Application Of Nonlinear Dynamics Research Articles

Dynamic nature of analytical soliton solutions of the nonlinear ZKBBM and GZKBBM equations

A solitary wave, characterized as a localized perturbation in a medium, emerges as a result of a delicate equilibrium between nonlinear and dispersive phenomena. Solitons, a subtype of solitary waves, exhibit persistent shape and velocity during propagation, representing a fundamental phenomenon observed widely in natural systems and possessing various applications in nonlinear dynamics. This investigation focuses on two nonlinear evolution equations (NEEs), specifically the Zakharov–Kuznetsov–Benjamin–Bona–Mahony (ZKBBM) equation and the generalized Zakharov–Kuznetsov–Benjamin–Bona–Mahony (GZKBBM) equation, which find relevance in domains such as fluid dynamics and ocean engineering. Utilizing an ansatz-based methodology, soliton solutions of both bright and dark characteristics are derived, alongside exploration of rogue wave-type solutions. Notably, the manifestation of dark, bright, and rogue waves aligns with the physical interpretation of the generated solitons. Computational simulations conducted using Wolfram Mathematica aim to provide a comprehensive description of the physical phenomena. The novelty of this study lies in its unreported investigation, contributing new insights into the solitonic dynamics within the considered models.

A Novel Application of Non-linear Dynamics Investigating Cognitive Workload and Situational Trust in Highly Automated Vehicles

Vehicles with driving automation are becoming increasingly present despite the reported apprehension of potential consumers. The potential benefits, such as fewer crashes, lighter traffic, and increased transportation access, give merit in researching how to engender appropriate human- automation interaction that will ensure a smoother adoption of the technology. One method involves investigating how users receive information about the vehicle. Using a simulated highly automated vehicle, researchers examined how content temporality and modality affected the situational trust and cognitive workload of 36 participants using subjective measures and 15 participants using non-linear dynamics. Researchers found only one significant main effect of temporality on workload; however, post-hoc comparisons between groups were insignificant. Nevertheless, applying non-linear dynamics to driving research is a novel and underutilized approach. Researchers, designers, and users may benefit from using real-time measures rather than aggregate scores to understand how driver behavior changes based on the environment.

Special Issue “Application of Non-Linear Dynamics”

Nonlinear phenomena occur in engineering structures, biological systems, social processes, and in economics [...]

Editorial for Focus Issue: From chemical oscillations to applications of nonlinear dynamics: Dedicated to Richard J. Field on the occasion of his 80th birthday.

Editorial for Focus Issue: From chemical oscillations to applications of nonlinear dynamics: Dedicated to Richard J. Field on the occasion of his 80th birthday.

Regularized variational formulation for nonlinear dynamics of viscoplastic plates

In this work we present novel approach to Reissner–Mindlin plates, targeting the nonlinear dynamics applications and in particular robust scheme for improved performance in vibration and wave propagation computations, where the standard finite element isoparametric interpolations no longer provide the best approximation property. The first key ingredient of the present development is regularized variational formulation, recast in terms of stress resultants (bending moments and shear forces), which allows any convenient interpolations. The discrete approximation is here constructed by using the lowest order Raviart–Thomas vector space employed to discretize bending moment and shear force fields, providing the continuity of the stress resultants projections across the boundary between adjacent plate elements. The latter is of particular interest for dynamic analysis for it can capture smooth approximation for wave propagation phenomena. This particular space discrete approximation is further combined with the most appropriate time-integration schemes capable of enforcing either energy conservation or decay of high frequency modes, which delivers the schemes with higher stability and robustness in long-term computations. The developments are carried out for viscoplastic constitutive behavior of plate material, where the corresponding evolution equations are obtained by appealing to the penalty-like form of the principle of maximum plastic dissipation. The choice of viscoplasticity (rather than plasticity) is crucial in that allows development of second-order scheme by integrating simultaneously the momentum balance and viscoplastic strains evolution equations. Several numerical simulations are given to illustrate a very satisfying performance of the proposed hybrid-stress discrete approximation for thick plate element and of the energy conserving/decaying schemes.

Generalized fifth-order nonlinear evolution equation for the Sawada-Kotera, Lax, and Caudrey-Dodd-Gibbon equations in plasma physics: Painlevé analysis and multi-soliton solutions

This research aims to investigate a generalized fifth-order nonlinear partial differential equation for the Sawada-Kotera (SK), Lax, and Caudrey-Dodd-Gibbon (CDG) equations to study the nonlinear wave phenomena in shallow water, ion-acoustic waves in plasma physics, and other nonlinear sciences. The Painlevé analysis is used to determine the integrability of the equation, and the simplified Hirota technique is applied to construct multiple soliton solutions with an investigation of the dispersion relation and phase shift of the equation. We utilize a linear combination approach to construct a system of equations to obtain a general logarithmic transformation for the dependent variable. We generate one-soliton, two-soliton, and three-soliton wave solutions using the simplified Hirota method and showcase the dynamics of these solutions graphically through interaction between one, two, and three solitons. We investigate the impact of the system’s parameters on the solitons and periodic waves. The SK, Lax, and CDG equations have a wide range of applications in nonlinear dynamics, plasma physics, oceanography, soliton theory, fluid dynamics, and other sciences.

A short overview of solitons and applications

Solitons are solitary waves that maintain their shape and speed while propagating with constant velocity. They are ubiquitous in nature and have many applications in nonlinear dynamics. In this project, we give a brief historical overview of solitons. We also discuss solitary, traveling wave solutions of the classical wave equation and the famous KdV equation. Finally, we highlight a few important theoretical and physical applications of solitons.

An Efficient Image Privacy-Preserving Scheme Based On Mixed Chaotic Map and Compression

In the digital modern era, multimedia security has turned into a major concern by the rapid growth of network technologies and digital communications. Accordingly, from the last few decades, the application of nonlinear dynamics and chaotic phenomena for multimedia data security earn significant attention. In this paper, an efficient image-encryption technique based on a two-dimensional (2D) chaotic system combine with the finite field of the specific order is introduced. The proposed scheme consists of four modules which are the separation of bits, compression, 2D chaotic map, and small S-boxes. Initially, the suggested scheme separates the pixels of the image into the least significant bits (LSB) and the most significant bits (MSB). Subsequently, the compression algorithm on these separated bits is applied and instantly transformed the MSB of the image into LSB. The key objective of the first module is to minimize the range of the pixel value up to eight times less than the original image, which consequently reduces the time complexity of the scheme. In the end, a 2D chaotic map is used to reshuffle the bytes to interrupt the internal correlation amongst the pixels of the image. At the tail end, the small S-boxes have been used to substitute the permuted image. The significance of small S-boxes plays a vital role to maintain the optimum security level, prevent computational effort, and reduced time complexity. The result of the suggested encryption system is tailor-made for instantaneous communication.

A Tutorial Review on Time-Frequency Analysis of Non-Stationary Vibration Signals with Nonlinear Dynamics Applications

Time-frequency analysis (TFA) for mechanical vibrations in non-stationary operations is the main subject of this article, concisely written to be an introducing tutorial comparing different time-frequency techniques for non-stationary signals. The theory was carefully exposed and complemented with sample applications on mechanical vibrations and nonlinear dynamics. A particular phenomenon that is also observed in non-stationary systems is the Sommerfeld effect, which occurs due to the interaction between a non-ideal energy source and a mechanical system. An application through TFA for the characterization of the Sommerfeld effect is presented. The techniques presented in this article are applied in synthetic and experimental signals of mechanical systems, but the techniques presented can also be used in the most diverse applications and also in the numerical solution of differential equations.

Computational Methods in Interdisciplinary Applications of Nonlinear Dynamics

Nonlinear dynamics takes its origins from physics and applied mathematics [...]

Advancing training and transfer research through the application of nonlinear dynamics

ABSTRACT The study of training transfer as something that occurs over time with its own underlying process has been very limited in the training literature to date. This paper argues that we can better understand how transfer unfolds over time, and why it unfolds in any particular way, by considering important theoretical and mathematical concepts from nonlinear dynamics. We draw on nonlinear concepts, such as attractors, to describe how and when training interventions are likely to succeed and how subsequent transfer may unfold in relation to those concepts. We then explicate how taking a dynamic view of transfer forces us to change how our field currently studies transfer methodologically, and then give an extended example of how such an advancement may provide for richer theories regarding the process of transfer by focusing on the effects of supervisor support over time. We close with some practical recommendations informed by our view.

Identifying nonlinear dynamics of brain functional networks of patients with schizophrenia by sample entropy

Different regions in the human brain functionally connect with each other forming a brain functional network, and the time evolution of functional connectivity between different brain regions exhibits complex nonlinear dynamics. This study intends to characterize the nonlinear properties of dynamic functional connectivity and to explore how schizophrenia influences such nonlinear properties. The dynamic functional connectivity is constructed by analyzing resting-state functional magnetic resonance imaging data, and its nonlinear properties are characterized by sample entropy (SampEn), with larger SampEn values corresponding to more complexity. To identify the influence of schizophrenia on SampEn, the difference in SampEn between patients with schizophrenia and healthy controls is analyzed at different levels of the brain. It is shown that the patients exhibit significantly higher SampEn at different levels of the brain, and such phenomenon is mainly caused by a significantly higher SampEn in the visual cortex of the patients. Furthermore, it is also shown that SampEn of the visual cortex is significantly and positively correlated with the illness duration or the symptom severity scores. Because the visual cortex is implicated in the visual information processing, these results can shed light on abnormal visual functions of patients with schizophrenia, and also are consistent with the notion that the nonlinearity underlies the irregularity in psychotic symptoms of schizophrenia. This study extends the application of nonlinear dynamics in brain sciences and suggests that nonlinear properties are effective biomarkers in characterizing the brain functional networks of patients with brain diseases.

Generation of trapezoidal envelope pulses and soliton rains from passively mode-locked fiber laser with MoS2 saturable absorber on microfiber

We report the generation of trapezoidal envelope pulses and soliton rains in an erbium-doped fiber laser with an MoS2-deposited microfiber saturable absorber. The pulse duration of the trapezoidal envelope pulses increases from 7 to 95 ns with the increment of the pump power. The maximum intracavity pulse energy is as high as 34 nJ. At a low pump power, the proposed laser can be switched to the soliton-rains regime by properly changing the polarization states. The microfiber-based MoS2 all-fiber laser can serve as an optical source with improved pulse energy for potential applications in nonlinear dynamics.

Brief review on application of nonlinear dynamics in image encryption

Chaos-based cryptology has become one of the most common design techniques to design new encryption algorithms in the last two decades. However, many proposals have been observed to be weak against simple known attacks. However, security of proposals cannot be proved. An analysis roadmap is needed for the security analysis of new proposals. This study aims to address this shortcoming. Analysis and test results show that many chaos-based image encryption algorithms previously published in the nonlinear dynamics are actually not as secure as they are expressed although these algorithms do pass several statistical and randomness tests. A checklist has been proposed to solve these problems. The applications of the proposed checklist have been shown for different algorithms. The proposed checklist is thought to be a good starting point for researchers who are considering to work in chaos-based cryptography.

Utilizing Student Socio-coordinated Mimicry: Complex Movement Conversations in Physical Education

ABSTRACTThis article explores Complexity Theory and applications of nonlinear dynamics in physical education (PE). The authors of this article discuss Complexity Theory and its applications to students and student learning. Additionally, there will be discussion of how the networking learning process associated with socio-coordinated mimicry creates a “movement conversation” between learners rooted in the relational complexity of students within a PE lesson. Finally, the authors discuss research opportunities within PE, allowing for a close collaboration between pedagogical researchers and biomechanists to examine the emergent qualities within the “movement conversations” between students. Overall, this article seeks to illustrate the possibilities of utilizing Complexity Theory within PE pedagogy and research.

Evaluation of different SMA models performances in the nonlinear dynamics of pseudoelastic oscillators via a comprehensive modeling framework

The nonlinear dynamics of Shape Memory Alloys (SMA) oscillators with pseudoelastic behaviour has been studied extensively in the last years by using different constitutive models for the restoring force. The response of SMA devices is rather complex and is characterized by several aspects that, usually, are not taken into account within a single model. For this reason, the constitutive models that are typically used to study the nonlinear dynamics are often of a rather simplified nature that neglects one or more aspects.This works investigates the extent to which the choice of a more or less refined constitutive model can affect the evaluation of the nonlinear dynamic behaviour of a SMA oscillator. In order to compare different constitutive models, a comprehensive thermomechanical modelling framework capable to simulate different constitutive assumptions is proposed first. Then, numerical simulations are carried out to compare the different dynamical responses. The obtained results show that, for single trajectories with specific features, different models can give similar dynamical information, although with the exception of different transient behaviour. However, when the overall scenario of local dynamics is investigated by computing frequency-response curves, it becomes evident that the simplified models, and in particular those with polynomial restoring force, fail to capture main aspects such as the location of the jumps and the order of magnitude of response peaks. Moreover, they generally lead to significant errors in the estimation of the dissipated energy, which is crucial for the quantification of the structural damping. The results of this work should then be helpful to guide the choice of SMA models to be used in nonlinear dynamic applications.

Chaos emerging in soil failure patterns observed during tillage: Normalized deterministic nonlinear prediction (NDNP) and its application.

Real-world processes are often combinations of deterministic and stochastic processes. Soil failure observed during farm tillage is one example of this phenomenon. In this paper, we investigated the nonlinear features of soil failure patterns in a farm tillage process. We demonstrate emerging determinism in soil failure patterns from stochastic processes under specific soil conditions. We normalized the deterministic nonlinear prediction considering autocorrelation and propose it as a robust way of extracting a nonlinear dynamical system from noise contaminated motion. Soil is a typical granular material. The results obtained here are expected to be applicable to granular materials in general. From a global scale to nano scale, the granular material is featured in seismology, geotechnology, soil mechanics, and particle technology. The results and discussions presented here are applicable in these wide research areas. The proposed method and our findings are useful with respect to the application of nonlinear dynamics to investigate complex motions generated from granular materials.

Reprogrammable logic-memory device of a mechanical resonator

From the viewpoint of application of nonlinear dynamics, we report multifunctional operation in a single microelectromechanical system (MEMS) resonator. This paper addresses a reprogrammable logic-memory device that uses a nonlinear MEMS resonator with multi-states. In order to develop the reprogrammable logic-memory device, we discuss the nonlinear dynamics of the MEMS resonator with and without control input as logic and memory operations. Through the experiments and numerical simulations, we realize the reprogrammable logic function that consists of OR/AND gate by adjusting the excitation amplitude and the memory function by storing logic information in the single nonlinear MEMS resonator.

Application of Nonlinear Dynamics in Studying Flashover Fire in a Small Open Kitchen

Open kitchen designs are found in small units in tall residential buildings of Asian-Oceania regions for better space utilization. As many combustibles are stored in small residential units, fire originated in the open kitchen can grow and spread fast. Consequently, flashover can occur to give a big fire and result in severe casualties and property damage. Nonlinear dynamics can be applied to predict critical heat release rate to flashover in the unit with an open kitchen and will be illustrated in this paper. Based on a two-zone model, temperature of the hot smoke layer was taken as the system state variable. An evolution equation was developed with selective control parameters. Onsetting of flashover using a nonlinear dynamical system was demonstrated in the example residential units. Effects of the floor dimensions, the radiation feedback coefficient and thermal properties of wall material on the onset of flashover were then examined and analyzed. The developed nonlinear dynamical model for studying the onset of flashover gives a better understanding of the various control parameters.

Assessing accuracy of k ‐step‐ahead prediction of non‐linear dynamics with uncertainties

Prediction of k-step ahead requires an accurate model for a non-linear system. If the non-linearities are simply ignored, there will be the danger of overestimating the output value due to uncertainties. Considering that almost all models have uncertainties, in this study, the accuracy of k-step-ahead prediction is assessed considering the structural, parametric, and algorithmic uncertainties. Then, in order to remove uncertainties from data and achieve an accurate k-step-ahead prediction, interval type-2 fuzzy set is utilised. This study proposes a strategy for modelling symmetric interval type-2 fuzzy sets using their uncertainty degrees and centre of gravities. On the basis of these uncertainty measures, a method is introduced for constructing interval type-2 fuzzy set models using the uncertain interval data. The aim is to provide tools for evaluating a model or a set of models on the basis of predictive accuracy or efficiency for non-linear dynamic applications with uncertainties. Simulation studies demonstrate the effectiveness of the proposed control scheme.