The Sufficient and Necessary Condition of Lagrange Stability of Quasi-periodic Pendulum Type Equations

The quasi-periodic pendulum type equations are considered. A sufficient and necessary condition of Lagrange stability for this kind of equations is obtained. The result obtained answers a problem proposed by Moser under the quasi-periodic case.

LAGRANGE STABILITY IN MEAN SQUARE OF STOCHASTIC REACTION DIFFUSION EQUATIONS

This work is devoted to the discussion of stochastic reaction diffusion equations and some new theorems on Lagrange stability in mean square of the solution are established via Lyapunov method which is nothing to be done in the past.

CRITICAL DAMPING OF THE SECOND-ORDERPENDULUM-LIKE SYSTEMS

First,the properties of solutions of a typical second-order pendulum-like system with a specified nonlinear function were discussed.Then the case with a general form of nonlinearity is considered and its global properties were studied by using the qualitative theory of differential equations.As a result,sufficient conditions for estimating the critical damp are established,which improves the work by Leonov et al.

STABILITY IN LAGRANGE SENSE FOR A CLASS OF STOCHASTIC STATIC NEURAL NETWORKS WITH MIXED TIME DELAYS

In this paper, the stability in Lagrange sense of a class of stochastic static neural networks with mixed time delays is studied. Based on the Lyapunov stability theory and with the help of stochastic analysis technique, the criteria for the stability in Lagrange sense of stochastic static neural networks with mixed time delays is obtained. One example is given to verify the advantage and applicability of the proposed results.

The KAM theorem with a large perturbation and application to the network of Duffing oscillators

We prove that there is an invariant torus with the given Diophantine frequency vector for a class of Hamiltonian systems defined by an integrable large Hamiltonian function with a large non-autonomous Hamiltonian perturbation. As for application, we prove that a finite network of Duffing oscillators with periodic external forces possesses Lagrange stability for almost all initial data.

Globally exponentially attractive sets of the family of Lorenz systems

In this paper, the concept of globally exponentially attractive set is proposed and used to consider the ultimate bounds of the family of Lorenz systems with varying parameters. Explicit estimations of the ultimate bounds are derived. The results presented in this paper contain all the existing results as special cases. In particular, the critical cases, b→ 1^＋ and a→0^＋, for which the previous methods failed, have been solved using a unified formula.

Quasiperiodic Motions for Asymmetric Oscillators

We prove the existence of quasiperiodic solutions and Lagrange stability for a class of differential equations with jumping nonlinearity x+ax^+-bx^-+φ(x)=p(t), where a, b】0, p(t)∈ C(R/2πZ) and φ: R→R is an unbounded function.