Assessing the Non-Linear Dynamics of a Hopf–Langford Type System

In this paper, the non-linear dynamical behavior of a 3D autonomous dissipative system of Hopf–Langford type is investigated. Through the help of a mode transformation (as the system’s energy is included) it is shown that the 3D nonlinear system can be separated of two coupled subsystems in the master (drive)-slave (response) synchronization type. After that, based on the computing first and second Lyapunov values for master system, we have attempted to give a general framework (from bifurcation theory point of view) for understanding the structural stability and bifurcation behavior of original system. Moreover, a family of exact solutions of the master system is obtained and discussed. The effect of synchronization on the dynamic behavior of original system is also studied by numerical simulations.

Coupled Nonlinear Dynamics in the Three-Mode Integrable System on a Regular Chain

The article suggests the nonlinear lattice system of three dynamical subsystems coupled both in their potential and kinetic parts. Due to its essentially multicomponent structure the system is capable to model nonlinear dynamical excitations on regular quasi-one-dimensional lattices of various physical origins. The system admits a clear Hamiltonian formulation with the standard Poisson structure. The alternative Lagrangian formulation of system’s dynamics is also presented. The set of dynamical equations is integrable in the Lax sense, inasmuch as it possesses a zero-curvature representation. Though the relevant auxiliary linear problem involves a spectral third-order operator, we have managed to develop an appropriate two-fold Darboux–Backlund dressing technique allowing one to generate the nontrivial crop solution embracing all three coupled subsystems in a rather unusual way.

Development of a hybrid SmEdA/SEA model for predicting the power exchanged between low and high modal density subsystems

Statistical modal Energy distribution Analysis (SmEdA) was developed from classical Statistical Energy Analysis (SEA). It allows computing power flow between coupled subsystems from the deterministic modes of uncoupled subsystems without assuming the SEA modal energy equipartition. SmEdA is well adapted in mid-frequency when the subsystems have not a very high modal density. However, for some systems e.g. the plate-cavity system, one subsystem can exhibit a low modal density while the other one a high one. The goal of the paper is then to propose an extension of SmEdA formulation that allows describing one subsystem by its deterministic modes, and the other one as a diffuse field statistically supposing modal energy equipartition. The uncertain subsystem is then characterized by sets of natural frequencies and mode shapes constructed based on Gaussian Orthogonal Ensemble matrix and the cross-spectrum density of a diffuse field, respectively. This formulation permits not only the computation of mean noise response but also the variance generated by the uncertainties and furthermore without bringing in much computation. It is demonstrated that the obtained analytical results from the proposed hybrid SmEdA/SEA are consistent with numerical results computed by FEM with an appropriate degree of uncertainty.

Independent Markov decomposition: Toward modeling kinetics of biomolecular complexes

To advance the mission of in silico cell biology, modeling the interactions of large and complex biological systems becomes increasingly relevant. The combination of molecular dynamics (MD) simulations and Markov state models (MSMs) has enabled the construction of simplified models of molecular kinetics on long timescales. Despite its success, this approach is inherently limited by the size of the molecular system. With increasing size of macromolecular complexes, the number of independent or weakly coupled subsystems increases, and the number of global system states increases exponentially, making the sampling of all distinct global states unfeasible. In this work, we present a technique called independent Markov decomposition (IMD) that leverages weak coupling between subsystems to compute a global kinetic model without requiring the sampling of all combinatorial states of subsystems. We give a theoretical basis for IMD and propose an approach for finding and validating such a decomposition. Using empirical few-state MSMs of ion channel models that are well established in electrophysiology, we demonstrate that IMD models can reproduce experimental conductance measurements with a major reduction in sampling compared with a standard MSM approach. We further show how to find the optimal partition of all-atom protein simulations into weakly coupled subunits.

Decentralized control for large scale systems with inherently coupled subsystems

This paper brings a novel scalable control design methodology for Large-Scale Systems. Such systems are considered as multi-agent systems with inherent interactions between neighboring agents. The presented design methodology uses single-agent dynamics and their interaction topology, rather than relying on the model of the entire system. The dimension of the design problem therefore remains the same with growing number of agents. This allows a feasible control design even for large systems. Moreover, the proposed design is based on simple Linear Matrix Inequalities, efficiently solvable using standard computational tools. Numerical results validate the proposed approach.

Closeness-centrality-correlation for detecting interdependency between coupled systems

Generalized synchronization is a common interdependency between coupled systems which exists in many branches of life, social and physical science. In this paper, a novel method, called closeness-centrality-correlation is proposed for the detection of this interdependency. The proposed method is based on a global network measure (i.e., closeness centrality) of recurrence networks resulting from time series. We illustrate the feasibility of the proposed method using a paradigmatic coupled model and compare its performance to other commonly used interdependency methods. The numerical results show that the proposed method is quite satisfactory for detecting interdependency and outperforms the existing joint probability of recurrence method especially for the case that the dynamics of the two coupled subsystems are significantly different. Moreover, through analyzing the time series contaminated by white noise, we demonstrate that our method is robust against white noise. Finally, an application to recorded electroencephalogram data shows that the proposed measure is more reliable to detect the transitions of the interdependencies among the noisy electroencephalogram time series and thus provides longer pre-warning time for the onset of epilepsy.

Nonlinear substructuring in the modal domain: numerical validation and experimental verification in presence of localized nonlinearities

In many systems of interest, most of the structure is well approximated as linear but some parts must be treated as nonlinear to get accurate response predictions: significant nonlinear effects are due to the connections between coupled subsystems, such as in automotive or aerospace structures. The present work aims at predicting the nonlinear behavior of coupled systems using a substructuring technique in the modal domain. This study focuses on the effects of nonlinear connections on the dynamics of an assembly in which the coupled subsystems can be considered as linear. Each connection is instead considered as a quasi-linear substructure with stiffness that is function of amplitude or energy. The iterative procedure used here is enhanced with respect to previous works by enforcing a better control of the total energy at each iteration allowing to obtain the solution for a prescribed set of energy levels. Also, the initial guess and the convergence criterion have been modified to speed up the procedure. This technique is applied to a system made of two continuous linear subsystems coupled by nonlinear connections. The numerical results of the coupling are first compared to the ones obtained by using the Harmonic Balance technique on the model of the complete assembly to evaluate its effectiveness and understand the effects of modal truncation. Besides, a nonlinear connecting element, specifically designed in order to have a nearly cubic hardening behavior, is used in an experimental setup. Substructuring results are compared to experimental results measured on the assembled system, in order to evaluate the correlation between mode shapes and the accuracy in the resonance frequency at several excitation levels.

Analysis of Random Mechanical Vibrations in Symmetrical Thin Plates Using Full-Field Vibration Measurements

A successful application of statistical energy analysis for analyzing energy exchanges between weakly coupled subsystems theoretically requires a diffuse vibrational field in all subsystems. So as to verify the conditions of establishment of the diffuse field in practice, full-field vibration measurements were conducted with a high-speed camera on a simply supported rectangular plate excited by a wide band random force. The results constitute an experimental investigation of the diffuse field region in the frequency-structural damping domain and a validation of previously obtained numerical results. The domain of the diffuse field is confined to high frequencies and low damping, with limits than can be easily defined. However, it is shown that the vibrational field is not fully spatially homogeneous due to enhancement of response induced by the effect of coherence of rays. Theoretical values of the enhancement factor obtained using an image source analysis are confirmed by measurement results.

Multisystem Optimization for an Integrated Production Scheduling with Resource Saving Problem in Textile Printing and Dyeing

Resource saving has become an integral aspect of manufacturing in industry 4.0. This paper proposes a multisystem optimization (MSO) algorithm, inspired by implicit parallelism of heuristic methods, to solve an integrated production scheduling with resource saving problem in textile printing and dyeing. First, a real-world integrated production scheduling with resource saving is formulated as a multisystem optimization problem. Then, the MSO algorithm is proposed to solve multisystem optimization problems that consist of several coupled subsystems, and each of the subsystems may contain multiple objectives and multiple constraints. The proposed MSO algorithm is composed of within-subsystem evolution and cross-subsystem migration operators, and the former is to optimize each subsystem by excellent evolution operators and the later is to complete information sharing between multiple subsystems, to accelerate the global optimization of the whole system. Performance is tested on a set of multisystem benchmark functions and compared with improved NSGA-II and multiobjective multifactorial evolutionary algorithm (MO-MFEA). Simulation results show that the MSO algorithm is better than compared algorithms for the benchmark functions studied in this paper. Finally, the MSO algorithm is successfully applied to the proposed integrated production scheduling with resource saving problem, and the results show that MSO is a promising algorithm for the studied problem.