29 papers · ranked by Valyu relevance
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…
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…
W. Tecumseh Fitch
The recognition that nonlinear phenomena, including subharmonics, bifurcations and deterministic chaos, are present in human and animal vocalizations is a relatively recent one. I give a brief history of this revolution in our understanding of the voice, based on interviews with some of the key players and personal…
Wei Zhang, Mingjun Wei
A theoretic framework for dynamics is obtained by transferring dynamics from state space to its dual space. As a result, the linear structure where dynamics are analytically decomposed to subcomponents and invariant subspaces decomposition based on local Koopman spectral theory are revealed. However, nonlinear dynamics…
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…
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…
Blai Vidiella, Ernest Fontich, Sergi Valverde, Josep Sardanyés
Transients in ecology are extremely important since they determine how equilibria are approached. The debate on the dynamic stability of ecosystems has been largely focused on equilibrium states. However, since ecosystems are constantly changing due to climate conditions or to perturbations such as the climate crisis…
Peng Yue
In the past hundred years, chaos has always been a mystery to human beings, including the butterfly effect discovered in 1963 and the dissipative structure theory which won the chemistry Nobel Prize in 1977. So far, there is no quantitative mathematical-physical method to solve and analyze these problems. In this…
Alvaro H. Salas S, Gilder Cieza Altamirano, Lorenzo J. Martínez H
Future scientific and technological evolution in many areas of applied mathematics and modern physics will necessarily depend on dealing with complex systems. Such systems are complex in both their composition and behavior, namely, dealing with complex dynamical systems using different types of Duffing equations, such…
Ruud Stoof, Ángel Goñi-Moreno
Nonlinearity plays a fundamental role in the performance of both natural and synthetic biological networks. Key functional motifs in living microbial systems, such as the emergence of bistability or oscillations, rely on nonlinear molecular dynamics. Despite its core importance, the rational design of nonlinearity…
Yousef Yousefi, Khikmat Kh. Muminov
In this report, fundamental educational concepts of linear and nonlinear equations and solutions of nonlinear equations from the book High-Temperature Superconductivity: The Nonlinear Mechanism and Tunneling Measurements (Kluwer Academic Publishers, Dordrecht, 2002, pages 101-142) is given. There are a few ways to…
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…
Elisabeth Roesch, Michael P.H. Stumpf
Dynamical systems with intricate behaviour are all-pervasive in biology. Many of the most interesting biological processes indicate the presence of bifurcations, i.e. phenomena where a small change in a system parameter causes qualitatively different behaviour. Bifurcation theory has become a rich field of research in…
Santosh Manicka, Kathleen Johnson, Michael Levin, David Murrugarra
The extent to which the components of a biological system are (non)linearly regulated determines how amenable they are to therapy and control. To better understand this property termed ‘regulatory nonlinearity’, we analyzed a suite of 137 published Boolean network models, containing a variety of complex nonlinear…
D. T. Pham, Z. E. Musielak
Non-standard Lagrangians do not display any discernible energy-like terms, yet they give the same equations of motion as standard Lagrangians, which have easily identifiable energy-like terms. A new method to derive non-standard Lagrangians for second-order nonlinear differential equations with damping is developed and…
Jan Swierczek-Jereczek, Alexander Robinson, Javier Blasco, Jorge Alvarez-Solas + 1 more
'Jorge Alvarez-Solas' 'Marisa Montoya'] Rate-induced tipping (R-tipping) describes the fact that, for multistable dynamic systems, an abrupt transition can take place not only because of the forcing magnitude, but also because of the forcing rate. In the present work, we demonstrate through the case study of a…
Jan J. Kuiper, Bob W. Kooi, Garry D. Peterson, Wolf M. Mooij
Ecologists are challenged by the need to bridge and synthesize different approaches and theories to obtain a coherent understanding of ecosystems in a changing world. Both food web theory and regime shift theory shine light on mechanisms that confer stability to ecosystems, but from a different angle. Empirical food…
Yevhen F. Suprunenko, Aneta Stefanovska
Chronotaxic systems represent deterministic nonautonomous oscillatory systems which are capable of resisting continuous external perturbations while having a complex time-dependent dynamics. Until their recent introduction in Phys. Rev. Lett. 111, 024101 (2013) chronotaxic systems had often been treated as stochastic…
J. Nathan Kutz
Approximation techniques have been historically important for solving differential equations, both as initial value problems and boundary value problems. The integration of numerical, analytic and perturbation methods and techniques can help produce meaningful approximate solutions for many modern problems in the…
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…
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…
Ashley Fidler, Yen-Cheng Lin, James Gaynor, William McCurdy + 3 more
Nonlinear spectroscopies can disentangle spectra that are congested due to inhomogeneous broadening. In conjunction with theoretical calculations, attosecond extreme ultraviolet (XUV) four-wave mixing (FWM) spectroscopy is utilized here to probe the dynamics of autoionizing, inner valence excited Rydberg states of the…
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…
Zifan Ma, Liangyi Chen, Chuzhi Xu, Joseph Fournier
Two-dimensional infrared (2D IR) spectroscopy of mass-selected, cryogenically cooled molecular ions is presented. Nonlinear response pathways, encoded in the time-domain photodissociation action response of weakly-bound N2 messenger tags, are isolated using pulse shaping techniques following excitation with four…
Authors not listed
We present a chemical framework in which adaptive organization is achieved by tuning a gated quantum resonator (adaptive genomic resonator) {driven quantum oscillator} across a driven, dissipative reaction manifold (fitness landscape) {Hamiltonian potential surface}. In this view, catalytic elements set gain and phase…
William Sulis
The full range of biopsychosocial complexity is mind-boggling, spanning a vast range of spatiotemporal scales with complicated vertical, horizontal, and diagonal feedback interactions between contributing systems. It is unlikely that such complexity can be dealt with by a single model. One approach is to focus on a…
Authors not listed
The GENERIC framework provides a robust structure for nonequilibrium dynamics but lacks a principled method to select reversible ($L$) and irreversible ($M$) brackets. Similarly, finite-time optimizations minimizing path-averaged reciprocal temperature exist but remain isolated. Here, we introduce the \textbf{Entropy…
Jane Kondev, Marc Kirschner, Hernan G. Garcia, Gabriel L. Salmon + 1 more
Many biological processes can be thought of as the result of an underlying dynamics in which the system repeatedly undergoes distinct and abortive trajectories with the dynamical process only ending when some specific process, purpose, structure or function is achieved. A classic example is the way in which…
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…