Results 21 to 30 of about 18,615 (139)

Unstable recurrent patterns in Kuramoto-Sivashinsky dynamics [PDF]

, 2008
We undertake a systematic exploration of recurrent patterns in a 1-dimensional Kuramoto-Sivashinsky system. For a small, but already rather turbulent system, the long-time dynamics takes place on a low-dimensional invariant manifold.
A. Politi, C. Foias, C. Simo, P. Cvitanović, P. Cvitanović, P. Holmes, Predrag Cvitanović, R. Gilmore, R. Temam, U. Frisch, Yueheng Lan   +10 more
core   +1 more source

Dynamical Analysis and Soliton Solutions of the Truncated M-Fractional FitzHugh–Nagumo Equation

Fractal and Fractional
In this paper, we investigate the (1 + 1)-dimensional nonlinear truncated M-fractional FitzHugh–Nagumo model. The main objective is to analyze the dynamical behavior and obtain exact solutions for the model.
Beenish, Abdulaziz Khalid Alsharidi
doaj   +1 more source

Work Versus Force: Simultaneous Processes for Describing Interactions

Advanced Physics Research, EarlyView.
ABSTRACT Achieving a unified description of interactions remains an open challenge in theoretical physics, which currently describes four fundamental forces. This situation may be viewed differently when interactions are formulated in terms of processes (work as actio) rather than forces (force as actio), not only at the macroscopic level but also at ...
Grit Kalies, Duong D. Do, Cornelia Breitkopf   +2 more
wiley   +1 more source

Energetics, skeletal dynamics and long-term predictions in Kolmogorov-Lorenz systems

, 2007
We study a particular return map for a class of low dimensional chaotic models called Kolmogorov Lorenz systems, which received an elegant general Hamiltonian description and includes also the famous Lorenz63 case, from the viewpoint of energy and ...
E. Kalnay, E. N. Lorenz, F. Maimone, J. E. Marsden, R. Salmon, V. I. Arnold, V. Pelino   +6 more
core   +1 more source

Exploring Soliton Solutions and Chaotic Dynamics in the (3+1)-Dimensional Wazwaz–Benjamin–Bona–Mahony Equation: A Generalized Rational Exponential Function Approach

Fractal and Fractional
This paper investigates the explicit, accurate soliton and dynamic strategies in the resolution of the Wazwaz–Benjamin–Bona–Mahony (WBBM) equations.
Amjad E. Hamza, Muntasir Suhail, Amer Alsulami, Alaa Mustafa, Khaled Aldwoah, Hicham Saber   +5 more
doaj   +1 more source

The Benjamin–Ono Equation in the Zero‐Dispersion Limit for Rational Initial Data: Generation of Dispersive Shock Waves

Communications on Pure and Applied Mathematics, EarlyView.
ABSTRACT The leading‐order asymptotic behavior of the solution of the Cauchy initial‐value problem for the Benjamin–Ono equation in L2(R)$L^2(\mathbb {R})$ is obtained explicitly for generic rational initial data u0$u_0$. An explicit asymptotic wave profile uZD(t,x;ε)$u^\mathrm{ZD}(t,x;\epsilon)$ is given, in terms of the branches of the multivalued ...
Elliot Blackstone, Louise Gassot, Patrick Gérard, Peter D. Miller   +3 more
wiley   +1 more source

Optimal Phase Description of Chaotic Oscillators

, 2011
We introduce an optimal phase description of chaotic oscillations by generalizing the concept of isochrones. On chaotic attractors possessing a general phase description, we define the optimal isophases as Poincar\'e surfaces showing return times as ...
A. Pikovsky, A. S. Pikovsky, A. T. Winfree, Arkady Pikovsky, Björn Kralemann, E. M. Izhikevich, H. Kantz, Justus T. C. Schwabedal, M. Rosenblum, Michael Rosenblum, T. Hastie, W. H. Press, Y. Kuramoto   +12 more
core   +1 more source

Nonlinear Dynamics of a Passive Walker: Bifurcation and Stability Insights With Spring and Damper Mechanics

International Journal of Mechanical System Dynamics, EarlyView.
ABSTRACT This study explores the nonlinear dynamics associated with a passive dynamic walker (PDW), focusing on the bifurcation and stability insights derived from spring and damper mechanics. PDWs, which rely on gravity for stable locomotion without active control, exhibit a rich spectrum of behaviors, from periodic to chaotic motion.
Zhongqu Xie, Xue Gong, Qidi Fu, Pierluigi Arpenti, Shichao Zhou, Anhua You, Xiaolong Yang, Lingkun Chen, Yulin Wang   +8 more
wiley   +1 more source

Heteroclinic connections between periodic orbits and resonance transitions in celestial mechanics [PDF]

, 2000
In this paper we apply dynamical systems techniques to the problem of heteroclinic connections and resonance transitions in the planar circular restricted three-body problem.
Koon, Wang Sang, Lo, Martin W., Marsden, Jerrold E., Ross, Shane D.   +3 more
core   +3 more sources

Machine Learning for Local Detection of Separators in Three‐Dimensional Magnetic Fields

Journal of Geophysical Research: Machine Learning and Computation, Volume 3, Issue 3, June 2026.
Abstract Magnetic reconnection is a major plasma phenomenon occurring in various key environments ranging from the Sun and near‐Earth space to astrophysical plasmas. While magnetic reconnection is relatively well‐understood under two‐dimensional (2D) settings, it remains challenging to characterize in three‐dimensional (3D) magnetic fields.
Fanni Franssila, Markku Alho, Ioanna Bouri, Daniel Holmberg, Minna Palmroth, Teemu Roos   +5 more
wiley   +1 more source