Results 31 to 40 of about 26,339 (212)

Bifurcating Limit Cycles with a Perturbation of Systems Composed of Piecewise Smooth Differential Equations Consisting of Four Regions

Mathematics, 2023
Systems composed of piecewise smooth differential (PSD) mappings have quantitatively been searched for answers to a substantial issue of limit cycle (LC) bifurcations. In this paper, LC numbers (LCNs) of a PSD system (PSDS) consisting of four regions are
Erli Zhang, Jihua Yang, Stanford Shateyi
doaj   +1 more source

Melnikov Method for a Class of Generalized Ziegler Pendulums

Mathematics
The Melnikov method is applied to a class of generalized Ziegler pendulums. We find an analytical form for the separatrix of the system in terms of Jacobian elliptic integrals, holding for a large class of initial conditions and parameters. By working in
Stefano Disca, Vincenzo Coscia
doaj   +1 more source

Analysis of Tangential Nonlinear Vibration on Machine Hydrostatic Slide

Shock and Vibration, 2019
In this paper, the nonlinear dynamic responses of the hydrostatic slide were investigated and the effects of damping and external force to control the vibration system were discussed.
Zhongkui Zhang, Feng Gao, Yan Li, Han Zhang   +3 more
doaj   +1 more source

Heteroclinic intersections between Invariant Circles of Volume-Preserving Maps

, 2002
We develop a Melnikov method for volume-preserving maps with codimension one invariant manifolds. The Melnikov function is shown to be related to the flux of the perturbation through the unperturbed invariant surface.
Abraham R, Arnold V I, Baldomà M, Cartwright J H E, Delshams A, Delshams A, Easton R W, Easton R W, Feingold M, H E Lomel, Holmes P, J D Meiss, LomelíH E, LomelíH E, MacKay R S, MacKay R S, MacKay R S, Meiss J D, Mezic I, Piro O, Rom-Kedar V, Suris Y B, Treshev D V, Wiggins S   +23 more
core   +1 more source

Chaos in black holes surrounded by gravitational waves [PDF]

, 1997
The occurrence of chaos for test particles moving around Schwarzschild black holes perturbed by a special class of gravitational waves is studied in the context of the Melnikov method.
Arnold V I, Belinskii V A, Biesiada M, Bombelli L, Chandrasekhar S, Contopoulos G, Contopoulos G, Francisco G, Friedman J L, Karas V, Letelier P S, Melnikov V K, Moeckel R, P S Letelier, Sota Y, Vieira W M, W M Vieira, Xanthopoulos B C   +17 more
core   +2 more sources

Study of limit cycles in piecewise smooth perturbations of Hamiltonian centers via regularization method

Electronic Journal of Qualitative Theory of Differential Equations, 2017
In this article we study the existence and positions of limit cycles in piecewise smooth perturbations of planar Hamiltonian centers. By using the regularization method we provide an analytical expression for the first order Melnikov function frequently ...
Luis Mello, Denis Braga, Alexander Fonseca   +2 more
doaj   +1 more source

Exponentially small asymptotic formulas for the length spectrum in some billiard tables [PDF]

, 2015
Let $q \ge 3$ be a period. There are at least two $(1,q)$-periodic trajectories inside any smooth strictly convex billiard table, and all of them have the same length when the table is an ellipse or a circle.
Martín, Pau, Ramírez-Ros, Rafael, Tamarit-Sariol, Anna   +2 more
core   +3 more sources

Dynamical Analysis of Barium Titanate Crystal in Alternative Voltage RL Circuit

Chaos and Fractals
This brief paper theoretically investigates the dynamical characteristics of ferroelectric materials, specifically barium titanate $(BaTiO_3) $ crystal in alternative voltage resistor (R) and inductor (L) circuit.
Guy Joseph Eyebe, Justin Mibaile, Rolande Tsapla Fotsa, Gambo Betchewe, Alidou Mohamadou   +4 more
doaj   +1 more source

Continuation of the exponentially small transversality for the splitting of separatrices to a whiskered torus with silver ratio [PDF]

, 2014
We study the exponentially small splitting of invariant manifolds of whiskered (hyperbolic) tori with two fast frequencies in nearly-integrable Hamiltonian systems whose hyperbolic part is given by a pendulum. We consider a torus whose frequency ratio is
A Delshams, A Delshams, A Delshams, A Delshams, A Delshams, A Delshams, A Delshams, A Delshams, A Delshams, A Delshams, A Delshams, Amadeu Delshams, AV Pronin, C Simó, C Simó, D Kalman, D Sauzin, G Gallavotti, G Gallavotti, G Gallavotti, H Koch, H Poincaré, I Baldomá, L H Eliasson, L Niederman, M Guardia, M Rudnev, M Rudnev, Marina Gonchenko, P Lochak, Pere Gutiérrez, S Falcón, V F Lazutkin, V G Gelfreich, V I Arnold, VK Melnikov   +35 more
core   +5 more sources

A Melnikov Method for Homoclinic Orbits with Many Pulses [PDF]

Archive for Rational Mechanics and Analysis, 1998
The authors study the persistence of homoclinic orbits with many pulses for hyperbolic periodic orbits to a system being a perturbation of a four-dimensional integrable Hamiltonian system. The unperturbed system is supposed to have a one-parameter family of hyperbolic periodic orbits, such that stable and unstable manifolds of each periodic orbit ...
Kovačič, Gregor, Tin, Siu-Kei, Camassa, Roberto   +2 more
openaire   +3 more sources