Results 11 to 20 of about 10,996,377 (201)
On the Melnikov method for fractional-order systems [PDF]
Chaos, Solitons & FractalsAccepted
Li, Hang +4 more
exaly +5 more sources
An Application of the Melnikov Method to a Piecewise Oscillator [PDF]
Contemporary Mathematics, 2023 In this paper we present a new application of the Melnikov method to a class of periodically perturbed Duffing equations where the nonlinearity is non-smooth as otherwise required in the classical applications. Extensions of the Melnikov method to these situations is a topic with growing interests from the researchers in the past decade.
Gjata O., Zanolin F.
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Melnikov method for homoclinic bifurcation in nonlinear impact oscillators [PDF]
Computers and Mathematics With Applications, 2005 Based on an inverted pendulum impacting on rigid walls under external periodic excitation, a class of nonlinear impact oscillators is discussed for its homoclinic bifurcation. The Melnikov method established for smooth dynamical systems is extended to be
Weinian Zhang, Zhengdong Du
exaly +2 more sources
The Melnikov Method and Subharmonic Orbits in a Piecewise-Smooth System [PDF]
SIAM Journal on Applied Dynamical Systems, 2012 In this work we consider a two-dimensional piecewise smooth system, defined in two domains separated by the switching manifold $x=0$. We assume that there exists a piecewise-defined continuous Hamiltonian that is a first integral of the system. We also suppose that the system possesses an invisible fold-fold at the origin and two heteroclinic orbits ...
Albert Granados +2 more
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Melnikov method for perturbed completely integrable systems [PDF]
Bulletin of the Belgian Mathematical Society - Simon StevinWe consider a completely integrable system of differential equations in arbitrary dimensions whose phase space contains an open set foliated by periodic orbits. This research analyzes the persistence and stability of the periodic orbits under a nonlinear periodic perturbation. For this purpose, we use the Melnikov method and Floquet theory to establish
Crespo, Francisco +2 more
core +6 more sources
Journal of Mathematics, 2021 This work extends the high-order Melnikov method established by FJ Chen and QD Wang to heteroclinic orbits, and it is used to prove, under a certain class of perturbations, the heteroclinic orbit in a planar vector field that remains unbroken ...
Yi Zhong
doaj +2 more sources
The Melnikov method and Shilnikov bifurcations
, 2021 Ιn this master's thesis we shall see that the Poincaré sequences can reveal significant features of a system and that the appearance of fixed points is closely connected with periodic solutions. Poincaré maps can be used to detect underlying structure, such as periodic solutions having the forcing or a subharmonic frequency.
Χαλού Λούλα, Chalou Loula
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Melnikov's Method and Codimension-Two Bifurcations in Forced Oscillations
Journal of Differential Equations, 2002 The author considers a periodic perturbation of a planar Hamiltonian system of the form \[ \dot{x}=JD_x H(x)+\epsilon g(x,\omega t;\mu),\qquad x\in \mathbb{R}^2. \] It is assumed that the unperturbed system has a one-parameter family of periodic orbits \(q^{\alpha}(t)\) analytic with respect to \(\alpha\).
Kazuyuki Yagasaki
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Introducció al mètode de Melnikov [PDF]
, 2021 Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2021, Director: Ernest Fontich[en] Melnikov method is a method which aims to study the splitting between the stable and unstable manifold of fixed points or
Túnica Rosich, Marc
core +6 more sources
Homoclinic chaos and the Poincaré-Melnikov method [PDF]
, 2022 In this thesis is to describe the use of the Poincaré-Melnikov method in the detection of homoclinic phenomena, and hence chaotic dynamics. After a short review of the theory of dynamical system, it is introduced the Poincaré-Melnikov method and its ...
Azzari, Paride
core