Nonlinear Synchronization Research Articles

Nonlinear dynamics and synchronization of computational cognitive model in educational science

A computational cognitive model is derived from nonlinear interactions of (Neo) Piagetian-Vygostkian constructs to explain, and predict cognitive processes during collaborative learning. Learning is re-conceptualized as continuous perturbations of cognitive state which unfolds stable cognitive trajectories near Piagetian equilibrium. The model explicates topologically equivalent cognitive patterns, attributed to multi-modal representation of sensory information presented to the learners. Synchronization of the cognitive model is obtained via active control functions which predicts convergence of cognitive states. The synchronized cognitive model is stabilized using Lyapunov matrix equation. These qualitative behaviors emerged due to learner-to-learner and instructor-to-learner scaffolding driven by cognitive executive functions. The dynamical behaviors of the cognitive model are simulated using control parameters with estimated datasets showing viable cognitive trajectories.

Nonlinear model predictive acceleration synchronization technique for rigid-model-based tracking control of multi-DOF flexible systems

In this paper, the problem of stabilization and tracking control of uncertain flexible multivariable continuum mechanism systems with additional appendage considering boundedness of undesired vibrational effects are investigated. It is proposed that rather than controlling the entire dynamical system through installation of additional actuators on appendage, it is more desirable to stabilize the core system while considering undesired vibrational effect in the appendage as optimization cost. To this end, the nonlinear programming problem corresponding to a predictive control scheme is presented based on a cost defined according to magnitude of accelerations of undesired vibrations in the appendage. Stabilization of control algorithm is conducted based on demonstration of existence of feasible Lyapunov functions. Candidate Lyapunov functions are defined based on sliding functions analysis. The associated sliding functions are defined for core subsystems which correspond to degrees of freedom of dynamical system that are associated with reference signals. Undesired vibrations caused by other degrees of freedom corresponding to appendage are considered as segments of control cost in the optimization problem. To ensure the feasibility of control model in real-time applications, the control algorithm is obtained in discrete-time basis. Based on investigation of monotonically decreasing Lyapunov functions and expression of sliding functions as a combination of dynamical terms, reference inputs and control input terms, stabilizing constraints of closed-loop system are calculated. Similarly, based on combination of sliding surfaces with considered control and vibrational constraints, additional constraints for boundedness of vibrational terms in nonlinear programming problem are obtained. Numerical comparisons with a sliding control algorithm for core mechanical system and a reaching law method indicate improvements regarding reduction of undesired vibrational effects in appendage. Furthermore, regulation of appendage dynamics is conducted without installation of additional actuators, which reduces the implementation cost in comparison with a full-control scheme for core system and appendage.

Decoding Adaptive Visuomotor Behavior Mediated by Non-linear Phase Coupling in Macaque Area MT.

The idea that a flexible behavior relies on synchronous neural activity within intra- and inter-associated cortical areas has been a matter of intense research in human and animal neuroscience. The neurophysiological mechanisms underlying this behavioral correlate of the synchronous activity are still unknown. It has been suggested that the strength of neural synchrony at the level of population is an important neural code to guide an efficient transformation of the sensory input into the behavioral action. In this study, we have examined the non-linear synchronization between neural ensembles in area MT of the macaque visual cortex by employing a non-linear cross-frequency coupling technique, namely bicoherence. We trained a macaque monkey to detect a brief change in the cued stimulus during a visuomotor detection task. The results show that the non-linear phase synchronization in the high-gamma frequency band (100–250 Hz) predicts the animal’s reaction time. The strength of non-linear phase synchronization is selective to the target stimulus location. In addition, the non-linearity characteristics of neural synchronization are selectively modulated when the monkey covertly attends to the stimulus inside the neuron’s receptive field. This additional evidence indicates that non-linear neuronal synchronization may be affected by a cognitive function like spatial attention. Our neural and behavioral observations reflect that two crucial processes may be involved in processing of visuomotor information in area MT: (I) a non-linear cortical process (measured by the bicoherence) and (II) a linear process (measured by the spectral power).

When Sinus Tachycardia Becomes Too Much: Negative Effects of Excessive Upright Tachycardia on Cardiac Output in Vasovagal Syncope, Postural Tachycardia Syndrome, and Inappropriate Sinus Tachycardia.

Upright posture reduces venous return, stroke volume, and cardiac output (CO) while causing reflex sinus rate (heart rate [HR]) increase. Yet, in inappropriate sinus tachycardia (IST), postural tachycardia syndrome (POTS), and vasovagal syncope (VVS), symptomatic excessive HR occurs. We hypothesized that CO reaches maximum as function of HR in all. We recruited 12 healthy controls, 9 IST, 30 VVS, and 30 POTS patients (13-23years) selected randomly by disorder not by HR, each fulfilled appropriate diagnostic criteria. Subjects were instrumented for electrocardiography, beat-to-beat blood pressure, respiratory rate, CO-Modelflow algorithm, and central blood volume from impedance cardiography; 10-minute data were collected supine; subjects were tilted head-up for ≤10 minutes. We computed phase differences, ΔΦ, between fluctuations of HR (ΔHR) and CO (ΔCO) tabulating data when phases were synchronized, determined by a squared nonlinear phase synchronization index >0.5, describing extent/validity of CO/HR coupling. We graphed results supine, 1-minute post-tilt-up, mid-tilt, and pre-tilt-down using polar coordinates (HR-radius, ΔΦ-angle) plotting cos(ΔΦ) versus HR to determine if transition HR exists at which in-phase shifts to antiphase above which CO decreases when HR further increases. At baseline HR, diastolic and mean arterial pressures in IST and POTS were higher versus controls. Upright HR increased most in POTS then IST and VVS, with diverse changes in CO, SVR, and central blood volume. Each patient grouping was separately and collectively analyzed for HR change showing transition from in-phase to anti-phase (ΔΦ) as HR increased: HRtransition=115±6 (IST), 123±8 (POTS), 124±7 (VVS), P=ns. Controls never reached transitional HR. Excessive HR independently and equivalently reduces upright CO, in IST, POTS, and VVS.

Soleus single motor units show stronger coherence with Achilles tendon vibration across a broad bandwidth relative to medial gastrocnemius units while standing

To probe the frequency characteristics of somatosensory responses in the triceps surae muscles, we previously applied suprathreshold noisy vibration to the Achilles tendon and correlated it with ongoing triceps surae muscle activity (recorded via surface EMG) during standing. Stronger responses to tendon stimuli were observed in soleus (Sol) relative to medial gastrocnemius (MGas) surface EMG; however, it is unknown whether differences in motor unit activity or limitations of surface EMG could have influenced this finding. Here, we inserted indwelling EMG into Sol and MGas to record the activity of single motor units while we applied noisy vibration (10-115 Hz) to the right Achilles tendon of standing participants. We analyzed the relationship between vibration acceleration and the spike activity of active single motor units through estimates of coherence, gain, phase, and cross-covariance. We also applied sinusoidal vibration at frequencies from 10 to 100 Hz (in 5-Hz increments) to examine whether motor units demonstrate nonlinear synchronization or phase locking at higher frequencies. Relative to MGas single motor units, Sol units demonstrated stronger coherence and higher gain with noisy vibration across a bandwidth of 7-68 Hz, and larger peak-to-peak cross-covariance at all four stimulus amplitudes examined. Sol and MGas motor unit activity was modulated over the time course of the sinusoidal stimuli across all frequencies, but their phase-locking behavior was minimal. These findings suggest Sol plays a prominent role in responding to disturbances transmitted through the Achilles tendon across a broad frequency band during standing.NEW & NOTEWORTHY We examined the relationship between Achilles tendon stimuli and spike times of single soleus (Sol) and medial gastrocnemius (MGas) motor units during standing. Relative to MGas, Sol units demonstrated stronger coherence and higher gain with noisy stimuli across a bandwidth of 7-68 Hz. Sol and MGas units demonstrated minimal nonlinear phase locking with sinusoidal stimuli. These findings indicate Sol plays a prominent role in responding to tendon stimuli across a broad frequency band.

Synchronization of Non-linear Oscillators for Neurobiologically Inspired Control on a Bionic Parallel Waist of Legged Robot.

Synchronization of coupled non-linear oscillators inspired by a central pattern generator (CPG) can control the bionic robot and promote the coordination and diversity of locomotion. However, for a robot with a strong mutual coupled structure, such neurobiological control is still missing. In this contribution, we present a σ-Hopf harmonic oscillator with decoupled parameters to expand the solution space of the locomotion of the robot. Unlike the synchronization of original Hopf oscillators, which has been fully discussed, the asymmetric factor of σ-Hopf oscillator causes a deformation in oscillation waveform. Using the non-linear synchronization theory, we construct the transition state model of the synchronization process to analyze the asymmetrical distortion, period change and duty ratio inconsistency. Then a variable coupling strength is introduced to eliminate the waveform deformation and maintain the fast convergence rate. Finally, the approach is used for the locomotion control of a bionic parallel waist of legged robot, which is a highly coupled system. The effectiveness of the approach in both independent and synthesis behavior of four typical motion patterns are validated. The result proves the importance of controllability of the oscillation waveform and the instantaneous state of the synchronization, which benefits the transition and transformation of the locomotion and makes the coupling motion more flexible.

Nonlinear stochastic synchronization of complex dynamical networks with delays

This paper investigates the problem of synchronization for complex networks with time delays and stochastic uncertainties. Based on Lyapunov-Krasovskii functional theory, some sufficient conditions are derived. To deal with random uncertainties in networks, some suitable nonlinear adaptive controllers are designed, and some updating laws are used to deal with the feedback factor. The designed nonlinear adaptive controller can be used not only for synchronization of networks with delayed nodes, but also for the synchronization of networks with delayed random noises and delayed nodes. Finally, numerical examples illustrating the effectiveness of the proposed theoretical results are provided.

Phase-mixing v.s. phase synchronization in the dynamics of flow-shear induced edge transport barrier

Nonlinear relaxation oscillations of flow-shear induced transport barriers can be qualitatively reproduced using a phenomenological critical-gradient model [Leconte et al., Contrib. Plasma Phys. 56, 736 (2016)]. Here, we perform a more in-depth analysis of the mechanism of these nonlinear oscillations, associated with nonlinear phase synchronization, in an extended version of the model including random fluctuations.

Optimization of Excitation Frequencies of a Gearbox Using Algorithms Inspired by Nature

This work presents a methodology to enhance the preliminary design of a single-stage gearbox by diminishing the dynamic load between gears and bearings. The gearbox dynamic load decreases by separating its excitation frequencies; the proposed methodology satisfies the design parameters like power, speed, and useful life and optimizes the distribution of the excitation frequencies using algorithms based on nature as particle swarm optimization, genetic algorithms and bat algorithm. The algorithms maximize the separation between consecutive frequencies, even though the space of solutions has abrupt changes and discontinuities. The algorithm based on particle swarm optimization is the most stable and quick to converge. As shown in this work, the dynamic load produced by the interaction between the gearbox components can be diminished from the design stage. The methodology based on nature algorithms improves the distribution of excitation frequencies, and therefore, decreases the possibility of a nonlinear synchronization, resonances and beating frequencies; thus prolongs the life of the transmission components.

On the complete synchronization of a time-fractional reaction–diffusion system with the Newton–Leipnik nonlinearity

ABSTRACT In this paper, we consider a time-fractional reaction–diffusion system with the same nonlinearities of the Newton–Leipnik chaotic system. Through analytical tools and numerical results, we derive sufficient conditions for the asymptotic stability of the proposed model and show the existence of chaos. We also propose a nonlinear synchronization controller for a pair of systems and establish the local and global asymptotic convergence of the trajectories by means of fractional stability theory and the Lyapunov method.

Nonlinear and Non-Stationary Detection for Measured Dynamic Signal from Bridge Structure Based on Adaptive Decomposition and Multiscale Recurrence Analysis

To test the nonlinearity and non-stationarity of measured dynamic signals from a bridge structure with high-level noise and dense modal characteristics, a method that combines the adaptive signal decomposition with the recurrence analysis is proposed to solve the difficulty of testing nonlinearity and non-stationarity of bridge structure signals. A novel white noise assistance and cluster analysis are introduced to the ensemble empirical mode decomposition to alleviate mode-mixing issues and generate single-mode intrinsic mode functions. Combining the hypothesis-testing scheme of nonstationary and nonlinear synchronization and surrogate techniques, a data-driven recurrence quantification analysis method is proposed and a novel recurrence quantification measure pairs are set up. To demonstrate the efficacy of the proposed methodology, complex signals, which are collected from a carefully instrumented model of a cable-stayed bridge, are utilized as the basis for comparing with traditional nonlinear and non-stationary test methods. Results show that the proposed multiscale recurrence method is feasible and effective for applications to a nonlinear and non-stationary test for real complex civil structures.

Application effects of biogas slurry partly substituting for chemical fertilizer on autumn tomato production in winter-solar greenhouse

To explore the effects of biogas slurry coordinating chemical fertilizer on growth promotion of tomato, we used three kinds of typical biogas slurry as concentrated nutrient solution, respectively fermented from raw duck manure, pig manure, cow dung, while urea, monocalcium phosphate and potassium sulphate as auxiliary nutrition to balance the nutrient difference between different dilution ratios of biogas slurry. The results showed the biogas slurry partially substituting chemical fertilizer could significantly improve soil fertility, including available nitrogen, phospho-rus, and potassium. As for water soluble calcium, magnesium, iron, manganese and zinc in soil, biogas slurry application could activate their availability, with the magnitude of such effects depended on the fermentation level of raw materials and dilution ratio. Compared with chemical fertilizer, coordinating biogas liquid fertilizer significantly promoted the growth of tomato, with the yield increased by 55.9%-232.8% and the chemical fertilizer dosage decreased by 18.2%-85.0%. Furthermore, such effects became more prominent along with prolonged time. The fruit quality was significantly improved with the increases of lycopene, ascorbic acid and total sugar, and the decreases of acidity and nitrite concentration, and the decrease of NO2- by 35.6%-90.3%. In addition, the taste flavor of fruits was 7.0%-20.3% higher than that of chemical fertilizer treatment. The yield and quality of tomato took on nonlinear synchronization, and the relation between taste flavor and sugar/acid showed significantly positive correlation, which was affected by fertilizer type. Biogas slurry partly substituting chemical fertilizer could achieve the goals of high yield, high quality, environmental protection, efficient utilization of agricultural resources in tomato production.

Synchronization Control in Reaction‐Diffusion Systems: Application to Lengyel‐Epstein System

Synchronization and control in high dimensional spatial‐temporal systems have received increasing interest in recent years. In this paper, the problem of complete synchronization for reaction‐diffusion systems is investigated. Linear and nonlinear synchronization control schemes have been proposed to exhibit synchronization between coupled reaction‐diffusion systems. Synchronization behaviors of coupled Lengyel‐Epstein systems are obtained to demonstrate the effectiveness and feasibility of the proposed control techniques.

Epileptic foci localization based on mapping the synchronization of dynamic brain network

BackgroundCharacterizing the synchronous changes of epileptic seizures in different stages between different regions is profound to understand the transmission pathways of epileptic brain network and epileptogenic foci. There is currently no adequate quantitative calculation method for describing the propagation pathways of electroencephalogram (EEG) signals in the brain network from the short and long term. The goal of this study is to explore the innovative method to locate epileptic foci, mapping synchronization in the brain networks based on EEG.MethodsMutual information was used to analyze the short-term synchronization in the full electrodes; while nonlinear dynamics quantifies the statistical independencies in the long –term among all electrodes. Then graph theory based on the complex network was employed to construct a dynamic brain network for epilepsy patients when they were awake, asleep and in seizure, analyzing the changing topology indexes.ResultsEpileptic network achieved a high degree of nonlinear synchronization compared to awake time. and the main path of epileptiform activity was revealed by searching core nodes. The core nodes of the brain network were in connection with the onset zone. Seizures always happened with a high degree of distribution.ConclusionsThis study indicated the path of EEG synchronous propagation in seizures, and core nodes could locate the epileptic foci accurately in some epileptic patients.

A modified function-link fuzzy cerebellar model articulation controller using a PI-type learning algorithm for nonlinear system synchronization and control

This paper aims to propose a novel modified fuzzy cerebellar model articulation controller (CMAC) combined with a function-link network for the synchronization of nonlinear chaotic systems and control of an inverted pendulum in the presence of uncertainties, external disturbance, and different initial conditions. The proposed method overlaps the previous state and the current state of Gaussian basis functions (GBFs) on each layer to make a combination between two states. This makes the inputs be able to simultaneously stir the current state and previous state to adjust the appropriate error values so that the modified function-link fuzzy CMAC (FLMFC) can easily learn parameters, improve the computational efficiency and predict the next state of the inputs. The proposed control system combines an FLMFC with the sliding mode control; therefore the input space element of FLMFC can be simplified. A function-link network is embedded in the FLMFC to give a more accurate approximation of the weights. A PI-type learning method is used to online tune the parameters for the connective weights of the proposed FLMFC. The control system consists of an FLMFC and a compensation controller. A Lyapunov stability theorem is applied to find the adaptation laws of the proposed controller and to guarantee the system's stability. Simulation studies for the synchronization of chaotic systems and control of inverted pendulum show that favorable tracking performance can be achieved by using the proposed control system.

Parametric control to a type of quasi-linear high-order systems via output feedback

This paper investigates the design problem of output feedback control to a type of quasi-linear high-order systems containing time-variant coefficient matrices which include time-variant parameters and system variables. Based on the solution to a class of high-order generalized Sylvester matrix equation, we can design the left and right closed-loop eigenvectors and obtain two groups of arbitrary parameters, further establish a general complete parametrized expression for a quasi-linear high-order output feedback controller. By the presented parametric approach, the closed-loop system can be transformed into a linear time-invariant one with the desired eigenstructure. Finally, a nonlinear feedback synchronization problem of Genesio-Tesi and Coullet chaotic systems is presented to prove the effectiveness of the proposed approach.

Dynamics, Chaos Control, and Synchronization in a Fractional-Order Samardzija-Greller Population System with Order Lying in (0, 2)

This paper demonstrates dynamics, chaos control, and synchronization in Samardzija-Greller population model with fractional order between zero and two. The fractional-order case is shown to exhibit rich variety of nonlinear dynamics. Lyapunov exponents are calculated to confirm the existence of wide range of chaotic dynamics in this system. Chaos control in this model is achieved via a novel linear control technique with the fractional order lying in (1, 2). Moreover, a linear feedback control method is used to control the fractional-order model to its steady states when 0<α<2. In addition, the obtained results illustrate the role of fractional parameter on controlling chaos in this model. Furthermore, nonlinear feedback synchronization scheme is also employed to illustrate that the fractional parameter has a stabilizing role on the synchronization process in this system. The analytical results are confirmed by numerical simulations.

Complex networks for tracking extreme rainfall during typhoons.

Reconciling the paths of extreme rainfall with those of typhoons remains difficult despite advanced forecasting techniques. We use complex networks defined by a nonlinear synchronization measure termed event synchronization to track extreme rainfall over the Japanese islands. Directed networks objectively record patterns of heavy rain brought by frontal storms and typhoons but mask out contributions of local convective storms. We propose a radial rank method to show that paths of extreme rainfall in the typhoon season (August-November, ASON) follow the overall southwest-northeast motion of typhoons and mean rainfall gradient of Japan. The associated eye-of-the-typhoon tracks deviate notably and may thus distort estimates of heavy typhoon rainfall. We mainly found that the lower spread of rainfall tracks in ASON may enable better hindcasting than for westerly-fed frontal storms in June and July.

Application of Non-Linear Gaussian Regression-Based Adaptive Clock Synchronization Technique for Wireless Sensor Network in Agriculture

Efficient and low power utilizing clock synchronization is a challenging task for a wireless-sensor network (WSN). Therefore, it is crucial to design a light weight clock synchronization protocols for these networks. An adaptive clock offset prediction model for WSN is proposed in this paper that exchanges fewer synchronization messages to improve the accuracy and efficiency. Timing information required is collected by setting a small WSN set up to investigate the soil condition to control the irrigation in agriculture. The networks investigate soils moisture, temperature, humidity, and pressure content along with the sensors clock offset. First, the prediction model perceives the existing sensor clock offset to observe the clock characteristics and delay. Then, a Gaussian function is applied for adjusting the parameters weight of the observed value in the prediction model. The system results demonstrate that the proposed adaptive non-linear Gaussian regression synchronization model utilizes 20% less energy as consumed by time sync protocol for sensor-network and reference broadcast synchronization Protocol. It also reduces the synchronization error with respect to root-mean-square error (RMSE) by 24.85% as compared to linear prediction synchronization with RMSE 28.72% in terms of accuracy.

Global Finite-Time Multi-Switching Synchronization of Externally Perturbed Chaotic Oscillators

Quick recovery of the information signals in secure communications restricts the hacking duration. The short synchronization convergence time is a crucial parameter for faster recovery. This paper develops a novel nonlinear finite-time synchronization control algorithm. This controller accomplishes the global finite-time multi-switching synchronization between two externally perturbed chaotic systems in the drive–response system synchronization scheme. The proposed controller assures the global convergence of the error dynamics in finite-time based on the Lyapunov theory. This implicitly guarantees the global stability of the closed loop. This paper considers Lp(0 < p < 1) norm inequality for the construction of the Lyapunov function. This method provides a means to determine the parameters of the proposed finite-time controller. This paper also studies the significance of structural components of the proposed controller that are responsible for the finite-time synchronization convergence. Computer simulation results of ‘two identical chaotic Lorenz systems’ and ‘chaotic Lorenz and Chen systems’ validate the theoretical findings. The paper discusses the simulation results and compares them with peer works as well.