混沌时滞随机神经网络同步控制

研究了一类混沌时滞随机神经网络同步控制问题．采用更具一般性的时滞反馈控制器,通过巧妙地构造Lyapunov数,分别得到了均方指数同步和均方渐近同步两个判别准则．仿真例子表明,新准则是有效的．     

Linear systems subject to input saturation and time delay: Global asymptotic and Lp-stabilization

This Note deals with two problems on stabilization of linear systems by static feedbacks which are bounded and time-delayed, namely global asymptotic stabilization and finite gain $L^p$-stabilization, $p\in [1,\infty ]$. Regarding the first issue, we provide, under standard necessary conditions, two types of solutions for arbitrary small bound on the control and large (constant) delay. The first solution is based on the knowledge of a static stabilizing feedback in the zero-delay case and the second solution is of nested saturation type, which extends results of Mazenc et al. [IEEE Trans. Automat. Contr. 48 (1) (2003) 57–63]. For the finite-gain $L^p$-stabilization issue, we assume that the system is neutrally stable. We show the existence of a linear feedback such that, for arbitrary small bound on the control and large (constant) delay, finite gain $L^p$-stability holds with respect to every $L^p$-norm, $p\in [1,\infty ]$. Moreover, the corresponding $L^p$-gain is delay-independent. To cite this article: K. Yakoubi, Y. Chitour, C. R. Acad. Sci. Paris, Ser. I 340 2005).     

Semiconductor ring laser subject to delayed optical feedback: Bifurcations and stability

We study semiconductor ring lasers subject to delayed optical feedback from one or two short external cavities. In case of two cavities we consider the feedback strengths and phases to be either symmetric or asymmetric feedback. When feedback is symmetric, the laser operates in a bi-directional continuous wave or periodic regime for most parameter values. Only for some small parameter regions complex dynamics, such as quasi-periodicity and chaos are obtained. When the feedback is asymmetric complex dynamical regimes, including chaos, are obtained in large parameter regions. We explain complex dynamical regimes obtained in both symmetric and asymmetric feedback cases by linear stability of the stationary solutions calculated using DDE-BIFTOOL.     

Synchronization criterions and pinning control of general complex networks with time delay

The problems of synchronization and pinning control for general time-delay complex dynamical networks are investigated. In this paper, less conservative criterions for both continuous-time and discrete-time complex dynamical networks with time delay are obtained. Pinning control strategies are respectively, designed to make these complex dynamical networks synchronized. Moreover, the problems of designing controllers are converted into solving optimal problems of a series of linear matrix inequalities, which reduces the computation complexity. Finally, numerical simulations verify the effectiveness of our methodology.     

Synchronization control for the competitive complex networks with time delay and stochastic effects

The synchronization control problem for the competitive complex network with time delay and stochastic effects is investigated by using the stochastic technique and Lyapunov stability theory. The competitive complex network means that the dynamical varying rate of a part of nodes is faster than other nodes. Some synchronization criteria are derived by the full controller and pinning controller, respectively, and these criteria are convenient to be used for concision. A numerical example is provided to illustrate the effectiveness of the method proposed in this paper.     

Information processing,memories, and synchronization in chaotic neural network with the time delay

Information processing and two types of memory in an analog neural network model with time delay that produces chaos similar to the human and animal EEGs are considered. There are two levels of information processing in this neural network: the level of individual neurons and the level of the neural network. Similar to the state of brain, the state of chaotic neural network is defined. It is characterized by two types of memories (memory I and memory II) and correlation structure between the neurons. In normal (unperturbed) state, the neural network generates chaotic patterns of averaged neuronal activities (memory I) and patterns of oscillation amplitudes (memory II). In the presence of external stimulation, the activity patterns change, showing changes in both types of memory. As in experiments on stimulation of the brain, the neural network model shows synchronization of neuronal activities due to stimulus measured by Pearson's correlation coefficient. An increase in neural network asymmetry (increase of the neural network excitability) leads to the phenomenon similar to the epilepsy. Modeling of brain injury, Parkinson's disease, and dementia is performed by removing and weakening interneuron connections. In all cases, the chaotic neural network shows a decrease of the degree of chaos and changes in both types of memory similar to those observed in experiments with healthy human subjects and patients with Parkinson's disease and dementia. © 2005 Wiley Periodicals, Inc. Complexity 11:39–52, 2005     

Synchronization of different dimensional chaotic systems with time varying parameters, disturbances and input nonlinearities

In this paper, the problems of robust exponential generalized and robust exponential Q-S chaos synchronization are investigated between different dimensional chaotic systems. We consider the more practical and realistic cases when unknown time varying parameters with uncertainties, environmental disturbances, and nonlinearity of input control signals are present. The adaptive technique is employed to design the appropriate controllers and the validity of the proposed controllers are proved using Lyapunov stability theorem. Furthermore, numerical simulations are performed to show the efficiency of the presented scheme.     

Robust global exponential synchronization of general Lur’e chaotic systems subject to impulsive disturbances and time delays

In this paper, we aim to study the robust global exponential synchronization problem for a general class of Lur’e chaotic systems subject to time delays and impulsive disturbances. Furthermore, we also provide an estimation of the maximum Lyapunov exponent. By using the Lyapunov function method and linear matrix inequality (LMI) technique, sufficient conditions for the robust global exponential synchronization and estimation of its maximum Lyapunov exponent are obtained for the class of Lur’e chaotic systems with and without time delays, respectively. Furthermore, by applying the M-matrix theory, some of these sufficient conditions are shown to be expressible in forms of fairly simple algebraic conditions. For illustration, several examples are solved by using the sufficient conditions obtained.     

Exponential synchronization of chaotic systems subject to uncertainties in the control input

A sliding mode control technique is introduced for exponential synchronization of chaotic systems. These systems are described by a general form including matched and unmatched nonlinear functions. A new hitting-free switching surface of proportional-integral type is proposed. This type of switching surface is without the hitting process if the attraction of sliding manifold is ensured. This property makes it easy to exponentially synchronize the master-slave chaotic systems. Based on this switching surface, a robust sliding mode controller (SMC) is derived to guarantee the attraction of sliding manifold even when the system is subjected to input uncertainties. An example is included to illustrate the results developed in this paper.     

Robust synchronization of chaotic behavior in unidirectional coupled RCLSJ models subject to uncertainties

This paper deals with the problem of robust synchronization for a class of unidirectional coupled RCL-shunted Josephson junction (RCLSJ) models. A nonlinear controller is proposed based on variable structure control technique to ensure that these coupled RCLSJ models with different parameters can be asymptotically synchronized even when uncertainties are present in the coupled system. Finally, a comparative example is given to emphasize the simplicity and robustness of the proposed method.     

Permanence in a periodic delay logistic system subject to constant impulsive stocking

In this paper, a periodic impulsive delay single population system with hereditary effect is established. The constant impulse is realized at fixed moments of time. By using the comparison principle of impulsive differential equations and analysis techniques, the permanence of the system is obtained. It shows that the constant impulsive stocking plays an important role. Numerical simulations are presented to substantiate our analytical results. Copyright © 2009 John Wiley & Sons, Ltd.     

Synchronization of the unified chaotic system and application in secure communication

This paper studies the synchronization of the unified chaotic system via optimal linear feedback control and the potential use of chaos in cryptography, through the presentation of a chaos-based algorithm for encryption.     

Longer time steps in explicit dynamics subject to small nonlinearities

An approach that increases the critical time step in explicit time integration is presented. By derivation as a variational integrator, symplecticity and momentum preservation are ensured. The linear response is assumed to be dominant and is integrated implicitly, while the nonlinear forces are explicitly integrated. MOLLY filters the high-frequent portions of the nonlinear forces and increases the critical time step. An SDOF example and a structural example using modal reduction verify the improved stability. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Properties of stationary states of delay equations with large delay and applications to laser dynamics

We consider properties of periodic solutions of the differential‐delay system, which models a laser with optical feedback. In particular, we describe a set of multipliers for these solutions in the limit of large delay. As a preliminary result, we obtain conditions for stability of an equilibrium of a generic differential‐delay system with fixed large delay τ. We also show a connection between characteristic roots of the equilibrium and multipliers of the mapping obtained via the formal limit τ→∞. Copyright © 2004 John Wiley & Sons, Ltd.     

Neuron phase shift adaptive to time delay in locomotor control

Based on neurophysiological evidence, theoretical studies have shown that walking can be generated by mutual entrainment of oscillations of a central pattern generator (CPG) and a body. However, it has also been shown that the time delay in the sensorimotor loop destabilizes mutual entrainment, and results in the failure to walk. Recently, it has been reported that if (a) the neuron model used to construct the CPG is replaced by physiologically faithful neuron model (Bonhoeffer–Van der Pol type) and (b) the mechanical impedance of the body (muscle viscoelasticity) is controlled depending on the angle between two legs, the phase relationship between CPG activity and body motion could be flexibly locked according to the loop delay and, therefore, mutual entrainment can be stabilized. That is, locomotor control adaptive to the loop delay can emerge from the coupling between CPG and body. Here, we call this mechanism flexible-phase locking. In this paper, we construct a system of coupled oscillators as a simplified model of a walking system to theoretically investigate the mechanism of flexible-phase locking, and to analyze the simplified model. The analysis suggests that the following are required as the essential mechanism: (i) an asymptotically stable limit cycle of the coupling system of CPG and body and (ii) a sign difference between afferent and efferent coupling coefficients.     

Determining order quantities in multi-product inventory systems subject to multiple constraints and incremental discounts

This paper presents a mixed-integer programming model for ordering items in multi-product multi-constraint inventory systems from suppliers who offer incremental quantity discounts. The model is based on a piecewise linear approximation of the number of orders function. It allows any number of linear constraints and determines if independent or common (fixed) cycle ordering has a lower total cost. The paper discusses implementation issues and presents results of computational tests on example problems from the operational research literature as well as randomly generated test problems.     

Time periodic and almost time periodic solutions to rotating stratified fluids subject to large forces

Consider the 3D incompressible Boussinesq equations for rotating stably stratified fluids. It is shown that this set of equations possesses a unique time periodic or almost time periodic solutions for external forces satisfying these properties, which, however, do not necessarily need to be small. An explicit bound on the size of the external force, depending on the buoyancy frequency N, is given, which then allows for the unique existence of time periodic or almost periodic solutions. In particular, the size of the external forces can be taken large with respect to the buoyancy frequency. The approach depends crucially on the dispersive effect of the rotation and the stable stratification.     

Delay-dependent stability for 2D systems with time-varying delay subject to state saturation in the Roesser model

This paper addresses the problem of delay-dependent stability of 2D systems with time-varying delay subject to state saturation in the Roesser model. By introducing diagonally dominant matrices, new delay-dependent conditions are obtained in terms of linear matrix inequalities (LMIs) where the lower and upper delay bounds along horizontal and vertical directions, respectively, are known. numerical examples are provided to demonstrate the proposed results.     

The most intensive fluctuation in chaotic time series and relativity principle

Relativity principle in mechanics and principle of invariant speed of light lead to Einstein theory. The exponent of p-order momentum, derived from a piece of multi-scale chaotic time series, varies with the order p and cannot exceeds a maximum, so there exists the principle of scale relativity. Its special case is the same one as Lorenz transformation from Einstein theory.