Results 11 to 20 of about 774 (145)
Exploring Limit Cycle Bifurcations in the Presence of a Generalized Heteroclinic Loop
Mathematics, 2023 This work revisits the number of limit cycles (LCs) in a piecewise smooth system of Hamiltonian with a heteroclinic loop generalization, subjected to perturbed functions through polynomials of degree m.
Erli Zhang, Stanford Shateyi
doaj +1 more source
Second Order Melnikov Functions of Piecewise Hamiltonian Systems [PDF]
International Journal of Bifurcation and Chaos, 2020 In this paper, we consider the general perturbations of piecewise Hamiltonian systems. A formula for the second order Melnikov functions is derived when the first order Melnikov functions vanish. As an application, we can improve an upper bound of the number of bifurcated limit cycles of a piecewise Hamiltonian system with quadratic polynomial ...
Françoise, Jean-Pierre +2 more
openaire +2 more sources
Global Bifurcation Behaviors and Control in a Class of Bilateral MEMS Resonators
Fractal and Fractional, 2022 The investigation of global bifurcation behaviors the vibrating structures of micro-electromechanical systems (MEMS) has received substantial attention. This paper considers the vibrating system of a typical bilateral MEMS resonator containing fractional
Yijun Zhu, Huilin Shang
doaj +1 more source
On the number of zeros of Melnikov functions [PDF]
Annales de la Faculté des sciences de Toulouse : Mathématiques, 2011 We provide an effective uniform upper bound for the number of zeros of the first non-vanishing Melnikov function of a polynomial perturbations of a planar polynomial Hamiltonian vector field. The bound depends on degrees of the field and of the perturbation, and on the order k
Benditkis, Sergey, Novikov, Dmitry
openaire +2 more sources
Determinant grammar of the Russian language as an academic grammar of a new type
Russian Language Studies, 2023 The relevance of the research is caused by the need to find a method that provides a complete and systematic presentation of Russian grammar. The aim of the study is to discuss the prospects for creating a grammar that will clarify the reasons for the ...
Olga I. Valentinova +2 more
doaj +1 more source
The Number of Limit Cycles Bifurcating from an Elementary Centre of Hamiltonian Differential Systems
Mathematics, 2022 This paper studies the number of small limit cycles produced around an elementary center for Hamiltonian differential systems with the elliptic Hamiltonian function H=12y2+12x2−23x3+a4x4(a≠0) under two types of polynomial perturbations of degree m ...
Lijun Wei, Yun Tian, Yancong Xu
doaj +1 more source
A note on the Melnikov function [PDF]
Vietnam Journal of Mechanics, 2007 With one (Poincaré section) parameter and a particular motion law (that associated to certain determined point of horno-heteroclinic orbits), the usual form of the Melnikov function seems to be not convenient for certain problems. Another favorable form can be obtained by using a supplementary parameter - the arbitrary time constant in the general ...
openaire +2 more sources
Prediction of chaos in a Josephson junction by the Melnikov-function technique [PDF]
Physical Review B, 1986 The Melnikov function for prediction of Smale horseshoe chaos is applied to the rf-driven Josephson junction. Linear and quadratic damping resistors are considered. In the latter case the analytic solution including damping and dc bias is used to obtain an improved threshold curve for the onset of chaos.
Bartuccelli, M. +3 more
openaire +3 more sources
Nilpotence of orbits under monodromy and the length of Melnikov functions
Physica D: Nonlinear Phenomena, 2021 Let $F\in\mathbb{C}[x,y]$ be a polynomial, $γ(z)\in π_1(F^{-1}(z))$ a non-trivial cycle in a generic fiber of $F$ and let $ω$ be a polynomial $1$-form, thus defining a polynomial deformation $dF+εω=0$ of the integrable foliation given by $F$. We study different invariants: the orbit depth $k$, the nilpotence class}$n$, the derivative length}$d ...
Mardešić, Pavao +3 more
openaire +4 more sources
Morse and Melnikov functions for NLS Pde's [PDF]
Communications in Mathematical Physics, 1994 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Li, Y., McLaughlin, David W.
openaire +2 more sources