Results 21 to 30 of about 10,996,377 (201)
On the Melnikov function [PDF]
ریاضی و جامعه, 2023 In this article, we have tried to introduce one of the most important topics in the subject of dynamical systems, namely the Melnikov function, in simple language.
Majid Karimi Amaleh
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Brodogradnja, 2021 The trimaran vessel rolls strongly at low forward speed and may capsize in high sea conditions due to chaos and loss of stability, which is not usually considered in conventional limit-based criteria.
Yihan Zhang +3 more
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Singular Separatrix Splitting and the Melnikov Method: An Experimental Study [PDF]
Experimental Mathematics, 1999 We consider families of analytic area-preserving maps depending on two pa- rameters: the perturbation strength E and the characteristic exponent h of the origin. For E=0, these maps are integrable with a separatrix to the origin, whereas they asymptote to flows with homoclinic connections as h->0+.
Delshams, Amadeu, Ramírez-Ros, Rafael
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Beyond the Melnikov method: A computer assisted approach
Journal of Differential Equations, 2017 We present a Melnikov type approach for establishing transversal intersections of stable/unstable manifolds of perturbed normally hyperbolic invariant manifolds (NHIMs). The method is based on a new geometric proof of the normally hyperbolic invariant manifold theorem, which establishes the existence of a NHIM, together with its associated invariant ...
Capiński, Maciej J. +1 more
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On the Exponents of Exponential Dichotomies
Mathematics, 2020 An exponential dichotomy is studied for linear differential equations. A constructive method is presented to derive a roughness result for perturbations giving exponents of the dichotomy as well as an estimate of the norm of the difference between the ...
Flaviano Battelli, Michal Fečkan
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Chaotic Dynamics of Non-Autonomous Nonlinear System for a Sandwich Plate with Truss Core
Mathematics, 2022 This paper deals with the multi-pulse chaotic dynamics of a sandwich plate with truss core under transverse and in-plane excitations. In order to analyze the complicated nonlinear behaviors of the sandwich plate model by means of the improved extended ...
Dongmei Zhang, Feng Li
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Shock and Vibration, 2016 Nonlinear magnetic forces are always used to enlarge resonant bandwidth of vibration energy harvesting systems with piezoelectric cantilever beams. However, how to determine properly the distance between two magnets is one of the key engineering problems.
Zhongsheng Chen +4 more
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Journal of Low Frequency Noise, Vibration and Active Control, 2019 This paper deals with the transitions through Melnikov thresholds and the corresponding fast–slow dynamics in a family of bi-parametric mechanical oscillators subjected to an amplitude modulation force both analytically and numerically. Applying Melnikov
Qianqian Wang +3 more
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Chaotic motion around a black hole under minimal length effects
European Physical Journal C: Particles and Fields, 2020 We use the Melnikov method to identify chaotic behavior in geodesic motion perturbed by the minimal length effects around a Schwarzschild black hole. Unlike the integrable unperturbed geodesic motion, our results show that the perturbed homoclinic orbit,
Xiaobo Guo +4 more
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Poincaré-Melnikov-Arnold Method for Twist Maps [PDF]
, 1999 The Poincar\'e--Melnikov--Arnold method is the standard tool for detecting splitting of invariant manifolds for systems of ordinary differential equations close to ``integrable'' ones with associated separatrices. This method gives rise to an integral (continuous sum) known as the Melnikov function (or Melnikov integral).
Delshams Valdés, Amadeu +1 more
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