Results 21 to 30 of about 10,399 (114)
Systematic derivation of amplitude equations and normal forms for dynamical systems
Chaos: An Interdisciplinary Journal of Nonlinear Science, 1998 We present a systematic approach to deriving normal forms and related amplitude equations for flows and discrete dynamics on the center manifold of a dynamical system at local bifurcations and unfoldings of these. We derive a general, explicit recurrence relation that completely determines the amplitude equation and the associated transformation from ...
Ipsen, M. +2 more
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Self-similar cuspidal formation by runaway thermocapillary forces in thin liquid films
New Journal of Physics, 2019 Many physical systems give rise to dynamical behavior leading to cuspidal shapes which represent a singularity of the governing equation. The cusp tip often exhibits self-similarity as well, indicative of scaling symmetry invariant in time up to a change
Chengzhe Zhou, Sandra M Troian
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Single-Mode and Dual-Mode Nongomogeneous Dissipative Structures in the Nonlocal Model of Erosion
Моделирование и анализ информационных систем, 2015 We consider a periodic boundary-value problem for a nonlinear equation with the deviating spatial argument in the case when the deviation is small. This equation is called a spatially nonlocal erosion equation.
A. M. Kovaleva, D. A. Kulikov
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Physical Review Special Topics. Accelerators and Beams, 2013 We present a mathematical analysis of planar motion of energetic electrons moving through a planar dipole undulator, excited by a fixed planar polarized plane wave Maxwell field in the x-ray free electron laser (FEL) regime.
James A. Ellison +3 more
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Geometry of Normal Forms for Dynamical Systems
, 2018 We discuss several aspects of the geometry of vector fields in (Poincare'-Dulac) normal form. Our discussion relies substantially on Michel theory and aims at a constructive approach to simplify the analysis of normal forms via a splitting based on the action of certain groups.
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Partial Differential Equations in Applied MathematicsWe study the well-known generalised version of the nonlinear Cahn–Hilliard evolution equation, supplemented with periodic boundary conditions. We study local bifurcations in the vicinity of spatially homogeneous equilibrium states.
A.N. Kulikov, D.A. Kulikov
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Universal Dynamics of Damped-Driven Systems: The Logistic Map as a Normal Form for Energy Balance
, 2022 26 pages, 31 ...
Kutz, J. Nathan +4 more
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MathematicsDeep learning models have demonstrated remarkable success in recognising tipping points and providing early warning signals. However, there has been limited exploration of their application to dynamical systems governed by coloured noise, which ...
Yazdan Babazadeh Maghsoodlo +3 more
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Computation of the Unique Normal Form for Nonlinear Dynamical Systems in the Mechanical Applications
DEStech Transactions on Engineering and Technology Research, 2017 In the mechanical applications, research for degenerate bifurcations is usually connected with the normal form theory of nonlinear dynamical systems. In this paper, we mainly concern with the unique normal form for a class of three dimensional vector fields by the method of transformation with parameters. With the aid of the Maple software, a recursive
Li-ying KOU, Jing LI, Jian-pan FENG
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Normal forms of Hopf Singularities: Focus Values Along with some Applications in Physics
پژوهشهای ریاضی, 2018 This paper aims to introduce the original ideas of normal form theory and bifurcation analysis and control of small amplitude limit cycles in a non-technical terms so that it would be comprehensible to wide ranges of Persian speaking engineers and ...
Majid Gazor, Nasrin Sadri
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