Types Of Dynamical Behavior Research Articles

(2+1)-dimensional two-component soliton excitations and their dynamical evolutions for the partially nonlocal nonlinearity

The (2+1)-dimensional two-component nonlocal solitons of coupled nonlinear Schrödinger equation with the partially nonlocal nonlinearity are analytically obtained. Two component optical fields exhibit different types of dynamical behaviors. The dark soliton and bright soliton for two field components describe two co-propagating fields at different frequencies and they are both quickly stabilized to propagate parallel to the z-axis after the initial oscillations. Superposed rogue waves in bright soliton and dark soliton are also constructed for two field components.

Grazing and Symmetry-Breaking Bifurcations Induced Oscillations in a Switched System Composed of Duffing and van der Pol Oscillators

By introducing a switching scheme related to the state and time, a typical switched model alternating between a Duffing oscillator and van der Pol oscillator is established to explore the typical dynamical behaviors as well as the mechanism of the switched system. Shooting methods to locate the limit cycle and specify bifurcation sets are described by defining an appropriate Poincaré map. Different types of multiple-Focus/Cycle and single-Focus/Cycle period oscillations in the system can be observed. Symmetry-breaking, period-doubling, and grazing bifurcation curves are obtained in the plane of bifurcation parameters, dividing the parameters plane into several regions corresponding to different kinds of oscillations. Meanwhile, based on the numerical simulation and bifurcation analysis, the mechanisms of several typical dynamical behaviors observed in different regions are presented.

Numerical Modelling of the Dynamic Voltage in HTS Materials under the Action of DC Transport Currents and Different Oscillating Magnetic Fields.

The dynamic voltage is a unique phenomenon of superconducting materials. It arises when the superconductor is carrying a DC transport current and spontaneously in subject to an AC magnetic field. This study excavates the aspects that previous studies have not comprehensively investigated: the dynamic voltage in a DC-carrying superconducting tape exposed to different oscillating AC magnetic fields. First, the fundamental physics of dynamic voltage/flux of superconductors is reviewed and further analysed in detail. We used the superconducting modelling method using the H-formulation merged into the finite-element method (FEM) software, to re-produce the typical dynamic voltage behaviour of a superconducting tape. The modelling was verified by both the analytical and experimental results, in order to precisely prove the reliability of the modelling. Afterwards, the modelling was performed for a DC-carrying superconducting tape under four different oscillating magnetic fields (sine, triangle, sawtooth and square), and their corresponding dynamic voltages and energy losses were analysed and compared. Results show the sinusoidal magnetic field can lead to the optimal combination of reasonable dynamic voltage but relatively lower loss, which is suitable for those superconducting applications requiring dynamic voltage as the energy source, e.g., flux pumps. This article presents novel investigation and analysis of the dynamic voltage in superconducting materials, and both the methodology and results can provide useful information for the future design/analysis of superconducting applications with DC transport currents and AC magnetic fields.

Dynamical behavior of cardiac conduction system under external disturbances: simulation based on microcontroller technology

The heart rhythm is one of the most interesting aspects of the dynamic behavior of biological systems. Understanding heart rhythms is essential in the dynamic analysis of the heart. Each type of dynamic behaviour can describe normal or pathological physiology. The heart is made up of nodes ranging from SA node (natural pacemaker) to Purkinje fibers. The electric current originates in the sinus node and travels through the heart until it reaches the Purkinje fibers, causing after its passage through each of the nodes a heartbeat thus constituting the electrocardiogram (ECG). Since the origin of the electric current is the sinus node, in this article we study numerically and experimentally by microcontroller the influence of the sinus node on the propagation of electric current through the heart. A study of the sinus node in its autonomous state shows us that in their coupled state, the nodes of the heart qualitatively reproduce the time series of the action potential of this latter, which leads to the recording of the ECG. A study when the sinus node is subjected to periodic pulsed excitation assumed to come from blood pressure, with the blood pressure, shows that for some selected frequencies, it is found that the nodes of the heart and the ECG exhibit responses having the same shape and the same frequencies as those of the pulsatile blood pressure. This suggests the possibility of using such a conversion and excitation mechanism to replicate the functioning of cardiac conduction system. The chaotic analysis of the sinus node subjected to a sinusoidal type disturbance is also presented, it shows that in its chaotic state, the nodes of the heart, as well as the ECG, provide very high frequency signals. This requires the control of the sinus node (natural pacemaker) in such a situation.

Cavitation Dynamics and Inertial Cavitation Threshold of Lipid Coated Microbubbles in Viscoelastic Media with Bubble-Bubble Interactions.

Encapsulated microbubbles combined with ultrasound have been widely utilized in various biomedical applications; however, the bubble dynamics in viscoelastic medium have not been completely understood. It involves complex interactions of coated microbubbles with ultrasound, nearby microbubbles and surrounding medium. Here, a comprehensive model capable of simulating the complex bubble dynamics was developed via taking the nonlinear viscoelastic behaviors of the shells, the bubble–bubble interactions and the viscoelasticity of the surrounding medium into account simultaneously. For two interacting lipid-coated bubbles with different initial radii in viscoelastic media, it exemplified that the encapsulating shell, the inter-bubble interactions and the medium viscoelasticity would noticeably suppress bubble oscillations. The inter-bubble interactions exerted a much stronger suppressing effect on the small bubble within the parameters examined in this paper, which might result from a larger radiated pressure acting on the small bubble due to the inter-bubble interactions. The lipid shells make the microbubbles exhibit two typical asymmetric dynamic behaviors (i.e., compression or expansion dominated oscillations), which are determined by the initial surface tension of the bubbles. Accordingly, the inertial cavitation threshold decreases as the initial surface tension increases, but increases as the shell elasticity and viscosity increases. Moreover, with the distance between bubbles decreasing and/or the initial radius of the large bubble increasing, the oscillations of the small bubble decrease and the inertial cavitation threshold increases gradually due to the stronger suppression effects caused by the enhanced bubble–bubble interactions. Additionally, increasing the elasticity and/or viscosity of the surrounding medium would also dampen bubble oscillations and result in a significant increase in the inertial cavitation threshold. This study may contribute to both encapsulated microbubble-associated ultrasound diagnostic and emerging therapeutic applications.

The Role of Random Structures in Tissue Formation: From a Viewpoint of Morphogenesis in Stochastic Systems

In this article, we investigate a type of biological tissue formation system with a random structure of reaction or/and diffusion, analyzing the connection with the results obtained in [Rajapakse & Smale, 2017a] for the corresponding deterministic systems and showing the major difference from these results. Interestingly, we find a dynamical phenomenon leading to morphogenesis or emergence in such a system. Also we find their transitions in this system, while only one type of dynamical behavior occurs for the deterministic systems that satisfy typical conditions. Using the stability theory of stochastic systems, we quantitatively elucidate how such a phenomenon is emergent in complex networks with random structures. We believe that our analytical results could be beneficial to understand the underlying mechanisms of complexity-induced functions in tissue formation within real environments.

Dynamic characteristics of droplet impingement on carbon nanotube array surfaces with varying wettabilities

This work experimentally investigated the water droplet impingement behaviors on carbon nanotube (CNT) array surfaces characterized by different wettabilities from hydrophilicity to superhydrophobicity. By varying the impact velocity, six typical dynamic behaviors of droplet impact were identified and a related droplet regime map was developed under different wettabilities. To further investigate the evolution behavior of droplet impact, the dynamic contact angle (DCA) and spreading factor were measured and analyzed. The damped oscillations of DCA were observed for wettable and mildly hydrophobic CNT array surfaces, while the approximate impact inertia independence was verified for high hydrophobicity or even superhydrophobicity. The contact line velocity in the vicinity of triple phase interface was found to be highly related to the DCA variation at the initial stage of spreading. The discrepancy of DCA on different wettable surfaces reduced significantly with the increase of Weber number. The reduction in post-impact CAs and resultant wettability enhancement after droplet impingement was mainly attributed to self-assembly structures caused by the capillary action during the spreading phase.

Experimental study on permanent deformation characteristics of coarse-grained soil under repeated dynamic loading

Practical assessment of subgrade settlement induced by train operation requires developing suitable models capable of describing permanent deformation characteristics of subgrade filling under repeated dynamic loading. In this paper, repeated load triaxial tests were performed on coarse-grained soil (CGS), and the axial permanent strain of CGS under different confining pressures and dynamic stress amplitudes was analysed. Permanent deformation behaviors of CGS were categorized based on the variation trend of permanent strain rate with accumulated permanent strain and the shakedown theory. A prediction model of permanent deformation considering stress state and number of load cycles was established, and the ranges of parameters for different types of dynamic behaviors were also divided. The results indicated that the variational trend of permanent strain rate with accumulated permanent strain can be used as a basis for classifying dynamic behaviors of CGS. The stress state (confining pressure and dynamic stress amplitude) has significant effects on the permanent strain rate. The accumulative characteristics of permanent deformation of CGS with the number of load cycles can be described by a power function, and the model parameters can reflect the influence of confining pressure and dynamic stress amplitude. The study’s results could help deepen understanding of the permanent deformation characteristics of CGS.

From Pseudostreamer Jets to Coronal Mass Ejections: Observations of the Breakout Continuum

Abstract The magnetic breakout model, in which reconnection in the corona leads to destabilization of a filament channel, explains numerous features of eruptive solar events, from small-scale jets to global-scale coronal mass ejections (CMEs). The underlying multipolar topology, pre-eruption activities, and sequence of magnetic-reconnection onsets (first breakout, then flare) of many observed fast CMEs/eruptive flares are fully consistent with the model. Recently, we demonstrated that most observed coronal-hole jets in fan/spine topologies also are induced by breakout reconnection at the null point above a filament channel (with or without a filament). For these two types of eruptions occurring in similar topologies, the key question is, why do some events generate jets while others form CMEs? We focused on the initiation of eruptions in large bright points/small active regions that were located in coronal holes and clearly exhibited null-point (fan/spine) topologies: such configurations are referred to as pseudostreamers. We analyzed and compared Solar Dynamics Observatory/Atmospheric Imaging Assembly, Solar and Heliospheric Observatory/Large Angle and Spectrometric Coronagraph Experiment, and Reuven Ramaty High Energy Solar Spectroscopic Imager observations of three events. Our analysis of the events revealed two new observable signatures of breakout reconnection prior to the explosive jet/CME outflows and flare onset: coronal dimming and the opening up of field lines above the breakout current sheet. Most key properties were similar among the selected erupting structures, thereby eliminating region size, photospheric field strength, magnetic configuration, and pre-eruptive evolution as discriminating factors between jets and CMEs. We consider the factors that contribute to the different types of dynamic behavior, and conclude that the main determining factor is the ratio of the magnetic free energy associated with the filament channel compared to the energy associated with the overlying flux inside and outside the pseudostreamer dome.

Dynamic behavior analysis of a mechanical system with two unstable modes coupled to a single nonlinear energy sink

This paper investigates a problem of passive mitigation of vibratory instabilities caused by two unstable modes by means of a single nonlinear energy sink (NES). For this purpose, a linear four-degree-of-freedom (DOF) primary structure having two unstable modes (reproducing the typical dynamic behavior of a friction system) and undergoing, as it is linear, unbounded motions when it is unstable, is coupled to a NES. In this work, the NES involves an essentially cubic restoring force and a linear damping force. We are interested in characterizing analytically the response regimes resulting from the coupling of the two unstable linear modes of the primary structure and the nonlinear mode of the NES. To this end, from a suitable rescaling of the governing equations of the coupled system in which the dynamics of the primary structure is reduced to its unstable modal coordinates, the complexification-averaging method is applied. The resulting averaged system appears to be a fast-slow system with four fast variables and two slow ones related to the two unstable modes of the primary structure. The critical manifold of the averaged dynamics is obtained through the geometric singular perturbation theory and appears as a two-dimensional parametric surface (with respect to two of the four fast variables) which evolves in the whole six-dimensional variable space. The asymptotic analysis reveals that the NES attachment can produce some bounded responses and suggests that the system may have simultaneous stable attractors. Numerical simulations complement the study, highlighting a possible competition between stable attractors and allowing us to investigate their basins of attraction. In each considered situation, a good agreement has been observed between theoretical results and numerical simulations, which validates the proposed asymptotic analysis.

Bifurcations and chaos in nonlinear Lindblad equations

The Lindblad equation describes the dissipative time evolution of a density matrix that characterizes an open quantum system in contact with its environment. The widespread ensemble interpretation of a density matrix requires its time evolution to be linear. However, when the dynamics of the density matrix is of a quantum system results not only from the interaction with an external environment, but also with other quantum systems of the same type, the ensemble interpretation is inappropriate and nonlinear dynamics arise naturally. We therefore study the dynamical behavior of nonlinear Lindblad equations using the example of a two-level system. By using techniques developed for classical dynamical systems we show that various types of bifurcations and even chaotic dynamics can occur. As specific examples that display the various types of dynamical behavior, we suggest explicit models based on systems of interacting spins at finite temperature and exposed to amagnetic field that can change in dependence of the magnetization. Due to the interaction between spins, which is treated at mean-field level, the Hamiltonian as well as the transition rates of the Lindblad equation become dependent on the density matrix.

Spatially and Temporally Resolved Heterogeneities in a Miscible Polymer Blend.

Mapping the spatial and temporal heterogeneities in miscible polymer blends is critical for understanding and further improving their material properties. However, a complete picture on the heterogeneous dynamics is often obscured in ensemble measurements. Herein, the spatial and temporal heterogeneities in fully miscible polystyrene/oligostyrene blend films are investigated by monitoring the rotational diffusion of embedded individual probe molecules using defocused wide-field fluorescence microscopy. In the same blend film, three significantly different types of dynamical behaviors (referred to as modes) of the probe molecules can be observed at the same time, namely, immobile, continuously rotating, and intermittently rotating probe molecules. This reveals a prominent spatial heterogeneity in local dynamics at the nanometer scale. In addition to that, temporal heterogeneity is uncovered by the nonexponential characteristic of the rotational autocorrelation functions of single-molecule probes. Moreover, the occurrence probabilities of these different modes strongly depend on the polystyrene: oligostyrene ratios in the blend films. Remarkably, some probe molecules switch between the continuous and intermittent rotational modes at elevated temperature, indicating a possible alteration in local dynamics that is triggered by the dynamic heterogeneity in the blends. Although some of these findings can be discussed by the self-concentration model and the results provided by ensemble averaging techniques (e.g., dielectric spectroscopy), there are implications that go beyond current models of blend dynamics.

Bifurcations and chaos in nonlinear Lindblad equations

The Lindblad equation describes the dissipative time evolution of a density matrix that characterizes an open quantum system in contact with its environment. The widespread ensemble interpretation of a density matrix requires its time evolution to be linear. However, when the dynamics of the density matrix is of a quantum system results not only from the interaction with an external environment, but also with other quantum systems of the same type, the ensemble interpretation is inappropriate and nonlinear dynamics arise naturally. We therefore study the dynamical behavior of nonlinear Lindblad equations using the example of a two-level system. By using techniques developed for classical dynamical systems we show that various types of bifurcations and even chaotic dynamics can occur. As specific examples that display the various types of dynamical behavior, we suggest explicit models based on systems of interacting spins at finite temperature and exposed to a magnetic field that can change in dependence of the magnetization. Due to the interaction between spins, which is treated at mean-field level, the Hamiltonian as well as the transition rates of the Lindblad equation become dependent on the density matrix.

Local dynamic behaviors of long 0-π Josephson junction

The mathematical discontinuity existing in the phase-difference dynamic model for the Josephson junction results in the challenge of the dynamic analysis on the Josephson junction. Focusing on the non-smooth characteristics of the dynamic model for the long 0-π Josephson junction, two typical local dynamic behaviors, including the moving breather and the semifluxon interaction, are investigated by the structure-preserving approach based on the multi-symplectic idea in this paper. Firstly, the symmetric form with two segmented local conservation laws is derived form the non-smooth sine-Gordon-type model controlling the evolution of the phase-difference in the long 0-π Josephson junction. And then, the numerical experiments on the above local dynamic behaviors are performed using the proposed structure-preserving approach. The novel discoveries on the local dynamic behaviors of the long 0-π Josephson junction include: The non-dissipative characteristic of the moving breather that revises the widely accepted conclusion on the dissipative characteristic of the moving breather, and the asymmetric phase jumps for the pinned semifluxons that can be used to comprehend the anharmonic supercurrent in the Josephson junction. The above findings on the local dynamic behaviors of the long 0-π Josephson junction will give some guidance on the design of digital single flux quantum circuits.

Finite-time function projective synchronization control method for chaotic wind power systems

Wind power is a rapidly growing renewable energy source that plays an increasingly important role in power systems. However, its dynamic behaviors are complex because of the instability of wind speed, strong coupling, highly nonlinear subsystems, and mass grid connections. Chaotic oscillation is one of the most typical complex dynamic behaviors of wind power systems. This behavior can seriously influence the stable operation of wind power systems and cause great harm. This study proposed a control method for finite-time function projective synchronization on the basis of the chaos synchronization principle and finite-time theory for wind power systems. Wind power systems with or without uncertain parameters were considered. First, we built a high-dimensional wind power system and analyzed its chaotic behaviors. Lyapunov exponents were derived to prove the existence of chaos and bifurcation. Second, we aimed to increase the robustness of the controller by adding parameter observers to the controller. The result helped solve the problem of unknown parameters. If a wind power system comprises unknown parameters, the unknown parameters can be defined as the system's states. An unknown parameter observer was designed to realize the identification of unknown parameters. Third, we proposed a control method for finite-time function projective synchronization. Finite-time stability theory and function projective synchronization theory were used to construct the controller. These theories can ensure the quick synchronization of a chaotic wind power system with a stable wind power system in finite time. Finally, the mathematical proof of the stability theorem was derived, and a corresponding numerical simulation was performed to validate the chaos control method for wind power systems.

Estimation of Dynamic Networks for High-Dimensional Nonstationary Time Series.

This paper is concerned with the estimation of time-varying networks for high-dimensional nonstationary time series. Two types of dynamic behaviors are considered: structural breaks (i.e., abrupt change points) and smooth changes. To simultaneously handle these two types of time-varying features, a two-step approach is proposed: multiple change point locations are first identified on the basis of comparing the difference between the localized averages on sample covariance matrices, and then graph supports are recovered on the basis of a kernelized time-varying constrained -minimization for inverse matrix estimation (CLIME) estimator on each segment. We derive the rates of convergence for estimating the change points and precision matrices under mild moment and dependence conditions. In particular, we show that this two-step approach is consistent in estimating the change points and the piecewise smooth precision matrix function, under a certain high-dimensional scaling limit. The method is applied to the analysis of network structure of the S&P 500 index between 2003 and 2008.

Recursive Exponential Slow Feature Analysis for Fine-Scale Adaptive Processes Monitoring With Comprehensive Operation Status Identification

Due to the compensation of the control loops, industrial processes under feedback control generally reveal typical dynamic behaviors for different operation statuses. Conventional adaptive methods may update model falsely and thus result in invalid monitoring results, since they cannot effectively extract the feedback dynamic information and fail to accurately differentiate real anomalies from normal process changes. In this study, a recursive exponential slow feature analysis (ESFA) algorithm is developed for fine-scale adaptive monitoring to solve the problem of false model updating. First, an ESFA method is proposed to nonlinearly extract slow features, so that the general trend of the process variations can be better captured. On the basis of the ESFA model, a fine-scale adaptive monitoring scheme is developed to accurately capture the normal changes of industrial processes, including normal slow varying and normal shift of operation conditions. In this way, the normal slow varying can be effectively distinguished from incipient faults with unusual dynamic behaviors to avoid falsely adapting for the fault case, and the monitoring model can be correctly updated for new operation status after distinguishing real process anomalies from normal shifts of operation conditions. A simulation process and two real industrial processes are adopted to validate the performance of the proposed adaptive monitoring method. Experimental results show that the proposed method can effectively identify different operation statuses to decide whether to update the monitoring model or to raise an alarm.

Stabilization and circuit implementation of a novel chemical oscillating chaotic system

Purpose This paper is aimed at investigating a novel chemical oscillating chaotic system with different attractors at fixed parameters. The typical dynamical behavior of the new chemical oscillating system is discussed, and it is found that the state selection is dependent on initial values. Then, the stabilization problem of the chemical oscillating attractors is investigated analytically and numerically. Subsequently, the novel electronic circuit of the proposed chemical oscillating chaotic system are constructed, and the influences of the changes of circuit parameters on chemical oscillating chaotic attractors are investigated. Design/methodology/approach The different attractors of the novel chemical oscillating chaotic system are investigated by changing the initial values under fixed parameters. Moreover, the active control and adaptive control methods are presented to make the chemical oscillating chaotic systems asymptotically stable at the origin based on the Lyapunov stability theory. The influences on chemical oscillating chaotic attractors are also verified by changing the circuit parameters. Findings It is found that the active control method is easier to be realized by using physical components because of its less control signal and lower cost. It is also confirmed that the adaptive control method enjoys strong anti-interference ability because of its large number of selected controllers. What can be seen from the simulation results is that the chaotic circuits are extremely dependent on circuit parameters selection. Comparisons between MATLAB simulations and Multisim simulation results show that they are consistent with each other and demonstrate that changing attractors of the chemical oscillating chaotic system exist. It is conformed that circuit parameters selection can be effective to control and realize chaotic circuits. Originality/value The different attractors of the novel chemical oscillating chaotic system are investigated by changing the initial values under fixed parameters. The characteristic of the chemical oscillating attractor is that the basin of attraction of the three-dimensional attractor is located in the first quadrant of the eight quadrants of the three-dimensional space, and the ranges of the three variables are positive. This is because the concentrations of the three chemical substances are all positive.

Improving performance: recent progress on vibration-driven locomotion systems

Improving locomotion performance is the primary objective in studying vibration-driven locomotion systems. In this paper, we report out recent progress within this topic from three aspects. First, dry friction-induced stick-slip motions, which are typical non-smooth dynamical behaviors, are analyzed and categorized based on sliding bifurcation analysis, and the sticking feature of the system is utilized to achieve directional locomotion as well as to increase average locomotion speed without additional energy input. Second, a strong global nonlinearity, bistability, is introduced into the internal oscillation, with which, unique benefits are obtained, including broad frequency bandwidth for high average locomotion speed and multiple locomotion modes. Third, by incorporating two internal oscillators into the system, planar locomotion capability is acquired; various trajectories can be executed by simply tuning the frequencies of the two internal oscillators. In addition to theoretical and numerical efforts, based on our designed prototypes, the proposed strategies and the achieved performance boosts are experimentally verified. We believe that this progress report, along with the discussions on challenging issues and directions worth exploring, could serve as a solid foundation and useful guideline of future research.

Numerical investigations on crack propagation and crack branching in brittle solids under dynamic loading using bond-particle model

In this article, the bond-particle methodology (BPM) is applied to investigate the crack propagation and crack branching, which is belong to dynamic fracture instabilities, in PMMA brittle solids under dynamic loading. The microscopic parameters in BPM are first calibrated using the comparison with the previous experimental results not only in the field of qualitative analysis, but also in the field of quantitative analysis. The calibrating process illustrates that the selected microscopic parameters in BPM are suitable to effectively and accurately simulate dynamic fracture process in PMMA brittle solids subjected to dynamic loads. Then, the typical dynamic fracture behaviors of solids under dynamic loading are reproduced by BPM. Compared with the previous experimental and numerical results, the present numerical results are in good agreement with the existing ones not only in the field of qualitative analysis, but also in the field of quantitative analysis. Finally, the effects of dynamic loading magnitude, offset distance of the initial crack and initial crack length on dynamic fracture behaviors, including dynamic fracture patterns and critical crack propagation speed in brittle solids under dynamic loading are numerically investigated.