High-dimensional Nonlinear Dynamics Research Articles

Wavelength-tunable soliton molecule in spatiotemporal mode-locked Yb-doped fiber laser

Spatiotemporal mode-locking (STML) fiber lasers could realize the synchronized locked of multiple transverse and longitudinal modes, which could be regarded as an ideal platform to investigate high-dimensional nonlinear dynamics. The observation of STML in the soliton molecule state could offer a unique opportunity to reveal the mechanism of molecular complexity. Due to the distinctive spatiotemporal characteristics, realizing the wavelength tunable of soliton molecule in STML fiber laser is still challenging. In this letter, we report wavelength-tunable soliton molecules in an STML Yb-doped fiber laser. By rotating the wave plates at a fixed pump power, both single dissipative soliton (SDS) and various soliton molecules, including loose bounded dissipative soliton pairs (BDSPs), tight BDSPs, soliton molecules of triplet pulses or soliton molecules of quadruplets pulses, have all realized wavelength tunable with a tuning range of ∼25 nm. The realization of the wavelength tunable and the formation of the soliton molecule can all be attributed to the tunable comb filter and saturable absorber induced by the nonlinear polarization rotation technique. The formation of SDS and BDSPs was further confirmed by the numerical simulations. And the numerical results contribute to further comprehending the nonlinear dynamics of the STML fiber laser.

Promoting synchrony of power grids by restructuring network topologies.

The optimization of synchronization on distributed power grids is an important topic in recent years. We extensively study the optimization by restructuring grid topology in terms of connection rewirings. Due to the node-link dual property of power networks, i.e., the intrinsic generator-load dynamics of nodes and the multiple-attribute connections, we propose the frequency-correlation-optimization scheme to get grid topology with the largest anti-correlation by targeting the frequency-correlation function among nodes. The topology optimizations on both sparse and dense networks are successfully realized. The optimized topology exhibits more generator-consumer connections, indicating that a decentralization of the distribution of generator nodes on power grids favors synchronizability. The benefits of these frequency-correlation-optimized power grids to synchrony are verified. By comparing with the phase-coherence-optimization scheme that favors both the optimal topology and efficient synchronizability, we show that the frequency-correlation optimization and the phase-coherence optimization of power grids are usually compatible, while the former is more efficient and simpler in avoiding tedious simulations of high-dimensional nonlinear dynamics. Our explorations may shed light on the predesign and construction of modern distributed power grids, which are composed of decentralized miscellaneous power sources.

Output feedback model predictive control of spacecrafts based on proportional-integral observer

A novel attitude control algorithm is developed for spacecrafts based on the model predictive control and proportional-integral observer (PIO) in the presence of constraints. The high dimensional nonlinear dynamics are firstly transformed into three single-input single-output linear structural subsystems with coupled actions. Then these actions are viewed as disturbances estimated by the PIOs, and their values are embedded into the models to improve the accuracy of prediction. The predictive controller is composed of the analytical solution and the heuristic constraint handling. In addition, the angular position information is only needed for implementation. Finally, several simulations are used to verify the effectiveness of the developed algorithm. The results show that the designed system compensates the coupled actions well and makes the attitude control performance good.

Sparse identification of nonlinear dynamics with low-dimensionalized flow representations

We perform a sparse identification of nonlinear dynamics (SINDy) for low-dimensionalized complex flow phenomena. We first apply the SINDy with two regression methods, the thresholded least square algorithm and the adaptive least absolute shrinkage and selection operator which show reasonable ability with a wide range of sparsity constant in our preliminary tests, to a two-dimensional single cylinder wake at$Re_D=100$, its transient process and a wake of two-parallel cylinders, as examples of high-dimensional fluid data. To handle these high-dimensional data with SINDy whose library matrix is suitable for low-dimensional variable combinations, a convolutional neural network-based autoencoder (CNN-AE) is utilized. The CNN-AE is employed to map a high-dimensional dynamics into a low-dimensional latent space. The SINDy then seeks a governing equation of the mapped low-dimensional latent vector. Temporal evolution of high-dimensional dynamics can be provided by combining the predicted latent vector by SINDy with the CNN decoder which can remap the low-dimensional latent vector to the original dimension. The SINDy can provide a stable solution as the governing equation of the latent dynamics and the CNN-SINDy-based modelling can reproduce high-dimensional flow fields successfully, although more terms are required to represent the transient flow and the two-parallel cylinder wake than the periodic shedding. A nine-equation turbulent shear flow model is finally considered to examine the applicability of SINDy to turbulence, although without using CNN-AE. The present results suggest that the proposed scheme with an appropriate parameter choice enables us to analyse high-dimensional nonlinear dynamics with interpretable low-dimensional manifolds.

Model-Predictive Control With Inverse Statics Optimization for Tensegrity Spine Robots

Robots with flexible spines based on tensegrity structures have potential advantages over traditional designs with rigid torsos. However, these robots can be difficult to control due to their high-dimensional nonlinear dynamics and actuator constraints. This article presents two controllers for tensegrity spine robots, using model-predictive control (MPC) and inverse statics (IS) optimization. The controllers introduce two different approaches to making the control problem computationally tractable. The first utilizes smoothing terms in the MPC problem. The second uses a new IS optimization algorithm, which gives the first feasible solutions to the problem for certain tensegrity robots, to generate reference input trajectories in combination with MPC. Tracking the IS reference input trajectory significantly reduces the number of tuning parameters. The controllers are validated against simulations of 2-D and 3-D tensegrity spines. Both approaches show noise insensitivity and low tracking error and can be used for different control goals. The results here demonstrate the first closed-loop control of such structures.

Crisis route to chaos in semiconductor lasers subjected to external optical feedback

Semiconductor lasers subjected to optical feedback have been intensively used as archetypical testbeds for high-speed (sub-ns) and high-dimensional nonlinear dynamics. By simultaneously extracting all the dynamical variables, we demonstrate that for larger current, the commonly named ``quasiperiodic'' route is in fact based on mixed external-cavity solutions that lock the oscillation frequency of the intensity, voltage, and separation in optical frequency through a mechanism involving successive rejections along the unstable manifold of an antimode. We show that chaos emerges from a crisis resulting from the inability to maintain locking as the unstable manifold becomes inaccessible.

Detecting the relevance to performance of whole-body movements

Goal-directed whole-body movements are fundamental in our daily life, sports, music, art, and other activities. Goal-directed movements have been intensively investigated by focusing on simplified movements (e.g., arm-reaching movements or eye movements); however, the nature of goal-directed whole-body movements has not been sufficiently investigated because of the high-dimensional nonlinear dynamics and redundancy inherent in whole-body motion. One open question is how to overcome high-dimensional nonlinear dynamics and redundancy to achieve the desired performance. It is possible to approach the question by quantifying how the motions of each body part at each time point contribute to movement performance. Nevertheless, it is difficult to identify an explicit relation between each motion element (the motion of each body part at each time point) and performance as a result of the high-dimensional nonlinear dynamics and redundancy inherent in whole-body motion. The current study proposes a data-driven approach to quantify the relevance of each motion element to the performance. The current findings indicate that linear regression may be used to quantify this relevance without considering the high-dimensional nonlinear dynamics of whole-body motion.

Nonlinear dynamic analysis of the whole vehicle on bumpy road

Through the research into the characteristics of 7-DoF high dimensional nonlinear dynamics of a vehicle on bumpy road, the periodic movement and chaotic behavior of the vehicle were found. The methods of nonlinear frequency response analysis, global bifurcation, frequency chart and Poincare maps were used simultaneously to derive strange super chaotic attractor. According to Lyapunov exponents calculated by Gram-Schmidt method, the unstable region was compartmentalized and the super chaotic characteristic of the nonlinear system was verified. Numerical results by 4-order Runge-Kutta method presented the multiform dynamic behavior of the system.

Proccedings of the conference on New Aspects of High-dimensional Nonlinear Dynamics

Proccedings of the conference on New Aspects of High-dimensional Nonlinear Dynamics

Learning dynamics from nonstationary time series: analysis of electroencephalograms.

We propose an empirical modeling technique for a nonstationary time series analysis. Proposed methods include a high-dimensional (N>3) dynamical model construction in the form of delay differential equations, a nonparametric method of respective time delay calculation, the detection of quasistationary regions of the process by recurrence analysis in the space of model coefficients, and final fitting of the model to quasistationary segments of observed time series. We also demonstrate the effectiveness of our approach for nonstationary signal classification in the space of model coefficients. Applying the empirical modeling technique to electroencephalogram (EEG) records analysis, we find evidence of high-dimensional nonlinear dynamics in quasistationary EEG segments. Recurrence analysis of model parameters reveals long-term correlations in nonstationary EEG records. Using the dynamical model as a nonlinear filter, we find that different emotional states of subjects can be clearly distinguished in the space of model coefficients.