23 papers · ranked by Valyu relevance
Farshad Kheiri, Shyam Sundaram, Anatol Bragin
This study uses nonlinear analysis techniques to distinguish between mind wandering (MW) and focused attention (FA) states using EEG data. EEG recordings from 21 sessions were segmented into intervals of 2, 3, 5, 6, 10, and 15 seconds, and seven nonlinear features were extracted to capture the brain’s dynamic…
Malte Krack
As the motions of nonconservative autonomous systems are typically not periodic, the definition of nonlinear modes as periodic motions cannot be applied in the classical sense. In this paper, it is proposed 'make the motions periodic' by introducing an additional damping term of appropriate sign and magnitude. It is…
José M. Amigó, Fernando Montani
Nonlinear dynamics is the study of dynamical systems in finite dimensions, whether in discrete or continuous time, in which the evolution equation (a difference or differential equation, respectively) is not linear in the state variables [1,2]. A potential result of nonlinear dynamics is sensitivity to initial…
Fei He, Yuan Yang
The human nervous system is one of the most complicated systems in nature. Complex nonlinear behaviours have been shown from the single neuron level to the system level. For decades, linear connectivity analysis methods, such as correlation, coherence and Granger causality, have been extensively used to assess the…
Abdolvahhab Rostamijavanani, Shanwu Li, Yongchao Yang
To fully understand, analyze, and determine the behavior of dynamical systems, it is crucial to identify their intrinsic modal coordinates. In nonlinear dynamical systems, this task is challenging as the modal transformation based on the superposition principle that works well for linear systems is no longer…
Aniketh Kalur, Peter Seiler, Maziar S. Hemati
The dynamics of transitional flows are governed by an interplay between the non-normal linear dynamics and quadratic nonlinearity in the incompressible Navier-Stokes equations. In this work, we propose a framework for nonlinear stability analysis that exploits the fact that nonlinear flow interactions are constrained…
Galal M. Moatimid, T. S. Amer, A. A. Galal
Due to the growing concentration in the field of the nonlinear oscillators (NOSs), the present study aims to use the general He's frequency formula (HFF) to examine the analytical representations for particular kinds of strong NOSs. Three real-world examples are demonstrated by a variety of engineering and scientific…
Suraj K. Nayak, Arindam Bit, Anilesh Dey, Biswajit Mohapatra + 1 more
'Kunal Pal'] Electrocardiogram (ECG) signal analysis has received special attention of the researchers in the recent past because of its ability to divulge crucial information about the electrophysiology of the heart and the autonomic nervous system activity in a noninvasive manner. Analysis of the ECG signals has been…
D. J. Ewins, B. Weekes, A. delli Carri
Model validation using data from modal tests is now widely practiced in many industries for advanced structural dynamic design analysis, especially where structural integrity is a primary requirement. These industries tend to demand highly efficient designs for their critical structures which, as a result, are…
Ritabrata Dutta
This paper features and elaborates recent developments and modifications in asymptotic techniques in solving differential equation in non linear dynamics. These methods are proved to be powerful to solve weakly as well as strongly non linear cases. Obtained approximate analytical solutions are valid for the whole…
M. G. Blyth, Ludovic Renson, Lucia Marucci
Mathematical modelling allows us to concisely describe fundamental principles in biology. Analysis of models can help to both explain known phenomena, and predict the existence of new, unseen behaviours. Model analysis is often a complex task, such that we have little choice but to approach the problem with…
Cátia Fortunato, Jorge Bennasar-Vázquez, Junchol Park, Joanna C. Chang + 4 more
There is rich variety in the activity of single neurons recorded during behaviour. Yet, these diverse single neuron responses can be well described by relatively few patterns of neural co-modulation. The study of such low-dimensional structure of neural population activity has provided important insights into how the…
Mahy Ahmed, Hamdy M. Ahmed, Niveen Badra, Islam Samir
In this study, we investigate the (2+1)-dimensional Kadomtsev-Petviashvili-Sawada-Kotera-Ramani (KPSKR) equation, a physically significant model describing nonlinear wave phenomena in higher-dimensional spaces. Utilizing the improved modified extended tanh-function method, we derive a diverse spectrum of exact…
Róbert Vrábeľ
This paper investigates the application of piecewise linear approximation for the control of nonlinear systems, particularly focusing on the effective linearization of systems modeled by the differential equation y (n) + f(y, y′ , . . . , y(n−1)) = u(t). We explore the use of PID controllers in conjunction with…
Authors not listed
Nonlinear monotonically increasing bounded functions help to visualize and analyze data on various scales. However, many monotonic functions such as logarithm or power laws have either function values or derivatives that become unbounded at some regions of the $x-$ axis. On the other hand, sigmoid or hyperbolic…
Ying Wang, Min Li, Ronaldo García Reyes, Deirel Paz-Linares + 4 more
Parameterizing electroencephalography (EEG) signals in the spectral domain reveals physiologically relevant components of neural stochastic processes, yet the linearity or nonlinearity of these components remains debated and could not solved by the current Spectral Parameter Analysis (SPA). We address this using BiSCA…
Younes Chahlaoui, Asghar Ali, Jamshad Ahmad, Sara Javed + 1 more
'Muhammad Aqeel'] The fractional coupled Konno-Onno model, which is frequently used in numerous fields of scientific and engineering disciplines, is being investigated in the current study in order to gain an understanding of complex phenomena and systems. The two main goals of this study are to be accomplished.…
Erfan Nozari, Jennifer Stiso, Lorenzo Caciagli, Eli J. Cornblath + 5 more
A central challenge in the computational modeling of neural dynamics is the trade-off between accuracy and simplicity. At the level of individual neurons, nonlinear dynamics are both experimentally established and essential for neuronal functioning. One may therefore expect the collective dynamics of massive networks…
Authors not listed
Inverse problems, where we seek the values of inputs to a model that lead to a desired set of outputs, are a challenges subset of problems in science and engineering. In this work we demonstrate the use of two generative AI methods to solve inverse problems. We compare this approach to two more conventional approaches…
Authors not listed
The modeling of chemical reactions using artificial intelligence is rapidly advancing but still heavily relies on abundant and costly experimental data. In the context of computational chemistry, we present SymChemAI, a chemically informed neural network capable of simulating the dynamic evolution of reactions from…
Authors not listed
The analysis of nonadiabatic molecular dynamics (NAMD) data presents significant challenges due to its high dimensionality and complexity. To address these issues, we introduce ULaMDyn, a Python-based, open-source package designed to automate the unsupervised analysis of large datasets generated by NAMD simulations.…
Authors not listed
Moving bed reactors (MBRs) are widely used in various industrial processes, making the development of mathematical models crucial for their design, optimization, and control. This study presents a semi-analytical solution (SAS) for a lumped parameter kinetic and heat transfer model of a tubular MBR, where a first-order…
Aleksandr Fedorov, Anna Perechodjuk, David Linke
Artificial neural networks (ANNs) are powerful tools for solving a wide range of tasks in fundamental and applied science. However, training and building reliable ANN models requires a lot of data which so far hinders their wider application in kinetic modelling where typically only small (experimental) datasets are…