in addition to primary states with delay-independent phase lags observed near the Hopf bifurcation. Extending the theory on Hopf normal-form oscillators, we are able to account for realistic interaction functions, yielding good agreement with experimental findings.

Time delay control of symmetry-breaking primary and secondary oscillation death

We show that oscillation death as a specific type of oscillation suppression, which implies symmetry breaking, can be controlled by introducing time-delayed coupling. In particular, we demonstrate that time delay influences the stability of an inhomogeneous steady state, providing the opportunity to modulate the threshold for oscillation death. Additionally, we find a novel type of oscillation death representing a secondary bifurcation of an inhomogeneous steady state.

Nonparametric segmentation of heart beat intervals

allow for a more reliable quantification of coupling and are compared with established methods such as mutual information and cross recurrence analysis. Results: It is shown that the use of nonlinear approaches brings a significant improvement of fitting compared with linear models. Several transformations are highly similar within the individual groups but significantly different among the groups. The method of symbolic coupling traces is used to analyze and quantify time-delayed coupling of cardiovascular measurements during different sleep stages. Significantly different regulatory mechanisms are detected not only between the deep sleep and the other sleep stages but also between healthy subjects and patients. Conclusions: The proposed coupling method may help to indicate pathologic changes in cardiovascular regulation and also effects of continuous positive airway pressure therapy on the cardiovascular system. Moreover, newly derived synchronization methods of cardiovascular physics may help to find indicators for different health risks.

Coupled lasers: phase versus chaos synchronization

The synchronization of chaotic lasers and the optical phase synchronization of light originating in multiple coupled lasers have both been extensively studied. However, the interplay between these two phenomena, especially at the network level, is unexplored. Here, we experimentally compare these phenomena by controlling the heterogeneity of the coupling delay times of two lasers. While chaotic lasers exhibit deterioration in synchronization as the time delay heterogeneity increases, phase synchronization is found to be independent of heterogeneity. The experimental results are found to be in agreement with numerical simulations for semiconductor lasers.