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In this paper, a four-neuron delayed bidirectional associative memory (BAM) model with inertia is considered. Weak resonant double Hopf bifurcations are completely analyzed in the parameter space of the coupling weight and the coupling delay by the perturbation-incremental scheme (PIS). Numerical simulations are given for justifying the theoretical results. To the best of our knowledge, the paper is the first one to introduce inertia to a four-neuron delayed system and clarify the relationship between system parameters and dynamical behaviors.

Interaction between distant neuronal populations is essential for communication within the nervous system and can occur as a highly nonlinear process. To better understand the functional role of neural interactions, it is important to quantify the nonlinear connectivity in the nervous system. We introduce a general approach to measure nonlinear connectivity through phase coupling: the multi-spectral phase coherence (MSPC). Using simulated data, we compare MSPC with existing phase coupling measures, namely n : m synchronization index and bi-phase locking value. MSPC provides a system description, including (i) the order of the nonlinearity, (ii) the direction of interaction, (iii) the time delay in the system, and both (iv) harmonic and (v) intermodulation coupling beyond the second order; which are only partly revealed by other methods. We apply MSPC to analyze data from a motor control experiment, where subjects performed isotonic wrist flexions while receiving movement perturbations. MSPC between the perturbation, EEG and EMG was calculated. Our results reveal directional nonlinear connectivity in the afferent and efferent pathways, as well as the time delay $(43\pm 8\mathrm{\text{ms}})$ between the perturbation and the brain response. In conclusion, MSPC is a novel approach capable to assess high-order nonlinear interaction and timing in the nervous system.

Communication between neuronal populations is facilitated by synchronization of their oscillatory activity. Although nonlinearity has been observed in the sensorimotor system, its nonlinear connectivity has not been widely investigated yet. This study investigates nonlinear connectivity during the human stretch reflex based on neuronal synchronization. Healthy participants generated isotonic wrist flexion while receiving a periodic mechanical perturbation to the wrist. Using a novel cross-frequency phase coupling metric, we estimate directional nonlinear connectivity, including time delay, from the perturbation to brain and to muscle, as well as from brain to muscle. Nonlinear phase coupling is significantly stronger from the perturbation to the muscle than to the brain, with a shorter time delay. The time delay from the perturbation to the muscle is 33 ms, similar to the reported latency of the spinal stretch reflex at the wrist. Source localization of nonlinear phase coupling from the brain to the muscle suggests activity originating from the motor cortex, although its effect on the stretch reflex is weak. As such nonlinear phase coupling between the perturbation and muscle activity is dominated by the spinal reflex loop. This study provides new evidence of nonlinear neuronal synchronization in the stretch reflex at the wrist joint with respect to spinal and transcortical loops.

Time delay introduced by sampling and calculation exists between the perturbation and the duty ratio updating in the digital control loop. This time delay degrades the transient performance of digital control switching power supplies. By overcoming the sampling and calculation time effect and to calibrate the ripple that occurs during switching cycles, new control algorithm is proposed in this paper to improve the transient performance of switching power supplies by eliminating the time delay in the control loop. Simulation results show the improvement of load transient performance by the proposed algorithms. Experimental system is also set up to verify the analysis and computer simulation results.

The problem of asymptotical stabilization of a kind of time-delay, discontinuous and uncertain systems is considered by means of functional differential inclusion method which is used for discontinuous differential equations. These discontinuous systems are transformed into functional differential inclusion systems. Adaptive feedback laws are presented to stabilize the systems. An example is simulated to illustrate the effectiveness of the proposed design.

A class of singular nonlinear systems with set-valued mappings are studied in this paper. Criteria are given based on the Lyapunov function to check the absolute stability of the systems, then the results are extended to the time delay systems and the time delay systems with uncertainty. Three examples are simulated to show the effectiveness of the proposed stability conditions.

In this paper, the proposed hierarchical control scheme adds new control loop to control the reactive power reference by a fuzzy logic controller to have the benefit of increasing the system stability margins and moreover, eigenvalue, robustness and time delay analysis of proposed control scheme are presented. The reported droop-based control methods of VSI-based microgrids including hierarchical droop-based control scheme are limited to primary and secondary control levels while the proposed control scheme is completely analyzed so that the three hierarchical control levels modeled for both grid-connected mode and islanded mode. This scheme maintains the stability of microgrids not only for the small-signal events, but also for large-signal disturbances such as three phase and single phase to ground faults, heavy motor starting, etc. However, power sharing to loads and network is sufficiently done. To demonstrate the effectiveness of the proposed hierarchical controller, simulation studies have been performed on a microgrid consisting of four units of distributed generation with local loads and in presence of main grid using MATLAB/SIMULINK software and validated using OPAL RT real-time digital simulator.

This paper investigates the exponential synchronization of chaotic systems with time delays via periodically intermittent control. Under the new differential inequality, some novel synchronization criteria are derived. In contrast to the existing works, the proposed results are less conservative because they can obtain more precise synchronized rate under the identical control conditions and remove the restrictions on the control period (or the control width) and the time delay. By using special parameters, the feasible region D(ξ), which guarantees the response system synchronizes with the drive system with synchronized rate 0.5ξ, is obtained. The Lu chaotic attractor and a first-order chaotic system with time delay are presented to demonstrate the effectiveness of the proposed results.

It has been known that time delays may not only degrade the performance of the closed-loop control systems, but also induce instability due to the introduction of extra phase lag. The focus of this paper is to find out a way to design a robust controller for networked control systems (NCSs) with time-varying communication delays. To this aim, a mixed fuzzy-PID/neural network compensating scheme is proposed so as to alleviate the influence resulting from uncertain communication delays while maintaining system performance. A condition ensuring stability of the NCS is derived from the system's input–output viewpoint. The effectiveness and superiority of our proposed approach are fully verified in an experimentally networked pneumatic control system.

The interaction of prey (small fish) and predator (large fish) in lakes/ ponds at temperate and tropical regions varies when water level fluctuates naturally during seasonal time. We relate the perceptible effect of fear and anti-predator behavior of prey with the water-level fluctuations and describe how these are influenced by the seasonal changing of water level. So, we consider these as time-dependent functions to make the system more realistic. Also, we incorporate the time-dependent delay in the negative growth rate of prey in predator–prey model with Crowley–Martin-type functional response. We clearly provide the basic dynamics of the system such as positiveness, permanence and nonpersistence. The existence of positive periodic solution is studied using Continuation theorem, and suffiecient conditions for globally attractivity of positive periodic solution are also derived. To make the system more comprehensive, we establish numerical simulations, and compare the dynamics of autonomous and nonautonomous systems in the absence as well as the presence of time delay. Our results show that seasonality and time delay create the occurrence of complex behavior such as prevalence of chaotic disorder which can be potentially suppressed by the cost of fear and prey refuge. Also, if time delay increases, then system leads a boundary periodic solution. Our findings assert that the predation, fear of predator and prey refuge are correlated with water-level variations, and give some reasonable biological interpretations for persistence as well as extinction of species due to water-level variations.

Genetic oscillators have been widely used in modeling key processes of biological systems, especially cell cycles and circadian rhythms. In particular, repressilatory genetic oscillators have been employed in modeling the dynamics of mRNA and protein interactions with transcriptional and translational feedback loops at the molecular level. In addition, synchronization of these oscillators is crucial for understanding the underlying mechanisms of the associated biological processes. In this paper, models of fractional-order genetic oscillators and their coupling are established, where the aspects of time delay, coupling strength, noise, and stability are all taken into consideration. Communication in the proposed coupling model is based on quorum sensing. The synchronization of the fractional-order repressilator model has been examined through simulations which show three main findings. Firstly, the synchronization of the fractional-order repressilator model can be optimized through coupling weight selection. Secondly, the synchronization can be enhanced by increasing the fractional order and decreasing the time delay and the noise intensity. Finally, transitions between the states of the fractional-order repressilatory oscillator can be achieved through varying the fractional order. The simulation results verify the biological relevance of the genetic oscillator models, and their potential for explaining the underlying mechanisms of the associated biological processes.

This paper studies the dynamics of interacting Tilapia fish and Pelican bird population in the Salton Sea. We assume that the diseases spread in Tilapia fish follows the Holling type II response function, and the interaction between Tilapia and Pelican follows the Beddington–DeAngelis response function. The dynamics of diffusive and delayed system are discussed separately. Analytically, all the feasible equilibria and their stability are discussed. The criterion for Turing instability is derived. Based on the normal form theory and center manifold arguments, the existence of stability criterion and the direction of Hopf bifurcation are obtained. Numerical simulation shows the occurrence Hopf bifurcation, double Hopf bifurcation and transcritical bifurcation scenarios. The snap shot shows the spot, spot-strip mix patterns in the whole domain. Further, the stability switching phenomena is observed in the delayed system. Our comprehensive study highlights the effect of different parameters, multiple time delay and extinction in Pelican populations.

This paper studies affine formation control problem of general linear multi-agent systems (MASs) over undirected graph in the presence of time delays. Different delay conditions are considered and predictive observers are designed for the followers to predict the states in the future. Then, affine formation control laws are designed based on the predicted states, and sufficient conditions are derived to ensure the convergence of the formation errors. With an adaptive mechanism, the proposed control laws can be implemented without the usage of global information. Under the proposed protocols, the MASs can form a target formation shape and realize time-varying geometric transformations continuously. Finally, simulations are conducted to verify the effectiveness of the theoretical results.

Graphic simulation based on virtual reality technology is applied to the tele-operation robot system with tele-presence to make full use of the immersion feeling and the forecast property of the 3-D graphic stereoscopic display, which not only provides the operator with friendly work windows but also can overcome the effect of the communication time delay in tele-operation. In order to investigate the ineluctability communication time delay in force tele-presence of the tele-operation robot system, a tele-presence system based on the virtual reality is setup in this paper. The system structure, geometrical noumenon modeling, and man-machine interface are introduced in detail. In the tele-operation system, graphical robot technology is used to solve the time delay, and the relating experiments have proved the validity of the reappearance of the movement of an actual robot by a graphical robot.

A restart strategy with time delay is proposed to a multi-agent consensus algorithm for an approximated distributed minimax optimization. The restart strategy controls a step length of a subgradient method and resets a local clock under certain criteria in the algorithm. A synchronization protocol with time delay is introduced in the algorithm to execute the restart strategy simultaneously. A numerical example illustrates that the proposed algorithm works well particularly in high approximation ratios.

In this paper, we consider the sliding mode control of delayed T-S fuzzy neural network with normbounded uncertainties. Based on the Lyapunov-Krasovskii stability theory, we originally research the sliding mode control method for T-S fuzzy neural network with time delay on the basis of the linear matrix inequalities (LMIs). A numerical example is given to validate the effectiveness of our method.