Weak-Coupling Theory for Semiclassical Periodically Driven Two-Level Systems： Beyond Rotating-Wave Approximation

We present a weak-coupling theory of semiclassical periodically driven two-level systems. The explicit analytical approximating solution is shown to reproduce highly accurately the exact results well beyond the regime of the rotating-wave approximation.

The Existence of Periodic Orbits for Higher Dimensional Autonomous Systemswith Small Perturbations

By means of theory of toplogical degree in nonlinear functional analysis combining with qualitative analysis method in ordinary differential equations, we discuss the existence of nontrivial periodic orbits for higher dimensional autonomous system with small perturbations.

MULTIPLE SOLUTIONS FOR HAMILTONIAN SYSTEMS WITH PERIODIC NONLINEARITY AND STRONG RESONANCE

I. Introduction In this paper we are looking for solutions of the following Hamiltonian system of second order: where x= （x1, x2） and V satisfies （V. 1） V: R×R2→R is a C1-function, 1-periodic In t, （V.2） V is periodic in x1 with the period T>0, （V. 3） V→O, Vx→O as |x2|→∞, uniformly in （t, x1）.

Analytical Solution of Weak-Coupling Periodically Driven Two-Level System

We present an approximate analytical solution to periodically driven two-level system in the weak-coupling regime. The analytical solution is in good agreement with the exact numerical solution in resonance and near resonance cases when Ω 〈 0.3ωa with Ω and ωa denoting the Rabi and transition frequencies respectively.

Vibrational Stabilization by Reshaping Arnold Tongues: A Numerical Approach

This paper presents two contributions to the stability analysis of periodic systems modeled by a Hill equation: The first is a new method for the computation of the Arnold Tongues associated to a given Hill equation which is based on the discretization of the latter. Using the proposed method, a vibrational stabilization is performed by a change in the periodic function which guarantees stability, given that the original equation has unbounded solutions. The results are illustrated by some examples.

Perturbations of Multipliers of Systems of Periodic Ordinary Differential Equations

The paper deals with periodic systems of ordinary differential equations(ODEs).A new approach to the investigation of variations of multipliers under perturbations is suggested.It enables us to establish explicit conditions for the stability and instability of perturbed systems.

EXISTENCE OF ALMOST PERIODIC SOLUTIONS FOR DIFFERENCE SYSTEMS

In this work, we first define the notions of almost periodic sequences, asymptotically almost periodic sequences, as well as uniformly almost periodic sequences,and reveal their basic properties. Then for the almost periodic difference systems of general form we establish the criteria of existence for almost periodic solutions.Especially, several existence theorems are proved in terms of discrete Liapunov functions.

Infinitely Many Periodic Solutions for a Class of Second-order Hamiltonian Systems

In this paper we study the existence of infinitely many periodic solutions for second-order Hamiltonian systems{ü（t）＋A（t）u（t）＋▽F（t,u（t））=0,u（0）-u（T）=u^·（0）-u^·（T）=0,where F（t,u） is even in u,and ▽（t,u） is of sublinear growth at infinity and satisfies the Ahmad-Lazer-Paul condition.

On the Existence,Uniqueness and Stability of Periodic Solutions of Large Scale Systems with Unbounded Delay

In this paper,we consider the periodic solution problems for the systems with unbounded delay,and the existence,uniqueness and stability of the periodic solution are dealt with unitedly.First we establish the suitable delay-differential inequality,then study seperately the problems of periodic solution for the systems with bounded delay,with unbounded delay and the Volterra integral-dlfferentlal systems with infinite delay by using the character of matrix measure and the asymptotic fixed point theorem of poincaré’s periodic operator in the different phase spaces.A series of simple criteria for the existence,uniqueness and stability of these systems are obtained.

On the Periodic Solutions of Hamiltonian Systems of Second--order

§ 1. IntroductionIn the present paper, we study following Hamiltonian system of Second-order:(1) with the boundary conditionx (0) = x (2jr) , x’ (0) = x’ (2w) ,(2)where p(t) ￡O(R, Rn"), G(t, x) ￡O(RxR", R). P(-) and &( , x) are 25F-periodio functions. Vj, or G’x(t, a/) will denote the gradient with respect to x. Moreover, we shall always assume that G’x(t, x) is continuous.

Asymptotic behavior of the principal eigenvalue and the basic reproduction ratio for periodic patch models

This paper is devoted to the study of the asymptotic behavior of the principal eigenvalue and the basic reproduction ratio associated with periodic population models in a patchy environment for small and large dispersal rates.We first deal with the eigenspace corresponding to the zero eigenvalue of the connectivity matrix.Then we investigate the limiting profile of the principal eigenvalue of an associated periodic eigenvalue problem as the dispersal rate goes to zero and infinity,respectively.We further establish the asymptotic behavior of the basic reproduction ratio in the case of small and large dispersal rates.Finally,we apply these results to a periodic Ross-Macdonald patch model.

THE EXISTENCE OF POSITIVE PERIODIC SOLUTION FOR A LOTKA-VOLTERRA DIFFERENCE SYSTEM

A general periodic Lotka-Volterra difference system is studied in this paper. A set of easily verifiable sufficient conditions that guarantee the existence of the positive periodic solutions is obtained.

Observability of Periodically Switched Boolean Control Networks

In this paper,observability is studied for periodically switched Boolean control networks(PSBCNs),which are managed with periodic switching signal and consist of some Boolean control networks.Firstly,via semi-tensor product of matrices,PSBCNs are expressed as algebraic forms.Secondly,a parallel system is constructed by combining two same PSBCNs,based on which,the observability problem of the original PSBCN can be transformed into the set reachability problem of this parallel system.Then,two necessary and sufficient conditions are obtained to detect reachability of parallel systems and observability of PSBCNs.In addition,the proposed conditions are extended to the case of state constraints.Finally,a practical example and a numerical example are provided to illustrate the results.

On the l_2-stability of time-varying linear and nonlinear discrete-time MIMO systems

New conditions are derived for the l2-stability of time-varying linear and nonlinear discrete-time multiple-input multipleoutput （MIMO） systems, having a linear time time-invariant block with the transfer function F（z）, in negative feedback with a matrix of periodic/aperiodic gains A（k）, k = 0,1, 2,... and a vector of certain classes of non-monotone/monotone nonlinearities φp（-）, without restrictions on their slopes and also not requiring path-independence of their line integrals. The stability conditions, which are derived in the frequency domain, have the following features： i） They involve the positive definiteness of the real part （as evaluated on ｜z｜ = 1） of the product of Г （z） and a matrix multiplier function of z. ii） For periodic A（k）, one class of multiplier functions can be chosen so as to impose no constraint on the rate of variations A（k）, but for aperiodic A（k）, which allows a more general multiplier function, constraints are imposed on certain global averages of the generalized eigenvalues of （A（k ＋ 1）,A（k））, k = 1, 2 iii） They are distinct from and less restrictive than recent results in the literature.

ON A PERIODIC LOTKA-VOLTERRA SYSTEM WITH SEVERAL DELAYS

A periodic predator-prey system with several delays is studied in this paper. A set of easily verifiable sufficient conditions that guarantee the existence, uniqueness and global attractivity of the positive periodic solutions is obtained.