Stability of random impulsive coupled systems on networks with Markovian switching

Abstract

This article is intended to study global asymptotical stability in probability for random impulsive coupled systems on networks with Markovian switching. Two cases are considered. (1) Continuous dynamics are stable while impulses are unstable; (2) impulses are stable while continuous dynamics are unstable. To begin with, based on Lyapunov method as well as graph-theoretic technique, several new stability criteria in two cases are derived, that are, the Lyapunov-type criteria and the coefficients-type criteria. Then main results are used for a class of random impulsive coupled oscillators. Finally, the effectiveness of the obtained results is verified by numerical simulations.     

Existence of solutions for impulsive Dirichlet problems with the parameter inequality reverse

In this paper, we consider the existence and multiplicity for second‐order nonlinear impulsive differential equations with Dirichlet boundary condition and a parameter. By using critical point theory, we give some new criteria to guarantee that the impulsive problem has at least one solution or infinitely many solutions, assuming that the impulsive functions satisfy the superlinear growth condition and the parameter inequality is reverse. Our results extend and improve some recent results. Copyright © 2013 John Wiley & Sons, Ltd.     

Solvability of a class of impulsive damped vibration problems

In this paper, a class of impulsive damped vibration problems are considered. Existence results are obtained by using variational method and critical point theorem. The obtained results are also valid and new even if the impulsive damped vibration problem is reduced to impulsive Hamiltonian system and Hamiltonian system. Examples are presented to illustrate the feasibility and effectiveness of the results. Copyright © 2013 John Wiley & Sons, Ltd.     

一维p-Laplace二阶脉冲微分方程的奇异边值问题

脉冲现象作为一种瞬时突变现象,在现代科技各领域的实际问题中是普遍存在的.本文研究具有奇异边值的一维p-Laplace二阶微分方程在脉冲影响下的正解的存在性,介绍了解的一般性存在定理,并用A-A定理和不动点定理证明了一维p-Laplace二阶脉冲微分方程的奇异边值问题的正解存在性定理.     

Time‐resolved coherent anti‐Stokes Raman spectroscopy impulsively excited by supercontinuum

Time‐resolved coherent anti‐Stokes Raman scattering (CARS) impulsively excited by a supercontinuum (SC) is investigated. We show that it is critical to optimize the temporal overlapping of the constituent solitons of a SC in order to impulsively excite vibrational modes over a broad frequency range. The cross‐correlation frequency‐resolved optical gating technique is utilized to retrieve the optical response function of molecules under SC impulsive excitation, and background‐free CARS with spectral resolution significantly better than the bandwidth of the probe pulses is achieved. Copyright © 2011 John Wiley & Sons, Ltd.     

Existence,compactness, and connectedness of solution sets to nonlocal and impulsive Cauchy problems

In this paper, by using some well-known inequalities and Schaefer fixed point theorem, we show existence results for impulsive Cauchy problems with nonlocal conditions. The compactness of solution sets can be shown in some certain conditions. Moreover, connectedness of solution sets to impulsive Cauchy problems is shown.     

Exponential stability of nonlinear impulsive neutral integro-differential equations

In this paper, a nonlinear impulsive neutral integro-differential equation with time-varying delays is considered. By establishing a singular impulsive delay integro-differential inequality and transforming the n$n$-dimensional impulsive neutral integro-differential equation to a 2n$2n$-dimensional singular impulsive delay integro-differential equation, some sufficient conditions ensuring the global exponential stability in PC¹$P{C}^1$ of the zero solution of an impulsive neutral integro-differential equation are obtained. The results extend and improve the earlier publications. An example is also discussed to illustrate the efficiency of the obtained results.     

Analysis of the dynamical behavior for enzyme-catalyzed reactions with impulsive input

Previous work has concentrated on the nature and validity of this reactions. In the paper, the dynamical behavior of Michaelis–Menten type kinetics for enzyme-catalyzed biochemical reactions is studied. Under the practical background, we investigate the effects of impulsive substrate-input.      

Separating Vibrational Coherences in Ground/Excited Electronic States of Solvent/Solute Following Non-Resonant/Resonant Impulsive Excitation

In a quest to track down the origin of coherent vibrational motions observed in femtosecond pump-probe transients, whether they arise from ground/excited electronic state of solute or are contributed by the solvent, we demonstrate a method for extricating vibrations under resonant and non-resonant impulsive excitations using a diatomic solute in condensed phase (iodine in carbon tetrachloride) with aid of spectral dispersion of the chirped broadband probe. Most importantly, we show how a sum over intensities for a select region of detection wavelengths and Fourier transform of data over select temporal window untwine contributions from vibrational modes of different origins. Thus, in a single pump-probe experiment, vibrational features specific to solute as well as solvent are disentangled that are otherwise spectrally overlapping and are non-separable in conventional (spontaneous/stimulated) Raman spectroscopy employing narrowband excitation. We envision wide-ranging applications of this method to unveil vibrational features in complex molecular systems.     

Adaptive impulsive synchronization of uncertain delayed chaotic system with full unknown parameters via discrete‐time drive signals

This article investigates the adaptive impulsive synchronization of delayed chaotic system with full unknown parameters. Aiming at this problem, we propose a new adaptive strategy, in which both the adaptive–impulsive controller and the parameters adaptive laws are designed via the discrete‐time signals from the drive system. The corresponding theoretical proof is given to guarantee the effectiveness of the proposed strategy. Moreover, the concrete adaptive strategies are achieved for delayed Hopfield neural network, optical Ikeda system and the well‐known delayed Lü chaotic system. As expected, numerical simulations show the effectiveness of the proposed strategy. This method has potential applications in parameters estimation, secure communication, and cryptanalysis when only discrete signals are transmitted in communication channel. © 2014 Wiley Periodicals, Inc. Complexity 21: 43–51, 2016