JMP: Dynamical Systems

Dynamics of electrostatic microelectromechanical systems actuators

Yisong Yang, Ruifeng Zhang, and Le Zhao
Electrostatic actuators are simple but important switching devices for microelectromechanical systems applications. Due to the difficulties associated with the electrostatic nonlinearity, precise mathematical description is often hard to obtain for the dynamics of these actuators. Here we present tw ... [J. Math. Phys. 53, 022703 (2012)] published Mon Feb 13, 2012.

Total destruction of invariant tori for the generalized FrenkelKontorova model

Xifeng Su and Lin Wang
We consider generalized FrenkelKontorova models on higher dimensional lattices. We show that the invariant tori which are parameterized by continuous hull functions can be destroyed by small perturbations in the C topology with r < 1. ... [J. Math. Phys. 53, 022702 (2012)] published Mon Feb 13, 2012.

The holonomy group at infinity of the Painleve VI equation

Bassem Ben Hamed, Lubomir Gavrilov, and Martine Klughertz
We prove that the holonomy group at infinity of the Painleve VI equation is virtually commutative. ... [J. Math. Phys. 53, 022701 (2012)] published Fri Feb 3, 2012.

Periodic orbits and non-integrability in a cosmological scalar field

Jaume Llibre and Claudio Vidal
We apply the averaging theory of first order to study the periodic orbits of Hamiltonian systems describing a universe filled with a scalar field which possesses three parameters. The main results are the following. First, we provide sufficient conditions on the parameters of these cosmological mode ... [J. Math. Phys. 53, 012702 (2012)] published Tue Jan 10, 2012.

Global attractors for weighted p-Laplacian equations with boundary degeneracy

Shan Ma and Hongtao Li
Using a new a priori estimate method which is introduced by Zhong et al. [J. Differ. Equations 223(2), 367 (2006)], we establish the existence of a global attractor in L(Omega) and L(Omega)(q >= 2), respectively, for weighted p-Laplacian equations with boundary degeneracy and without any restriction ... [J. Math. Phys. 53, 012701 (2012)] published Thu Jan 5, 2012.

Invariant algebraic surfaces for the reduced three-wave interaction system

Adam Mahdi and Claudia Valls
In this paper, we consider the three-wave interaction system x-dot =gammax+deltay+z2y, y-dot =gammaydeltax+2xy, z=2z2zx, where gamma, delta are real parameters. Our main results are the complete characterization of all values of the parameters gamma, delta for which the three-wave interaction syst ... [J. Math. Phys. 52, 122702 (2011)] published Fri Dec 30, 2011.

Dynamically defined measures and equilibrium states

Ivan Werner
A technique of dynamically defined measures is developed and its relation to the theory of equilibrium states is shown. The technique uses Caratheodory's method and the outer measure introduced in a previous work by I. Werner [Math. Proc. Camb. Phil. Soc. 140(2), 333347 (2006)]. As an application, e ... [J. Math. Phys. 52, 122701 (2011)] published Thu Dec 15, 2011.

Dynamical systems defining Jacobi's theta-constants

Yurii V. Brezhnev, Simon L. Lyakhovich, and Alexey A. Sharapov
We propose a system of equations that defines WeierstrassJacobi's eta- and theta-constant series in a differentially closed way. This system is shown to have a direct relationship to a little-known dynamical system obtained by Jacobi. The classically known differential equations by DarbouxHalphen, C ... [J. Math. Phys. 52, 112704 (2011)] published Tue Nov 29, 2011.

Conditional stability theorem for the one dimensional Klein-Gordon equation

Aslihan Demirkaya and Milena Stanislavova
The paper addresses the conditional non-linear stability of the steady state solutions of the one-dimensional Klein-Gordon equation for large time. We explicitly construct the center-stable manifold for the steady state solutions using the modulation method of Soffer and Weinstein and Strichartz typ ... [J. Math. Phys. 52, 112703 (2011)] published Fri Nov 18, 2011.

Non-integrability of a class of Hamiltonian systems

Wenlei Li, Shaoyun Shi, and Bing Liu
In this paper, using the Morales-Ramis theory, we will give some new non-integrability results for a class of famous Hamiltonian models. ... [J. Math. Phys. 52, 112702 (2011)] published Thu Nov 10, 2011.

An integrable many-body problem

F. Calogero
Some years ago, Mikhailov and Sokolov identified as integrable the neat system of two evolution equations U-dot =V, V-dot =U, where U [equivalent] U(t) and V [equivalent] V(t) are two N x N matrices, N is an arbitrarypositive integer, t (time) is the independent variable, and superimposed dots ind ... [J. Math. Phys. 52, 102702 (2011)] published Thu Oct 20, 2011.

On Dirac equation on a time scale

Gro Hovhannisyan
We consider the non-autonomous linear Dirac equation on a time scale containing important discrete, continuous, and quantum time scales. A representation of the solutions is established via an approximate solutions in terms of unknown phase functions with the error estimates. JWKB and other asymptot ... [J. Math. Phys. 52, 102701 (2011)] published Tue Oct 4, 2011.

The Gould-Hopper polynomials in the Novikov-Veselov equation

Jen-Hsu Chang
We use the Gould-Hopper (GH) polynomials to investigate the Novikov-Veselov (NV) equation. The root dynamics of the sigma-flow in the NV equation is studied using the GH polynomials and then the Lax pair is found. In particular, when N = 3, 4, 5, one can get the Gold-fish model. The smooth rational ... [J. Math. Phys. 52, 092703 (2011)] published Wed Sep 28, 2011.

Exponential stability of stochastic differential delay systems with delayed impulse effects

Xiaotai Wu, Litan Yan, Wenbing Zhang, and Yang Tang
In this paper, we investigate the stability of stochastic delay differential systems with delayed impulses by Razumikhin methods. Some criteria on the pth moment exponential stability are obtained. It is shown that if a stochastic delay differential system is exponentially stable, then under some co ... [J. Math. Phys. 52, 092702 (2011)] published Thu Sep 15, 2011.

Stationary states of a nonlinear Schrodinger lattice with a harmonic trap

V. Achilleos, G. Theocharis, P. G. Kevrekidis, N. I. Karachalios, F. K. Diakonos et al.
We study a discrete nonlinear Schrodinger lattice with a parabolic trapping potential. The model, describing, e.g., an array of repulsive Bose-Einstein condensate droplets confined in the wells of an optical lattice, is analytically and numerically investigated. Starting from the linear limit of the ... [J. Math. Phys. 52, 092701 (2011)] published Thu Sep 8, 2011.

Wave attraction in resonant counter-propagating wave systems

M. Grenier, H.-R. Jauslin, C. Klein, and V. B. Matveev
Wave attraction is a general phenomenon that was first established in the context of the attraction of the polarization between two counter-propagating waves in optical fibers. This phenomenon has been observed experimentally, and its properties were studied through numerical simulations. The releva ... [J. Math. Phys. 52, 082704 (2011)] published Wed Aug 31, 2011.

On the recursion operators for the Gerdjikov, Mikhailov, and Valchev system

A. B. Yanovski
We consider the Recursion Operator approach to the soliton equations related to an auxiliary linear system introduced recently by Gerdjikov, Mikhailov, and Valchev (GMV system). We discuss the recursion operators obtained for the GMV system and show that they are particular cases of the generating o ... [J. Math. Phys. 52, 082703 (2011)] published Mon Aug 29, 2011.

Modulated amplitude waves with nonzero phases in Bose-Einstein condensates

Qihuai Liu and Dingbian Qian
In this paper we give a frame for application of the averaging method to Bose-Einstein condensates (BECs) and obtain an abstract result upon the dynamics of BECs. Using the averaging method, we determine the location where the modulated amplitude waves (periodic or quasi-periodic) exist and obtain t ... [J. Math. Phys. 52, 082702 (2011)] published Fri Aug 12, 2011.

On the periodic orbits and the integrability of the regularized Hill lunar problem

Jaume Llibre and Luci Any Roberto
The classical Hill's problem is a simplified version of the restricted three-body problem where the distance of the two massive bodies (say, primary for the largest one and secondary for the smallest one) is made infinity through the use of Hill's variables. The Levi-Civita regularization takes the ... [J. Math. Phys. 52, 082701 (2011)] published Wed Aug 10, 2011.

Geometric shape of invariant manifolds for a class of stochastic partial differential equations

Guanggan Chen, Jinqiao Duan, and Jian Zhang
Invariant manifolds play an important role in the study of the qualitative dynamical behaviors for nonlinear stochastic partial differential equations. However, the geometric shape of these manifolds is largely unclear. The purpose of the present paper is to try to describe the geometric shape of in ... [J. Math. Phys. 52, 072702 (2011)] published Thu Jul 28, 2011.

Asymptotic behavior of two-dimensional stochastic magneto-hydrodynamics equations with additive noises

Wenqiang Zhao and Yangrong Li
This paper is devoted to the investigation of the asymptotic behavior of solutions of the stochastic magneto-hydrodynamics equations driven by random exterior forced terms both in the velocity and in the magnetic field. The nonlinear term is supposed to be time-dependent and satisfies certain dissip ... [J. Math. Phys. 52, 072701 (2011)] published Wed Jul 27, 2011.