24 papers · ranked by Valyu relevance
Michael G. Rosenblum, Arkady Pikovsky
Phase reduction is a general tool widely used to describe forced and interacting self-sustained oscillators. Here we explore the phase coupling functions beyond the usual first-order approximation in the strength of the force. Taking the periodically forced Stuart-Landau oscillator as the paradigmatic model, we…
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…
Alex Sheremet, Yu Qin
The Cross Frequency Coupling (CFC) phenomenon is defined as a statistical correlation between characteristic parameters neural oscillations. This study demonstrates and analyzes the nonlinear mechanism of the CFC, with a focus on the coupling between slow and fast oscillations, as a model for theta-gamma coupling. We…
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…
Koretaka Yuge, Keigo Kamei
For classical discrete system under constant composition, typically reffered to as substitutional alloys, correspondence between interatomic many-body interactions and structure in thermodynamic equilibrium exhibit profound, complicated nonlinearity (canonical nonlinearity). Our recent studies clarify that the…
Vishal Juneja, Suresh Kumarasamy, Aryan Patel, Amrita Punnavajhala + 1 more
'Ramakrishna Ramaswamy'] Dynamical systems can be coupled in a manner that is designed to drive the resulting dynamics onto a specified lower dimensional submanifold in the phase space of the combined system. On the submanifold, the variables of the two systems have a well-defined unique functional relationship. This…
Kuo Lu, Qingsong Li, Xin Zhou, Guoxiong Song + 4 more
'Xuezhong Wu' 'Dingbang Xiao'] Capacitive micromechanical resonators share electrodes with the same bias voltage, resulting in the occurrence of electrostatic coupling between intrinsic modes. Unlike the traditional mechanical coupling, the electrostatic coupling is determined by the structural electric potential…
Stewart Heitmann, Michael Breakspear
The study of fluctuations in time-resolved functional connectivity is a topic of substantial current interest. As the term “dynamic functional connectivity” implies, such fluctuations are believed to arise from dynamics in the neuronal systems generating these signals. While considerable activity currently attends to…
Alessandro Sanzeni, Mark H. Histed, Nicolas Brunel
Combining information from multiple sources is a fundamental operation performed by networks of neurons in the brain, whose general principles are still largely unknown. Experimental evidence suggests that combination of inputs in cortex relies on nonlinear summation. Such nonlinearities are thought to be fundamental…
Tomislav Stankovski, Tiago Pereira, P. V. E. McClintock, Aneta Stefanovska
'Aneta Stefanovska'] The dynamical systems found in Nature are rarely isolated. Instead they interact and influence each other. The coupling functions that connect them contain detailed information about the functional mechanisms underlying the interactions and prescribe the physical rule specifying how an interaction…
Tomislav Stankovski, Tiago Pereira, Peter V. E. McClintock, Aneta Stefanovska
'Aneta Stefanovska'] Dynamical systems are widespread, with examples in physics, chemistry, biology, population dynamics, communications, climatology and social science. They are rarely isolated but generally interact with each other. These interactions can be characterized by coupling functions-which contain detailed…
Qihang Wu, Quan Wen, Cirong Liu
A central question in neuroscience is how the brain’s structural connectivity gives rise to its emergent, correlated dynamics. These large-scale dynamical correlations underlie functional networks that support cognitive functions. Here, we identify coupling correlation—the similarity between the input connectivity…
Justin Eilertsen, Wylie Stroberg, Santiago Schnell
A theoretical analysis is performed on the nonlinear ordinary differential equations that govern the dynamics of a coupled enzyme catalyzed reaction. The assay consists of a non-observable reaction and an indicator (observable) reaction, where the product of the first reaction is the enzyme for the second. Both…
Zeray Hagos, Tomislav Stankovski, Julian Newman, Tiago Pereira + 2 more
'Peter V. E. McClintock' 'Aneta Stefanovska'] Interacting dynamical systems are widespread in nature. The influence that one such system exerts on another is described by a coupling function; and the coupling functions extracted from the time-series of interacting dynamical systems are often found to be time-varying.…
Authors not listed
We outline two general theoretical techniques to simulate polariton quantum dynamics and optical spectra under the collective coupling regimes described by a Holestein-Tavis-Cummings (HTC) model Hamiltonian. The first one takes the advantage of sparsity of the HTC Hamiltonian, which allows one to reduce the cost of…
Maria Laureano, Diana Mendes, Manuel Ferreira
Synchronization, initially observed by Christiaan Huygens in 1665, has evolved from the study of periodic signals to encompass chaotic systems, where the sensitive dependence on initial conditions poses unique challenges. This review pointed to both theoretical foundations and contributions (concepts and methods) and…
Wlodzimierz Klonowski
Methods of contemporary physics are increasingly important for biomedical research but, for a multitude of diverse reasons, most practitioners of biomedicine lack access to a comprehensive knowledge of these modern methodologies. This paper is an attempt to describe nonlinear dynamics and its methods in a way that…
Authors not listed
Two-dimensional electronic spectroscopy (2DES) is a powerful experimental technique, as it directly probes the nonlinear (third-order) response function of the system, providing key insights into ultrafast energy transfer and relaxation processes. However, 2DES experiments are generally difficult to interpret, often…
Corey Weistuch, Luca Agozzino, Lilianne R. Mujica-Parodi, Ken A. Dill + 1 more
'Ken A. Dill' 'Lingchong You'] We give an approximate solution to the difficult inverse problem of inferring the topology of an unknown network from given time-dependent signals at the nodes. For example, we measure signals from individual neurons in the brain, and infer how they are inter-connected. We use Maximum…
Paolo Magrassi
The paper argues that attracting more economists and adopting a more-precise definition of dynamic complexity might help econophysics acquire more attention in the economics community and bring new lymph to economic research. It may be necessary to concentrate less on the applications than on the basics of economic…
Linyun Huang, Youngchul Bae
The aim of this study was to describe a novel extended dynamical love model with the external environments of the love story of Romeo and Juliet. We used the sinusoidal function as external environments as it could represent the positive and negative characteristics of humans. We considered positive and negative advice…
Justin Eilertsen, Wylie Stroberg, Santiago Schnell
The determination of a substrate or enzyme activity by coupling of one enzymatic reaction with another easily detectable (indicator) reaction is a common practice in the biochemical sciences. Usually, the kinetics of enzyme reactions is simplified with singular perturbation analysis to derive rate or time course…
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…
Justin Eilertsen, Wylie Stroberg, Santiago Schnell
The determination of a substrate or enzyme activity by coupling of one enzymatic reaction with another easily detectable (indicator) reaction is a common practice in the biochemical sciences. Usually, the kinetics of enzyme reactions is simplified with singular perturbation analysis to derive rate or time course…