Results 1 to 10 of about 166,080,641 (165)

Perturbative-Iterative Computation of Inertial Manifolds of Systems of Delay-Differential Equations with Small Delays

Algorithms, 2020
Delay-differential equations belong to the class of infinite-dimensional dynamical systems. However, it is often observed that the solutions are rapidly attracted to smooth manifolds embedded in the finite-dimensional state space, called inertial ...
Marc R. Roussel
doaj   +2 more sources

Algorithmic Probability-Guided Machine Learning on Non-Differentiable Spaces

Frontiers in Artificial Intelligence, 2021
We show how complexity theory can be introduced in machine learning to help bring together apparently disparate areas of current research. We show that this model-driven approach may require less training data and can potentially be more generalizable as
Santiago Hernández-Orozco, Santiago Hernández-Orozco, Hector Zenil, Hector Zenil, Hector Zenil, Hector Zenil, Jürgen Riedel, Jürgen Riedel, Adam Uccello, Narsis A. Kiani, Narsis A. Kiani, Jesper Tegnér   +11 more
doaj   +1 more source

The Cauchy atlas on the manifold of all complete ODE solutions

, 2003
In this paper the necessary and sufficient conditions for a mapping to be the dependence of the complete solution of some differentiable first-order ordinary differential equation on the initial Cauchy condition are deduced. The result is obtained by studying the Cauchy atlas on a manifold of complete solutions.
Chladek, P., Klapka, L.
openaire   +2 more sources

Dynamical analysis and bifurcations in a fractional integrable equation

Alexandria Engineering Journal
This paper investigates the dynamics of the nonlinear (1+1)-dimensional integrable beta-fractional Akbota equation, a Heisenberg ferromagnet-type model essential for understanding curve analysis and surface geometry.
Hongwei Ma, Riaz Ur Rahman, Solomon Manukure   +2 more
doaj   +1 more source

Bifurcation Geometry, Global Stability, and Nonlinear Nematicon Dynamics of the Generalized Hunter–Saxton Model

Mathematics
This study examines the generalized nonlinear Hunter–Saxton (HS) model: Φtx=ΦΦxx+γΦx2,γ≠0, that describes the evolution of spatial potential and angular velocity in the vector field of nematic liquid crystals.
Emad A. Az-Zo’bi
doaj   +1 more source

Harmonic solutions to perturbations of periodic separated variables ODEs on manifolds

Electronic Journal of Differential Equations, 2003
Consider the differential equation \[ x'=a(t)g(x), \] where \(a(t)\) is a continuous scalar \(T\)-periodic function with nonzero average and \(g(x)\) is a continuous tangent field on a smooth manifold without boundary. The author studies perturbations of the form \[ x'=a(t)g(x)+\lambda f(t,x), \] where the field \(f(t,x)\) is \(T\)-periodic in \(t ...
openaire   +3 more sources

LAIOR: a hyperbolic neural ODE variational framework for interpretable single-cell manifold learning and trajectory inference. [PDF]

Front Genet
Fu Z, Fu J, Zhang K, Ran T, Chen C.
europepmc   +1 more source

Data-driven reduced modeling of neural dynamics. [PDF]

Nat Commun
Marraffa A, Krause R, Mante V, Haller G.
europepmc   +1 more source

Exact traveling-wave solutions and dynamical behavior of nonlinear low-pass electrical models in the fractional framework. [PDF]

Sci Rep
Alsheekhhussain Z, Shah R, Sanaee H, Alshammari S, Alshammari M, Al-Sawalha MM.   +5 more
europepmc   +1 more source

A note on integrated local energy decay estimates for spherically symmetric black hole spacetimes. [PDF]

Math Ann
Holzegel G, Mavrogiannis G, Ruiz RV.
europepmc   +1 more source