Results 21 to 30 of about 26,339 (212)
Poincaré - Melnikov - Arnold method for analytic planar maps [PDF]
Nonlinearity, 1996 The Poincare-Melnikov-Arnold method for planar maps gives rise to a Melnikov function defined by an infinite and (a priori) analytically uncomputable sum. Under an assumption of meromorphicity, residues theory can be applied to provide an equivalent finite sum. Moreover, the Melnikov function turns out to be an elliptic function and a general criterion
Delshams Valdés, Amadeu +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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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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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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The local cyclicity problem: Melnikov method using Lyapunov constants
Proceedings of the Edinburgh Mathematical Society, 2022 AbstractIn 1991, Chicone and Jacobs showed the equivalence between the computation of the first-order Taylor developments of the Lyapunov constants and the developments of the first Melnikov function near a non-degenerate monodromic equilibrium point, in the study of limit cycles of small-amplitude bifurcating from a quadratic centre.
Luiz F. S. Gouveia, Joan Torregrosa
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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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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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Chaotic Behavior of the Biharmonic Dynamics System
International Journal of Mathematics and Mathematical Sciences, 2009 Motion of a biharmonic system under action of small periodic force and small damped force is studied. The biharmonic oscillator is a physical system acting under a biharmonic force like asinθ+bsin2θ. The article contains biharmonic oscillator analysis,
Vladimir S. Aslanov
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Limit cycle bifurcations in a planar piecewise quadratic system with multiple parameters
Advances in Difference Equations, 2020 This paper is concerned with the number of limit cycles bifurcating from a period annulus for some planar piecewise smooth non-Hamiltonian systems. We construct a planar piecewise quadratic system with multiple parameters, obtain its lower bound for the ...
Shuhua Gong, Maoan Han
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