Development of data-driven modeling method for nonlinear coupling components.

This research introduces a methodology for data-driven regression modeling of components exhibiting nonlinear characteristics, utilizing the sparse identification of nonlinear dynamics (SINDy) method. The SINDy method is extended to formulate regression models for interconnecting components with nonlinear traits, yielding governing equations with physically interpretable solutions. The proposed methodology focuses on extracting a model that balances accuracy and sparsity among various regression models. In this process, a comprehensive model was generated using linear term weights and an error histogram. The applicability of the proposed approach is demonstrated through a case study involving a sponge gasket with nonlinear characteristics. By contrasting the predictive model with experimental responses, the reliability of the methodology is verified. The results highlight that the regression model, based on the proposed technique, can effectively establish an accurate dynamical system model, accounting for realistic conditions.

Dynamic behavior of electro-osmosis in variable charge soils: Insights on termination and direction reversal.

Electro-osmosis offers an effective method for dewatering and remediating low permeability soil. Long-term observations on nonlinear behavior of electro-osmosis and the influencing factors are not commonly reported. Connection between cessation and direction reversal of electro-osmotic flow (EOF), and the evolution of electro-chemical parameters inside of the soil mass thus remains unclear. The dynamic response of EOF in variable charge soil could be significant, whereas the investigations on which are currently lacking. A series of electro-osmotic experiments were performed with two natural variable charge soils. The results indicated that initial electro-osmotic rate was positively proportional to electric current and initial electrical conductivity of the pore fluid, which could be explained by the ion migration model. The dynamic evolution of electro-osmotic rate and electro-chemical parameters corresponding to the solute and pH conditionings at the electrode compartments demonstrated that: 1) coupling effects of non-uniform distribution of voltage gradient and pH determined the magnitude and direction of EOF rate; 2) compared to the final pHIEP value, the bigger, close and smaller values of the novel index "voltage gradient weighed mean of spatial pH″ represented the forward, terminated and reversed EOF respectively; 3) the classical Helmholtz-Smoluchowski model are proved to be more applicable interpreting the coupled nonlinearity of electro-osmosis during the later steady phase. This work would facilitate future research for a comprehensive electro-osmotic model, and provide guidance to condition the initial and boundary conditions in application of electro-osmotic dewatering and electrokinetic remediation.

A neuron model with nonlinear membranes.

One-layer membrane separates the gradient field in and out of the cell, while some two-layer membranes filled with excitable media/material are important to regulate the energy flow when ions are propagated and diffused. The intracellular and extracellular media can be effectively separated by the membrane. It is important to clarify and describe the biophysical function and then the capacitive property can be reproduced in equivalent neural circuit. Here, we suggest the cell membrane has certain thickness and becomes flexible under external stimuli, therefore, it is considered as a kind of nonlinear media. To mimic the physical property of the two-layer cell membrane, a nonlinear resistor is used to connect two linear circuits, which is used to describe the electrical characteristic of two sides of the cell membrane, respectively. The combination of two linear circuits via a nonlinear resistor can describe the energy characteristic and firing mode in the flexible membrane of biophysical neurons. Circuit equations are defined and converted into equivalent nonlinear oscillator like a neuron. The voltage difference for the two capacitors can be consistent with the membrane potential for the neuron. The Hamilton energy function for this neuron can be mapped from the field energy in the electronic components, and it is also derived by using Helmholtz's theorem. The neuron can show similar spiking and bursting firing patterns, and uncertain diversity in membrane potentials is effective to support continuous firing patterns and mode transition under external stimulus. Furthermore, noisy disturbance is applied to induce coherence resonance. The results indicate that the lower coefficient variability and higher average energy level supports periodic firing in the neuron under coherence resonance. Therefore, this neuron model with nonlinear membranes (or two-layer form) is more suitable for identifying the biophysical property of biological neuron.

Aperiodically intermittent event-triggered pinning control on cluster synchronization of directed complex networks.

This paper is dedicated to investigating the exponential cluster synchronization in a class of nonlinearly coupled complex networks with non-identical nodes and an asymmetrical coupling matrix. A novel aperiodically intermittent pinning control (APIPC) protocol is presented, which takes full account of the cluster-tree topology structure of the networks and pins only the nodes in the current cluster that have directional links to neighboring clusters. Since it is difficult to precisely determine the intermittent control instants and rest instants of APIPC in advance, the event-triggered mechanism (ETM) is thus proposed. Based on the concept of the minimal control ratio and the segmentation analysis method, sufficient requirements for realizing the exponential cluster synchronization are derived. Moreover, the Zeno behavior of ETM is excluded by rigorous analysis. Eventually, the effectiveness and advantages of the established theorems and control strategies are demonstrated by two numerical simulations.

Spatial-temporal evolution of the allometric growth between economic scale and carbon emissions in China's cities and its driving mechanism.

Exploring the relationship between economic development and carbon emissions is a hot issue of concern to academia. Taking Chinese cities as the research object, this study constructed an allometric growth model of economic scale and carbon emissions to analyze the spatial-temporal evolution of their allometric growth from 2000 to 2017. Additionally, the geographical detector model was used to reveal the driving mechanism of allometric growth. The findings were as follows. (1) The spatial-temporal patterns of economic scale and carbon emissions were dominated by hot spots. Additionally, their size distribution was in an equilibrium stage. (2) The gap between the economic growth rate of Chinese cities and the growth rate of carbon emissions grew, reflecting the remarkable achievements in carbon emission reduction in Chinese cities as a whole. The scaling exponent declined from east to the west during 2000-2008, but showed the opposite trend during 2009-2017. The proportion of cities with negative allometric growth in the sample cities increased from 76.49 to 97.86%. (3) The influence of city investment intensity, energy utilization efficiency, technological development level, social consumption level, fiscal investment level and economic development level on allometric growth gradually decreases. These factors were also the main factors affecting the spatial-temporal heterogeneity of allometric growth. (4) The impact of various factors had a synergetic enhancement effect. These factors can be classified as economic factors, environmental factors and a combination of them. Under the nonlinear coupling of multiple factors, a spatially differentiated pattern of allometric growth was formed.

Critical Quantum Metrology in the Non-Linear Quantum Rabi Model.

The quantum Rabi model (QRM) with linear coupling between light mode and qubit exhibits the analog of a second-order phase transition for vanishing mode frequency which allows for criticality-enhanced quantum metrology in a few-body system. We show that the QRM including a nonlinear coupling term exhibits much higher measurement precisions due to its first-order-like phase transition at finite frequency, avoiding the detrimental slowing-down effect close to the critical point of the linear QRM. When a bias term is added to the Hamiltonian, the system can be used as a fluxmeter or magnetometer if implemented in circuit QED platforms.

H∞ filtering for nonlinearly coupled complex networks subjected to unknown varying delays and multiple fading measurements.

In this paper, the robust filtering problem for uncertain complex networks with time-varying state delay and stochastic nonlinear coupling based on H∞ performance criterion is studied. The random connections of coupling nodes are represented by utilizing independent random variables and the multiple fading measurements phenomenon is characterized by introducing diagonal matrices with independent stochastic elements. Moreover, the probabilistic time-varying delays in the measurement outputs are described by white sequences with the Bernoulli distributions. Furthermore, All system's matrices are supposed to have uncertainty and a quadratic bound is assumed for nonlinear part of the network. This bound can be obtained by solving a sum of squares (SOS) optimization problem. By applying the Lyapunov theory, we design a robust filter for each node of the network so that the filtering error system is asymptomatically stable and the H∞ performances are met. Then, the parameters of the filters are achieved by solving a linear matrix inequality (LMI) feasibility problem. Finally, the applicability and performance of the proposed H∞ filtering approach are demonstrated via a practical example.

Pinning multisynchronization of delayed fractional-order memristor-based neural networks with nonlinear coupling and almost-periodic perturbations.

This paper concerns the multisynchronization issue for delayed fractional-order memristor-based neural networks with nonlinear coupling and almost-periodic perturbations. First, the coexistence of multiple equilibrium states for isolated subnetwork is analyzed. By means of state-space decomposition, fractional-order Halanay inequality and Caputo derivative properties, the novel algebraic sufficient conditions are derived to ensure that the addressed networks with arbitrary activation functions have multiple locally stable almost periodic orbits or equilibrium points. Then, based on the obtained multistability results, a pinning control strategy is designed to realize the multisynchronization of the N coupled networks. By the aid of graph theory, depth first search method and pinning control law, some sufficient conditions are formulated such that the considered neural networks can possess multiple synchronization manifolds. Finally, the multistability and multisynchronization performance of the considered neural networks with different activation functions are illustrated by numerical examples.

Identifying bidirectional total and non-linear information flow in functional corticomuscular coupling during a dorsiflexion task: a pilot study.

BACKGROUND: The key challenge to constructing functional corticomuscular coupling (FCMC) is to accurately identify the direction and strength of the information flow between scalp electroencephalography (EEG) and surface electromyography (SEMG). Traditional TE and TDMI methods have difficulty in identifying the information interaction for short time series as they tend to rely on long and stable data, so we propose a time-delayed maximal information coefficient (TDMIC) method. With this method, we aim to investigate the directional specificity of bidirectional total and nonlinear information flow on FCMC, and to explore the neural mechanisms underlying motor dysfunction in stroke patients. METHODS: We introduced a time-delayed parameter in the maximal information coefficient to capture the direction of information interaction between two time series. We employed the linear and non-linear system model based on short data to verify the validity of our algorithm. We then used the TDMIC method to study the characteristics of total and nonlinear information flow in FCMC during a dorsiflexion task for healthy controls and stroke patients. RESULTS: The simulation results showed that the TDMIC method can better detect the direction of information interaction compared with TE and TDMI methods. For healthy controls, the beta band (14-30 Hz) had higher information flow in FCMC than the gamma band (31-45 Hz). Furthermore, the beta-band total and nonlinear information flow in the descending direction (EEG to EMG) was significantly higher than that in the ascending direction (EMG to EEG), whereas in the gamma band the ascending direction had significantly higher information flow than the descending direction. Additionally, we found that the strong bidirectional information flow mainly acted on Cz, C3, CP3, P3 and CPz. Compared to controls, both the beta-and gamma-band bidirectional total and nonlinear information flows of the stroke group were significantly weaker. There is no significant difference in the direction of beta- and gamma-band information flow in stroke group. CONCLUSIONS: The proposed method could effectively identify the information interaction between short time series. According to our experiment, the beta band mainly passes downward motor control information while the gamma band features upward sensory feedback information delivery. Our observation demonstrate that the center and contralateral sensorimotor cortex play a major role in lower limb motor control. The study further demonstrates that brain damage caused by stroke disrupts the bidirectional information interaction between cortex and effector muscles in the sensorimotor system, leading to motor dysfunction.

Finite-time cluster synchronization in complex-variable networks with fractional-order and nonlinear coupling.

This paper is primarily concentrated on finite-time cluster synchronization of fractional-order complex-variable networks with nonlinear coupling by utilizing the non-decomposition method. Firstly, two control strategies are designed which are relevant to complex-valued sign functions. Thereafter, by employing fractional-order stability theory and complex function theory, several criteria are deduced to ensure finite-time cluster synchronization under the framework within a new norm consisting of absolute values for real and imaginary components. Furthermore, the setting time is effectively estimated based on some significant properties of fractional-order Caputo derivation and Mittag-Leffler functions. Lastly, two numerical examples are given to verify the effectiveness of theoretical results.

Multimode Nonlinear Coupling Induced by Internal Resonance in a Microcantilever Resonator.

Coupled resonators represent a generic model for many physical systems. In this context, a microcantilever is a multimode resonator clamped at one end, and it finds extensive application in high-precision metrology and is expected to be of great potential use in emerging quantum technologies. Here, we explore the microcantilever as a flexible platform for realizing multimode nonlinear interactions. Multimode nonlinear coupling is achieved by (1:2) internal resonance (IR) and parametric excitation with efficient coherent energy transfer. Specifically, we demonstrate abundant tunable parametric behaviors via frequency and voltage sweeps; these behaviors include mode veering, degenerate four-wave mixing (D4WM) with satellite resonances, partial amplitude suppression, acoustic frequency comb (AFC) generation, mechanically induced transparency (MIT), and normal-mode splitting. The experiments depict a new scheme for manipulating multimode microresonators with IR and parametric excitation.

[Intermuscular coupling based on wavelet packet-cross frequency coherence].

Human motion control system has a high degree of nonlinear characteristics. Through quantitative evaluation of the nonlinear coupling strength between surface electromyogram (sEMG) signals, we can get the functional state of the muscles related to the movement, and then explore the mechanism of human motion control. In this paper, wavelet packet decomposition and n: m coherence analysis are combined to construct an intermuscular cross-frequency coupling analysis model based on wavelet packet- n: m coherence. In the elbow flexion and extension state with 30% maximum voluntary contraction force (MVC), sEMG signals of 20 healthy adults were collected. Firstly, the subband components were obtained based on wavelet packet decomposition, and then the n: m coherence of subband signals was calculated to analyze the coupling characteristics between muscles. The results show that the linear coupling strength (frequency ratio 1:1) of the cooperative and antagonistic pairs is higher than that of the nonlinear coupling (frequency ratio 1:2, 2:1 and 1:3, 3:1) under the elbow flexion motion of 30% MVC; the coupling strength decreases with the increase of frequency ratio for the intermuscular nonlinear coupling, and there is no significant difference between the frequency ratio n: m and m: n. The intermuscular coupling in beta and gamma bands is mainly reflected in the linear coupling (1:1), nonlinear coupling of low frequency ratio (1:2, 2:1) between synergetic pair and the linear coupling between antagonistic pairs. The results show that the wavelet packet- n: m coherence method can qualitatively describe the nonlinear coupling strength between muscles, which provides a theoretical reference for further revealing the mechanism of human motion control and the rehabilitation evaluation of patients with motor dysfunction.

Intermuscular coupling based on wavelet packet-cross frequency coherence / 生物医学工程学杂志

Human motion control system has a high degree of nonlinear characteristics. Through quantitative evaluation of the nonlinear coupling strength between surface electromyogram (sEMG) signals, we can get the functional state of the muscles related to the movement, and then explore the mechanism of human motion control. In this paper, wavelet packet decomposition and : coherence analysis are combined to construct an intermuscular cross-frequency coupling analysis model based on wavelet packet- : coherence. In the elbow flexion and extension state with 30% maximum voluntary contraction force (MVC), sEMG signals of 20 healthy adults were collected. Firstly, the subband components were obtained based on wavelet packet decomposition, and then the : coherence of subband signals was calculated to analyze the coupling characteristics between muscles. The results show that the linear coupling strength (frequency ratio 1:1) of the cooperative and antagonistic pairs is higher than that of the nonlinear coupling (frequency ratio 1:2, 2:1 and 1:3, 3:1) under the elbow flexion motion of 30% MVC; the coupling strength decreases with the increase of frequency ratio for the intermuscular nonlinear coupling, and there is no significant difference between the frequency ratio : and : . The intermuscular coupling in beta and gamma bands is mainly reflected in the linear coupling (1:1), nonlinear coupling of low frequency ratio (1:2, 2:1) between synergetic pair and the linear coupling between antagonistic pairs. The results show that the wavelet packet- : coherence method can qualitatively describe the nonlinear coupling strength between muscles, which provides a theoretical reference for further revealing the mechanism of human motion control and the rehabilitation evaluation of patients with motor dysfunction.

Quantification of maternal-fetal cardiac couplings in normal and abnormal pregnancies applying high resolution joint symbolic dynamics.

Maternal psycho-physiological activities affect the fetal development and its heart rate variability. In this work, the short-term maternal-fetal cardiac couplings in normal and abnormal fetuses were investigated by using the high resolution joint symbolic dynamics method. The analysis was applied on maternal and fetal beat-to-beat intervals of 66 normal and 19 abnormal fetuses that includes different types of congenital heart defects, tachycardia, Atrioventricular block and other types of abnormalities. Results showed that the weak decrease in maternal beat-to-beat variations associated with the strong increase in fetal beat-to-beat variations was found to be significantly higher for the abnormal cases compared to normal cases despite the heterogeneity of abnormality and gestational age (abnormal: 0.032 ±0.013, normal: 0.014 ±0.007, p < 0.01). These differences could be interpreted as impairment in the autonomic nervous system in abnormal cases. The atrioventricular block cases showed a rise in the strong increase and decrease fetal beat-to-beat variations compared to the normal cases while the tachycardia cases showed a decay in these coupling patterns.

Direct and converse nonlinear magnetoelectric coupling in multiferroic composites with ferromagnetic and ferroelectric phases.

In this paper, we develop a theoretical principle to calculate the direct and converse magnetoelectric (ME) coupling response of ferromagnetic/ferroelectric composites with 2-2 connectivity. We first present an experimentally based constitutive equation for Terfenol-D, and then build the mechanism of domain switch for the ferroelectric phase. In the latter, the change of Gibbs free energy, thermodynamic driving force and kinetic equations for domain growth are also established. These two sets of constitutive equations are shown to capture the experimental data of Terfenol-D and PZT, respectively, well. For the direct effect under an applied magnetic field, the induced electric field and the overall ME coupling coefficient are determined. For the converse effect under an applied electric field, the induced magnetization and the excited magnetic field are obtained. Both the induced electric filed under direct effect and the excited magnetic field under converse effect are shown to display the hysteretic characteristics, and also in good agreement with experiments. We conclude that the developed theory can both qualitatively and quantitatively reflect the essential features of nonlinear direct and converse ME coupling of the multiferroic composites.

Global exponential synchronization of multiple coupled inertial memristive neural networks with time-varying delay via nonlinear coupling.

In this paper, global exponential synchronization of multiple coupled inertial memristive neural networks with time-varying delay is investigated. First, by choosing suitable variable substitution, the inertial memristive neural networks are transformed into first-order differential equations. Next, a novel coupling scheme with linear diffusive term and discontinuous sign function term depending on the first order derivative of state variables is introduced. Based on this coupling scheme, several sufficient conditions for global exponential synchronization of multiple inertial memristive neural networks are derived by using Lyapunov stability theory and some inequality techniques. Finally, several numerical examples are presented to substantiate the effectiveness of the theoretical results.

An improved synchronization likelihood method for quantifying neuronal synchrony.

Indirect quantification of the synchronization between two dynamical systems from measured experimental data has gained much attention in recent years, especially in the computational neuroscience community where the exact model of the neuronal dynamics is unknown. In this regard, one of the most promising methods for quantifying the interrelationship between nonlinear non-stationary systems is known as Synchronization Likelihood (SL), which is based on the likelihood of the auto-recurrence of embedding vectors (similar patterns) in multiple dynamical systems. However, synchronization likelihood method uses the Euclidean distance to determine the similarity of two patterns, which is known to be sensitive to outliers. In this study, we propose a discrete synchronization likelihood (DSL) method to overcome this limitation by using the Manhattan distance in the discrete domain (l1 norm on discretized signals) to identify the auto-recurrence of embedding vectors. The proposed method was tested using unidirectional and bidirectional identical/non-identical coupled Hénon Maps, a Watts-Strogatz small-world network with nonlinearly coupled nodes based on Kuramoto model and the real-world ADHD-200 fMRI benchmark dataset. According to the results, the proposed method shows comparable and in some cases better performance than the conventional SL method, especially when the underlying highly connected coupled dynamical system goes through subtle changes in the bivariate case or sudden shifts in the multivariate case.

Global cluster synchronization in nonlinearly coupled community networks with heterogeneous coupling delays.

This investigation establishes the global cluster synchronization of complex networks with a community structure based on an iterative approach. The units comprising the network are described by differential equations, and can be non-autonomous and involve time delays. In addition, units in the different communities can be governed by different equations. The coupling configuration of the network is rather general. The coupling terms can be non-diffusive, nonlinear, asymmetric, and with heterogeneous coupling delays. Based on this approach, both delay-dependent and delay-independent criteria for global cluster synchronization are derived. We implement the present approach for a nonlinearly coupled neural network with heterogeneous coupling delays. Two numerical examples are given to show that neural networks can behave in a variety of new collective ways under the synchronization criteria. These examples also demonstrate that neural networks remain synchronized in spite of coupling delays between neurons across different communities; however, they may lose synchrony if the coupling delays between the neurons within the same community are too large, such that the synchronization criteria are violated.

Dispersive and dissipative coupling in a micromechanical resonator embedded with a nanomechanical resonator.

A micromechanical resonator embedded with a nanomechanical resonator is developed whose dynamics can be captured by the coupled-Van der Pol-Duffing equations. Activating the nanomechanical resonator can dispersively shift the micromechanical resonance by more than 100 times its bandwidth and concurrently increase its energy dissipation rate to the point where it can even be deactivated. The coupled-Van der Pol-Duffing equations also suggest the possibility of self-oscillations. In the limit of strong excitation for the nanomechanical resonator, the dissipation in the micromechanical resonator can not only be reduced, resulting in a quality factor of >3× 10(6), it can even be eliminated entirely resulting in the micromechanical resonator spontaneously vibrating.

Measuring ensemble interdependence in a string quartet through analysis of multidimensional performance data.

In a musical ensemble such as a string quartet, the musicians interact and influence each other's actions in several aspects of the performance simultaneously in order to achieve a common aesthetic goal. In this article, we present and evaluate a computational approach for measuring the degree to which these interactions exist in a given performance. We recorded a number of string quartet exercises under two experimental conditions (solo and ensemble), acquiring both audio and bowing motion data. Numerical features in the form of time series were extracted from the data as performance descriptors representative of four distinct dimensions of the performance: Intonation, Dynamics, Timbre, and Tempo. Four different interdependence estimation methods (two linear and two nonlinear) were applied to the extracted features in order to assess the overall level of interdependence between the four musicians. The obtained results suggest that it is possible to correctly discriminate between the two experimental conditions by quantifying interdependence between the musicians in each of the studied performance dimensions; the nonlinear methods appear to perform best for most of the numerical features tested. Moreover, by using the solo recordings as a reference to which the ensemble recordings are contrasted, it is feasible to compare the amount of interdependence that is established between the musicians in a given performance dimension across all exercises, and relate the results to the underlying goal of the exercise. We discuss our findings in the context of ensemble performance research, the current limitations of our approach, and the ways in which it can be expanded and consolidated.