Normal form and Hopf bifurcation for the memory‐based reaction‐diffusion equation with nonlocal effect
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DOI: 10.1002/mma.10185
Abstract: In this paper, we provide the normal form for the Hopf bifurcation of a class of the reaction‐diffusion equation with memory‐based diffusion and nonlocal effect, where the delay is present in the differential term, similar… read more here.
Keywords: normal form; hopf bifurcation; diffusion; bifurcation ... See more keywords
Convergence to Normal Forms of Integrable PDEs
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DOI: 10.1007/s00220-019-03661-8
Abstract: In an infinite dimensional Hilbert space we consider a family of commuting analytic vector fields vanishing at the origin and which are nonlinear perturbations of some fundamental linear vector fields. We prove that one can… read more here.
Keywords: integrable pdes; convergence normal; normal form; forms integrable ... See more keywords
Comparing the direct normal form and multiple scales methods through frequency detuning
Sign Up to like & getrecommendations! Published in 2018 at "Nonlinear Dynamics"
DOI: 10.1007/s11071-018-4534-1
Abstract: Approximate analytical methods, such as the multiple scales (MS) and direct normal form (DNF) techniques, have been used extensively for investigating nonlinear mechanical structures, due to their ability to offer insight into the system dynamics.… read more here.
Keywords: normal form; form multiple; direct normal; multiple scales ... See more keywords
Nonlinear Oscillations of a Spring Pendulum at the 1:1:2 Resonance by Normal Form Methods
Sign Up to like & getrecommendations! Published in 2020 at "Mathematics in Computer Science"
DOI: 10.1007/s11786-019-00427-2
Abstract: The object of this research is the process of small oscillations of a three-dimensional elastic pendulum, tuned to a 1:1:2 resonance to vertical and horizontal oscillations. The purpose is to develop a symbolic algorithm for… read more here.
Keywords: mathematics; normal form; resonance; method ... See more keywords
Forced Nonlinear vibration and bifurcation analysis of circular cylindrical nanocomposite shells using the normal form
Sign Up to like & getrecommendations! Published in 2021 at "International Journal of Non-linear Mechanics"
DOI: 10.1016/j.ijnonlinmec.2021.103733
Abstract: Abstract The current paper focuses on investigating the effect of different distribution types of single-walled carbon nanotube (SWCNT) reinforcement and the volume fraction of CNTs on the nonlinear vibration of simply supported nanocomposite circular cylindrical… read more here.
Keywords: vibration; normal form; nonlinear vibration; using normal ... See more keywords
Versal normal form for nonsemisimple singularities
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DOI: 10.1016/j.jde.2019.03.039
Abstract: Abstract The theory of versal normal form has been playing a role in normal form since the introduction of the concept by V.I. Arnol'd in [1] , [2] . But there has been no systematic… read more here.
Keywords: form; nonsemisimple singularities; versal normal; normal form ... See more keywords
Normal form of nonlinear oscillator model relevant to spin-torque nano-oscillator theory
Sign Up to like & getrecommendations! Published in 2018 at "Physica B: Condensed Matter"
DOI: 10.1016/j.physb.2017.10.021
Abstract: Abstract We introduce a normal form for the equation which describes nonlinear oscillations of spin-torque nano-oscillators (STNO). The general form of the equation might be reduced to the equation for STNO with uniformly magnetized free… read more here.
Keywords: normal form; frequency; oscillator; equation ... See more keywords
Normal forms of C∞ vector fields based on the renormalization group
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DOI: 10.1063/5.0031043
Abstract: The normal form theory for polynomial vector fields is extended to those for C∞ vector fields vanishing at the origin. Explicit formulas for the C∞ normal form and the near identity transformation that brings a… read more here.
Keywords: normal forms; renormalization group; vector fields; normal form ... See more keywords
Enumeration of subdifferentials of piecewise linear functions with abs-normal form
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DOI: 10.1080/10556788.2018.1458848
Abstract: The directional derivatives of a piecewise smooth function at a given point can be computed with Griewank's absolute normal form (ANF). When the given point is a non-differentiable point, the resulting derivative by ordinary algorithmic… read more here.
Keywords: enumeration subdifferentials; piecewise linear; point; normal form ... See more keywords
Multi-winged Lorenz attractors due to bifurcations of a periodic orbit with multipliers (−1,i,−i)
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DOI: 10.1088/1361-6544/ad882f
Abstract: We show that bifurcations of periodic orbits with multipliers (−1,i,−i) can lead to the birth of pseudohyperbolic (i.e. robustly chaotic) Lorenz-like attractors of three different types: one is a discrete analogue of the classical Lorenz… read more here.
Keywords: multi winged; normal form; bifurcations periodic; orbit ... See more keywords
Wake dynamics in buoyancy-driven flows: Steady-state-Hopf-mode interaction with O(2) symmetry revisited.
Sign Up to like & getrecommendations! Published in 2024 at "Physical review. E"
DOI: 10.1103/physreve.109.014216
Abstract: We present a detailed mathematical study of a truncated normal form relevant to the bifurcations observed in wake flow past axisymmetric bodies, with and without thermal stratification. We employ abstract normal form analysis to identify… read more here.
Keywords: dynamics buoyancy; wake dynamics; buoyancy driven; driven flows ... See more keywords