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A Characterization of Multiplicity-Preserving Global Bifurcations of Complex Polynomial Vector Fields
Springer Science and Business Media LLC - Tập 19 Số 3 - 2020
Asymptotic Stability of Coupled Oscillators with Time-Dependent Damping
Springer Science and Business Media LLC - Tập 15 - Trang 553-573 - 2015
The present paper is devoted to an investigation on the asymptotic stability for
the damped oscillators with multiple degrees of freedom, $$\begin{aligned}
{\mathbf {x}}'' + h(t)\,{\mathbf {x}}' + A\,{\mathbf {x}} = {\mathbf {0}}
\end{aligned}$$ and its generalization $$\begin{aligned} M\,{\mathbf {x}}'' +
C(t)\,{\mathbf {x}}' + K\,{\mathbf {x}} = {\mathbf {0}}, \end{aligned}$$ where
$$h: [0,\inft...
KAM Tori for a Two Dimensional Beam Equation with a Quintic Nonlinear Term and Quasi-periodic Forcing
Springer Science and Business Media LLC - Tập 21 - Trang 1-43 - 2022
This work studies a two-dimensional beam equation with a quintic nonlinear term
and quasi-periodic forcing $$\begin{aligned} u_{tt}+\Delta ^2 u+ \varepsilon
\phi (t)h(u)=0,\quad x\in {\mathbb {T}}^2,\quad t\in {\mathbb {R}}
\end{aligned}$$ with periodic boundary conditions, where $$\varepsilon $$ is a
small positive parameter; $$\phi (t)$$ is a real analytic quasi-periodic
function in t with frequ...
On the Solutions of Ordinary Differential Equations in the Form of Dulac Series
Springer Science and Business Media LLC - Tập 21 - Trang 1-16 - 2022
We consider a nonlinear ordinary differential equation of arbitrary order with
coefficients in the form of power series that converge in a neighborhood of the
origin. The methods created in power geometry in recent years make it possible
to compute formal solutions to that equation in the form of Dulac series. We
describe the corresponding algorithm and prove a sufficient convergence
condition for...
Nonholonomic systems and the geometry of constraints
Springer Science and Business Media LLC - Tập 5 - Trang 247-259 - 2004
In a recent paper [9] we analyze conservation of volume for a series of examples
of mechanical systems with linear, affine and non linear constraints aiming to
make evident some geometric aspects related with them. Here, we only consider
examples with linear constraints (defined by a constant rank distribution), in
which we have conservation of volume. Conservation of volume means,
equivalently, t...
Inverse Scattering Transform and Dynamics of Soliton Solutions for Nonlocal Focusing Modified Korteweg-de Vries Equation
Springer Science and Business Media LLC - - 2024
The Riemann–Hilbert problem is developed to study the general N-soliton solution
of the nonlocal modified Korteweg-de Vries equation in this work. The key to
proving this result is the analysis of the Riemann–Hilbert problem related to
the Cauchy problem of the nonlocal modified Korteweg-de Vries equation. The
general N-soliton solution is acquired by solving the Riemann–Hilbert problem of
the non...
Dynamical Behavior of a Stochastic Microorganism Flocculation Model with Nonlinear Perturbation
Springer Science and Business Media LLC - Tập 21 - Trang 1-19 - 2022
Due to many uncertain factors, the microorganism flocculation models could be
affected by environmental noise. The paper aims to discuss the dynamical
behavior of a stochastic microorganism flocculation model, including the
extinction and the persistence. Moreover, the expression of density function
near the positive equilibrium point is explicitly obtained. Our results indicate
that a larger whit...
Dynamics of One-Dimensional Motion of a Gas Under the Influence of Monochromatic Radiation
Springer Science and Business Media LLC - Tập 22 - Trang 1-21 - 2023
The concern with the dispersion of shock waves in perfect gas in the context of
monochromatic radiation is mentioned in this manuscript. The system of
Hyperbolic nonlinear partial differential equations (NLPDEs) is used to address
this issue. In order to study aforementioned equations, invariance under Lie
symmetry analysis is performed. Therefore, commutative relations, symmetry
groups and adjoin...
Classification of permutations and cycles of maximum topological entropy
Springer Science and Business Media LLC - Tập 4 - Trang 77-97 - 2003
Iff is a continuous self-map of a compact interval we can represent each finite
fully invariant set off by a permutation. We can then calculate the topological
entropy of the permutation. This provides us with a numerical measure of
complexity for any map which exhibits a given permutation type. In this paper we
present cyclic and noncyclic permutations which have maximum topological entropy
among...
Yet Another Class of New Solvable N-Body Problems of Goldfish Type
Springer Science and Business Media LLC - Tập 16 - Trang 561-577 - 2016
A new class of solvable N-body problems of goldfish type is exhibited and the
properties of their solutions are tersely discussed. It is moreover shown that
these are integrable Hamiltonian systems.
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