Nonlinear Dynamics Research Articles

NONLINEAR DYNAMICS METHODS APPLICATIONS TO PRODUCT LIFECYCLE MANAGEMENT

The research being carried out is aimed at applying nonlinear dynamics methods in product life cycle management to improve communication between processes and achieve environmental sustainability. The purpose of the article is to create a nonlinear mathematical model for analysing product lifecycle management. Chaotic nonlinear dynamical processes of product lifecycle are deterministic but have the property that even small uncertainties in initial conditions lead to exponentially growing errors in the management that limit long-term forecasts. The emergence of chaotic behaviour in processes of product lifecycle was explored, focusing on fluctuations. The study employed methods such as systems analysis, correlation analysis, nonlinear dynamics, and the Surrogate model of chaotic Lorenz waterwheel. It was identified that sharp technological innovations as the primary drivers of short-term fluctuations impacting fixed efficiency and effectiveness of product life cycle process development. The resulting nonlinear dynamic model allowed for flexible operation, transitioning between equilibrium, periodic, and chaotic states based on coefficient values for asset growth rates and time constants reflecting product life cycle process dynamics. The research results are valuable for companies seeking to reduce their environmental impact and implement circular economy principles.

INTELLIGENT INFORMATION TECHNOLOGIES TO SUPPORT DECISION-MAKING WHEN APPLYING THE CAD/CAM/CAE SYSTEM OF DESIGN AND USING ADDITIVE TECHNOLOGIES

The direction of research is the development of principles and methods for making scientifically based decisions in the design and additive manufacturing of bone substitutes based on apatite-biopolymer composites with functional properties depending on the nature of the localization of the cavity bone defect and its size. The relevance is due to the fact that the development of an intelligent decision-making support system based on neural network modeling, the development of methods for their training, tabagato-criterion optimization of design processes, will allow the creation of three-dimensional solid models of defects taking into account their spatial structure and bone substitutes for the synthesis of biomaterials with controlled composition, porosity and mechanical strength, which are optimal for a specific area of bone replacement, which will increase the effectiveness of treatment and prosthetics in orthopedics and traumatology. A set of methods for analyzing images of bone tissue, taking into account its spatial structure, which are obtained by sensors of different physical nature, with the use of neural network models, development of methods of their design, optimization, and training is proposed. A modification of the method of learning neural networks based on gradient descent, based on the application of the theory of nonlinear dynamics, is proposed. Corresponding theoretical provisions have been developed.

Nonlinear vibration analysis of thin plate with periodically distributed tunable-stiffness nonlinear oscillators in subsonic flow

This paper provides a new passive control method for nonlinear vibration of subsonic thin plates. The control method uses periodically distributed tunable-stiffness nonlinear oscillators (NLO). By using von Karman’s nonlinear plate theory and subsonic aerodynamic model, the nonlinear dynamic model of thin plate is established based on Hamilton’s principle. Through analyzing the system’s nonlinear dynamics bifurcation, the impact of periodic distribution on the stability is discussed. The amplitude-frequency responses are discussed under different NLO installation modes and design parameters by using Matcont software. The results show that the periodically distributed tunable-stiffness nonlinear oscillators can improve the stability of the system and have a remarkable suppression effect. The optimal control scheme for vibration suppression by periodically distributed tunable-stiffness nonlinear oscillators is obtained. The results obtained from this research can offer a valuable understanding of nonlinear vibration control, thereby enabling the identification of various control approaches that can be implemented in practical applications during future design endeavors.

Laboratory simulation to study the nonlinear evolution of right-hand circularly polarised wave in laser-produced plasmas

Abstract To simulate the astrophysical scenarios at the scale of laboratory astrophysics, the interaction of high-power lasers with plasmas is increasingly being used. So, in this perspective, a nonlinear wave-wave interaction between right-hand circularly polarised wave (R-mode wave) and electron plasma wave (EPW) is proposed to understand the localization of the pump R-mode wave and associated magnetic turbulence at electron scale in magnetized plasma relevant to laboratory astrophysics. The ponderomotive force and relativistic variation of electron mass are accountable for this nonlinear wave-wave interaction model. For this nonlinear dynamics, coupled model equations for EPW and R-mode wave are developed and solved by laboratory simulations utilizing finite difference and pseudo-spectral methods. The observed simulation findings, like the nonlinear evolution of the pump wave, typical scale size of the formed localized structures, and electron scale turbulent spectra associated with the coherent structures resemble various laboratory and space plasma scenarios. A semi-analytical model in the paraxial limits is also developed to understand the physics behind the localization process of the pump wave inside the plasma medium.

Nonlinear dynamics of three-layer microplates: simultaneous presence of the micro-scale and imperfect effects

Nonlinear dynamics of three-layer microplates: simultaneous presence of the micro-scale and imperfect effects

SBMLToolkit.jl: a Julia package for importing SBML into the SciML ecosystem.

Julia is a general purpose programming language that was designed for simplifying and accelerating numerical analysis and computational science. In particular the Scientific Machine Learning (SciML) ecosystem of Julia packages includes frameworks for high-performance symbolic-numeric computations. It allows users to automatically enhance high-level descriptions of their models with symbolic preprocessing and automatic sparsification and parallelization of computations. This enables performant solution of differential equations, efficient parameter estimation and methodologies for automated model discovery with neural differential equations and sparse identification of nonlinear dynamics. To give the systems biology community easy access to SciML, we developed SBMLToolkit.jl. SBMLToolkit.jl imports dynamic SBML models into the SciML ecosystem to accelerate model simulation and fitting of kinetic parameters. By providing computational systems biologists with easy access to the open-source Julia ecosystevnm, we hope to catalyze the development of further Julia tools in this domain and the growth of the Julia bioscience community. SBMLToolkit.jl is freely available under the MIT license. The source code is available at https://github.com/SciML/SBMLToolkit.jl.

Whole Body Control of Mobile Manipulators With Series Elastic Actuators for Cart Pushing Tasks.

Human-centered environments provide affordance for the use of two-handed mobile manipulators. Yet robots designed to function in and physically interact with such environments are not yet capable of meeting human users' requirements. This work proposes a whole body control framework of a two-handed mobile manipulator driven by series elastic actuators (SEAs) for cart pushing tasks. A whole body dynamic model for an integrated mobile platform and on-board arms is revealed, which takes into account the interaction forces with the cart. Then, the explicit force/position control of the mobile manipulator is performed. It enables the robot to interact dynamically with the environment while providing motion, i.e., the manipulators provide both output force control and motion control for pushing a cart. To cope with the highly nonlinear system dynamics and parameter variation of a SEA-driven mobile manipulator, this work proposes an adaptive robust controller based on a novel integral barrier Lyapunov function for cart pushing tasks by considering model uncertainty. The proposed controller enables the mobile manipulator to complete cart pushing tasks by regulating the position and output force of the mobile base and arms. The experimental results show the effectiveness of this approach in cart pushing tasks.

Nonlinear wave dynamics of fractional unstable and modified unstable nonlinear Schrödinger equations through analytical solutions

Nonlinear wave dynamics of fractional unstable and modified unstable nonlinear Schrödinger equations through analytical solutions

Influence of the magnetic flux on the dynamics of a self-sustaining system: analytical, numerical and analogical investigations

This paper investigates the nonlinear dynamics of a ferroelectric enzyme-substrate reaction modeled by the birhythmic van der Pol oscillator coupled to the magnetic flux. We derive the equilibrium points and study their stability. We analyze some bifurcation structures and the variation of the Lyapunov exponents. The phenomena of symmetric attractors and the anti-monotonicity are observed. By increasing the magnetic flux, we find that the equilibrium points are stable, tends to control chaotic regimes, and affects regular and quasi-regular ones. As the magnetic flux increases, the amplitude of the oscillations around the equilibrium points decreases and the amplitude of the limit cycles at the Hopf bifurcation tends to disappear. Further increasing the magnetic flux gives rise to chaotic dynamics. The electrical circuit and analogical simulations are derived using the PSpice software. The agreement between analogical and numerical results is acceptable.

Combination of fuzzy control and reinforcement learning for wind turbine pitch control

Abstract The generation of the pitch control signal in a wind turbine (WT) is not straightforward due to the nonlinear dynamics of the system and the coupling of its internal variables; in addition, they are subjected to the uncertainty that comes from the random nature of the wind. Fuzzy logic has proved useful in applications with changing system parameters or where uncertainty is relevant as in this one, but the tuning of the fuzzy logic controller (FLC) parameters is neither straightforward nor an easy task. On the other hand, reinforcement learning (RL) allows systems to automatically learn, and this capability can be exploited to tune the FLC. In this work, a WT pitch control architecture that uses RL to tune the membership functions and scale the output of a fuzzy controller is proposed. The RL strategy calculates the fuzzy controller gains in order to reduce the output power error of the WT according to the wind speed. Different reward mechanisms based on the output power error have been considered. Simulation results with different wind profiles show that this architecture performs better (123.7 W) in terms of power errors than an FLC without RL (133.2 W) or a simpler PID (208.8 W). Even more, it provides a smooth response and outperforms other hybrid controllers such as RL-PID and radial basis function neural network control.

Dynamics of invariant solutions of the DNA model using Lie symmetry approach

The utilization of the Lie group method serves to encapsulate a diverse array of wave structures. This method, established as a robust and reliable mathematical technique, is instrumental in deriving precise solutions for nonlinear partial differential equations (NPDEs) across a spectrum of domains. Its applications span various scientific disciplines, including mathematical physics, nonlinear dynamics, oceanography, engineering sciences, and several others. This research focuses specifically on the crucial molecule DNA and its interaction with an external microwave field. The Lie group method is employed to establish a five-dimensional symmetry algebra as the foundational element. Subsequently, similarity reductions are led by a system of one-dimensional subalgebras. Several invariant solutions as well as a spectrum of wave solutions is obtained by solving the resulting reduced ordinary differential equations (ODEs). These solutions govern the longitudinal displacement in DNA, shedding light on the characteristics of DNA as a significant real-world challenge. The interactions of DNA with an external microwave field manifest in various forms, including rational, exponential, trigonometric, hyperbolic, polynomial, and other functions. Mathematica simulations of these solutions confirm that longitudinal displacements in DNA can be expressed as periodic waves, optical dark solitons, singular solutions, exponential forms, and rational forms. This study is novel as it marks the first application of the Lie group method to explore the interaction of DNA molecules.

Alternative cliques of coexisting species in complex ecosystems

Abstract The possibility that some ecosystems can exist in alternative stable states has profound
implications for ecosystem conservation and restoration. Current ecological theory on
multistability mostly relies on few-species dynamical models, in which alternative states
are intrinsically related to specific non-linear dynamics. Recent theoretical advances,
however, have shown that multiple stable ‘cliques’ – small subsets of coexisting species–
can be present in species-rich models even under linear interactions. Yet, the mechanisms
governing the appearence and characteristics of these cliques remain largely unexplored.
In the present work, we investigate cliques in the generalized Lotka-Volterra model with
mathematical and computational techniques. Our findings reveal that simple probabilistic and dynamical constraints can explain the appearence, properties and stability
of cliques. Our work contributes to the understanding of alternative stable states in
complex ecological communities.

Repolarization dynamics stability in Brugada type-1 pattern subjects with positive and negative genetics

Abstract Background Brugada type-1 pattern (Brgd1) risk stratification in asymptomatic subjects and its repolarization dynamics are complex. Purpose This study aims to analyze, from alternative standpoints, superficial 12-lead ECG V1 repolarization patterns (repol.). This method diverges from standard ECG pattern characterization. It rather exploits nonlinear dynamics and stability of ECG repol. to assess stability driving cardiac dynamics. This work consists in analyzing 2 subjects with Brgd1: Subject1 with negative genetics and negative EP study. Subect2 with positive genetics. Target To deepen knowledge/insight and applications of control-and-stability-theory applied to 12-lead ECG, aiming to eventually diminish the number of invasive EP studies. Methods A stability control closed loop system has been designed to model electrophysiology dynamics of cardiac conduction: ECG segments being the input-output of the system. (Figure). A sequence of V1 repol. have been scanned, digitized, and quantitatively processed yielding stability parameters (poles in S-plane). Scanning and signal processing performed by Matlab R_2023b. Results Figures. Conclusions Based on our data, 12-lead-ECG repol. seem to be associated with increasing stability in Subject1, exhibiting negative genetics. On the other hand, less stability seems to be associated with Subject2, reporting positive genetic tests. In conclusion, furthering control-and-stability-theory applied to 12-lead ECGs aims to deeper comprehension of physiological and pathological substrates of malignant arrhythmias, and to focus on noninvasive risk stratification strategies for ICD implantation indication in BrS. Further development of this technique will be largely facilitated by the implementation of AI methodologies in the near future.

Online Bilateral Predictive Control for Time-Delayed Teleoperation of Snake-like Robots

Controlling the teleoperation of snake-like robots is challenging due to complex nonlinear dynamics and communication delays. This research proposes an online bilateral predictive control architecture to address these issues. This control structure is established by predicting environment force and the user’s future motion. The former uses a model-mediated approach by creating a virtual environment on the master side and the latter adopts an artificial neural network (ANN) for online operator’s motion prediction. The slave controller utilizes transmitted data from ANN to generate required backbone lengths, which are then transformed into the slave's local bending and torsional degrees of freedom through the inverse kinematics of the robot. Motion prediction is examined in two scenarios: when the ANN predicts the trained motions, and when it predicts a different motion. Simulation studies demonstrate that the proposed online bilateral predictive teleoperation structure successfully achieves real-time position synchronization and force feedback, by effectively bypassing communication delays.

Correction to: Graph analysis of nonlinear fMRI connectivity dynamics reveals distinct brain network configurations for integrative and segregated information processing

Correction to: Graph analysis of nonlinear fMRI connectivity dynamics reveals distinct brain network configurations for integrative and segregated information processing

TC-SINDy: Improving physics-based deterministic tropical cyclone track and intensity model via data-driven sparse identification of Nonlinear Dynamics

Physics-based deterministic tropical cyclone (TC) simulation models play an important role in TC risk analysis, for their unique capability to represent physical principles and incorporate climate change impacts. However, establishing effective deterministic models can be challenging. In this paper, we present a simple yet powerful framework that distills physics-based TC models from historical TC data. By treating TC evolutions as dynamical systems, we adaptively discover the TC track and intensity governing equations from historical TC and environmental data via the Sparse Identification of Nonlinear Dynamics (SINDy) approach. Our proposed TC-SINDy approach is able to identify parsimonious, interpretable yet effective physics-based TC models. Compared to alternative physics-based deterministic models, our models match historical records much better in terms of the intensity evolution, prevailing tracks, and key parameter statistics across the coastlines of the Western North Pacific (WNP) basin and the North Atlantic (NA) basin. Our proposed models were finally coupled with a widely used parametric wind field, and the obtained probabilistic distribution of the surface wind also matched the historical histograms. Overall, the proposed method presents a general data-driven framework for discovering physics-based TC models, enabling reliable effective TC simulations while reserving the capacity to accommodate the changing climate.

Symmetry and complexity: A Lie symmetry method tobifurcation, chaos, multistability and soliton solutions of thenonlinear generalized advection-diffusion-reaction equation

Abstract This paper deals into the complexities of nonlinear dynamics within the nonlinear generalized advection-
diffusion-reaction equation, which describes intricate transport phenomena involving advection, diffusion,
and reaction processes occurring simultaneously. Through the utilization of the Lie symmetry approach,
we thoroughly examine this proposed model, transforming the partial differential equation into an ordinary
differential equation using similarity reduction techniques to facilitate a more comprehensive analysis. Ex-
act solutions for this transformed equation are derived employing the extended simplest equation method
and the new extended direct algebraic method. To enhance understanding, contour plots along with 2D
and 3D visualizations of solutions are employed. Additionally, we explore bifurcation and chaotic be-
haviours through a qualitative analysis of the model. Phase portraits are meticulously scrutinized across
various parameter values, offering insights into system behavior. Introduction of an external periodic
strength allows us to utilize various tools including time series, 3D, and 2D phase patterns to discern
chaotic and quasi-periodic behaviors. Furthermore, a multistability analysis is conducted to examine the
impacts of diverse initial conditions. These findings underscore the efficacy and practicality of the pro-
posed methodologies in evaluating soliton solutions and elucidating phase dynamics across a spectrum of
nonlinear models, offering novel perspectives on intricate physical phenomena.

Data-driven reconstruction of chaotic dynamical equations: The Hénon–Heiles type system

In this study, the classical two-dimensional potential VN=12mω2r2+1NrNsin(Nθ), N∈Z+, is considered. At N=1,2, the system is superintegrable and integrable, respectively, whereas for N>2 it exhibits a richer chaotic dynamics. For instance, at N=3 it coincides with the Hénon–Heiles system. The periodic, quasi-periodic and chaotic motions are systematically characterized employing time series, Poincaré sections, symmetry lines and the largest Lyapunov exponent as a function of the energy E and the parameter N. Concrete results for the lowest cases N=3,4 are presented in complete detail. This model is used as a benchmark system to estimate the accuracy of the Sparse Identification of Nonlinear Dynamical Systems (SINDy) method, a data-driven algorithm which reconstructs the underlying governing dynamical equations. We pay special attention at the transition from regular motion to chaos and how this influences the precision of the algorithm. In particular, it is shown that SINDy is a robust and stable tool possessing the ability to generate non-trivial approximate analytical expressions for periodic trajectories as well.

Sampling free iterative PCE filter for state and parameter estimation of nonlinear dynamical systems

We present a novel filter for state and parameter estimation in non-linear dynamical systems, based on a generalised Kalman filter formulation. To achieve a sampling-free implementation, polynomial chaos expansion (PCE) and a Galerkin projection method are utilized for the propagation of uncertainties through the system dynamics. The non-linear dynamics of the system are then linearised by a sequence of Gauss-Newton iterations in combination with linear Kalman updates. Additionally, we introduce a new square root implementation of the PCE-based filter. The proposed filter is evaluated on the Lorenz-63 and Lorenz-84 models for the task of simultaneous state and parameter estimation and is compared with two related approaches. Finally, the computational complexity of our square-root implementation is compared against two existing square root approaches.

Transient Propagation of the Invasion Front in the Homogeneous Landscape and in the Presence of a Road.

Understanding the propagation of invasive plants at the beginning of invasive spread is important as it can help practitioners eradicate harmful species more efficiently. In our work the propagation regime of the invasive plant species is studied at the short-time scale before a travelling wave is established and advances into space at a constant speed. The integro-difference framework has been employed to deal with a stage-structured population, and a short-distance dispersal mode has been considered in the homogeneous environment and when a road presents in the landscape. It is explained in the paper how nonlinear spatio-temporal dynamics arise in a transient regime where the propagation speed depends on the detection threshold population density. Furthermore, we investigate the question of whether the transient dynamics become different when the homogeneous landscape is transformed into the heterogeneous one. It is shown in the paper how invasion slows down in a transient regime in the presence of a road.