Three dimensional analysis of the dynamic stability of piezoelectric circular cylindrical shells

Based on a three-dimensional theory, a set of Mathieu–Hill equations have been derived for the dynamic stability analysis of piezoelectric circular cylindrical shells subjected to combined periodic axial compression and radial electric field loading. Bolotin's method is employed to determine the dynamic instability regions. Obtained results show that both the piezoelectric effect and the electric field only have minor effect on the unstable region. On the contrary, the geometric parameters, the rigidity of constituent materials and the external loading play dominating role in the dynamic stability of piezoelectric shells.     

The alternating between complete synchronization and hybrid synchronization of hyperchaotic Lorenz system with time delay

The various cases of synchronization in two identical hyperchaotic Lorenz systems with time delay are studied. Based on Lyapunov stability theory, the sufficient conditions for achieving synchronization of two identical hyperchaotic Lorenz systems with time delay are derived, and a simple scheme only with a single linear controller is proposed. When the parameters in the response system are known, the alternating between complete synchronization and hybrid synchronization (namely, coexistence of antiphase and complete synchronization) is observed with the control feedback gain varying. Furthermore, when the parameters in the response system are unknown, for the same feedback controller, the complete synchronization and the hybrid synchronization can be obtained, respectively, as the associated parameters updated laws of the unknown parameters are chosen. Numerical simulation results are presented to demonstrate the proposed chaos synchronization scheme.     

Generalized synchronization of spatiotemporal chaos in a weighted complex network

The nodes of the network are composed of the spatiotemporal chaos systems. The relations between the nodes are built through a weighted connection and the nonlinear terms of the chaos systems themselves are taken as coupling functions. The structure of the coupling functions between the connected nodes and the range of the control gain are obtained based on Lyapunov stability theory. It is proven that generalized chaos synchronization of the weight complex network can be realized even if the coupling strength between the nodes is adopted as any weight value. Subsequently, the catalytic reaction diffusion system which has spatiotemporal chaos behavior is taken as example, and simulation results show the effectiveness of the synchronization principle.     

Complex network analysis of forced synchronization in a hydrodynamically self-excited jet

Previous experiments by Li and Juniper (2013) have shown that a hydrodynamically self-excited jet can synchronize with external acoustic forcing via one of two possible routes: a saddle-node (SN) bifurcation or a torus-death (TD) bifurcation. In this study, we use complex networks to analyze and forecast these two routes to synchronization in a prototypical self-excited flow – an axisymmetric low-density jet at an operating condition close to its first Hopf point. We build the complex networks using two different methods: the visibility algorithm and the recurrence condition. We find that the networks built with the visibility algorithm are high-clustering, hierarchical, and assortative in the degree of their vertices, although only the TD networks are scale free. Nevertheless, we find that the assortativity coefficient is a sufficiently sensitive indicator by which to distinguish between the SN and TD routes to synchronization and to forecast the onset of synchronization. As for the networks built with the recurrence condition, we find that their topological features differ between the two routes to synchronization, but vary predictably along either route. We quantify these variations using statistical measures such as the mean degree, spectral radius, and transitivity dimension. This study shows that complex networks can be a useful tool for distinguishing between the SN and TD routes to synchronization, and for forecasting the proximity of a system to its synchronization boundaries. These findings could open up new opportunities for complex networks to be used in the development of open-loop control strategies for hydrodynamically self-excited flows.     

Projective synchronization in a driven-response dynamical network with coupling time-varying delay

This paper studies the projective synchronization in a driven-response dynamical network with coupling time-varying delay model via impulsive control, in which the weights of links are time varying. Based on the stability analysis of the impulsive functional differential equations, some sufficient conditions for the projective synchronization are derived. Numerical simulations are provided to verify the correctness and effectiveness of the proposed method and results.     

The synchronization of general complex dynamical network via pinning control

In this paper, the globally synchronization of the general complex network is investigated. Firstly, we discuss the synchronization problem of the linearly coupled and directed network under the pinning control, and make comparison with the previous work about the undirected network. Sufficient conditions are obtained to guarantee the realization of synchronization. Secondly, the synchronization problem of nonlinearly coupled and undirected network under the pinning control is studied, and a criteria of getting synchronization is given. Furthermore, we introduced the adaptive adjustment of the coupling strength in nonlinearly coupled network. At last, we give simulation examples to verify our theoretical results.     

时间触发控制器局域网时钟同步算法

TTCAN是时间触发机制的,各节点间的精确时钟同步是TTCAN系统正常工作的基础和前提。针对TTCAN对时钟同步的精确性要求,分析了TTCAN level 2级别时钟抖动和突发错误对时钟同步的影响,提出了时间滤波算法。该算法通过引入去噪滤波器完成对时钟信号的提纯,从理论上抑制了高频时钟抖动和突发错误对时钟同步信号的影响。仿真结果表明,该算法在系统正常工作时能够滤除84%的由于时钟抖动导致的噪声;在工作稳定后发生突发错误发生时,能够滤除突发错误引发的94%的噪声干扰,可见提出的算法可以有效提高TTCAN时钟同步的精度。     

Stochastic synchronization of complex network via a novel adaptive nonlinear controller

In this paper, a novel adaptive nonlinear controller is designed to achieve stochastic synchronization of complex networks. We find that this novel adaptive nonlinear controller is less conservative and may be more widely used than the traditional adaptive linear controller. By using the properties of Weiner process, the stochastic synchronization of complex networks with stochastic perturbation via the proposed novel adaptive nonlinear controller can be achieved. Experimental tests demonstrate the superior performance of this novel adaptive nonlinear controller as compared to a conventional adaptive linear controller.     

Cluster synchronization and rhythm dynamics in a complex neuronal network with chemical synapses

Cluster synchronization and rhythm dynamics are studied for a complex neuronal network with the small world structure connected by chemical synapses. Cluster synchronization is considered as that in-phase burst synchronization occurs inside each group of the network but diversity may take place among different groups. It is found that both one-cluster and multi-cluster synchronization may exist for chemically excitatory coupled neuronal networks, however, only multi-cluster synchronization can be achieved for chemically inhibitory coupled neuronal networks. The rhythm dynamics of bursting neurons can be described by a quantitative characteristic, the width factor. We also study the effects of coupling schemes, the intrinsic property of neurons and the network topology on the rhythm dynamics of the small world neuronal network. It is shown that the short bursting type is robust with respect to the coupling strength and the coupling scheme. As for the network topology, more links can only change the type of long bursting neurons, and short bursting neurons are also robust to the link numbers.     

Anticipatory, complete and lag synchronization of chaos and hyperchaos in a nonlinear delay-coupled time-delayed system

We study the synchronization of chaos and hyperchaos in first-order time-delayed systems that are coupled using the nonlinear time-delay excitatory coupling. We assign two characteristic time delays: the system delay that is same for both the systems, and the coupling delay associated with the coupling path. We show that depending upon the relative values of the system delay and the coupling delay the coupled systems show anticipatory, complete, and lag synchronization. We derive a general stability condition for all the synchronization processes using the Krasovskii–Lyapunov theory. Numerical simulations are carried out to corroborate the analytical results. We compute a quantitative measure to ensure the occurrence of different synchronization phenomena. Finally, we set up an experiment in electronic circuit to verify all the synchronization scenario. It is observed that the experimental results are in good agreement with our analytical results and numerical observations.     

Adaptive coupling synchronization in complex network with uncertain boundary

It is difficult that all the boundaries of chaotic system were estimated precisely; this is why the coupling coefficient cannot be determined beforehand in the problem of synchronization of complex networks. Thus, an estimation of coupling coefficient should be given before designing some controllers. In addition, to realize the synchronization, the estimated coupling coefficient has to be large enough. However, it is not true that the larger the coupling coefficient the better the synchronization is. In fact, a coupling coefficient which is larger than what it needs to be means the energy waste. To overcome this difficulty, in this paper we propose an adaptive coupling method. And a new concept about asymptotic stability is presented. Numerical simulations are implemented on different complex networks. The results indicate that the synchronization can be achieved without a large estimated coefficient.     

Modelling the complete operation of a free-piston shock tunnel for a low enthalpy condition

Only a limited number of free-stream flow properties can be measured in hypersonic impulse facilities at the nozzle exit. This poses challenges for experimenters when subsequently analysing experimental data obtained from these facilities. Typically in a reflected shock tunnel, a simple analysis that requires small amounts of computational resources is used to calculate quasi-steady gas properties. This simple analysis requires initial fill conditions and experimental measurements in analytical calculations of each major flow process, using forward coupling with minor corrections to include processes that are not directly modeled. However, this simplistic approach leads to an unknown level of discrepancy to the true flow properties. To explore the simple modelling techniques accuracy, this paper details the use of transient one and two-dimensional numerical simulations of a complete facility to obtain more refined free-stream flow properties from a free-piston reflected shock tunnel operating at low-enthalpy conditions. These calculations were verified by comparison to experimental data obtained from the facility. For the condition and facility investigated, the test conditions at nozzle exit produced with the simple modelling technique agree with the time and space averaged results from the complete facility calculations to within the accuracy of the experimental measurements.     

Multimode vibration control using several piezoelectric transducers shunted with a multiterminal network

In this paper a new approach is presented to reduce vibrations for one- and two-dimensional mechanical structures, as beam or thin plates, by means of several piezoelectric transducers shunted with a proper electric network system. The governing equations of the whole system are coupled to each other through the direct and converse piezoelectric effect. More in detail, the mechanical equations are expressed in accordance with the modal theory considering n vibration modes and the electrical equations reduce to the one-dimensional charge equation of electrostatics for each of n considered piezoelectric transducers. In this electromechanical system, a shunting electric device forms an electric subsystem working as multi degrees of freedom (dof’s) damped vibration absorber for the mechanical subsystem. Herein, it is introduced a proper transformation of the electric coordinates in order to approximate the governing equations for the whole shunted system with n uncoupled, single mode piezoelectric shunting systems that can be readily damped by the methods reported in literature. A further numerical optimisation problem on the spatial distribution of the piezoelectric elements allows to achieve a better performance. Numerical case studies of two relevant systems, a double clamped beam and a fully clamped plate, allow to take into account issues relative to the proposed approach. Laboratory experiments carried out in real time on a beam clamped at both ends consent to validate the proposed technique.     

Study on spatiotemporal chaos tracking synchronization of a class of complex network

Spatiotemporal chaos tracking synchronization of a class of complex network is studied. The structure of the coupling functions between connected nodes of the network and the range of the linear coefficient of separated configuration in the state equation of the node are obtained based on the extended Milosavljevic control law. Each node of the network is a unilateral coupled map lattice in which a square map with an exponential term constructed by extending the logistic map is taken as the local function, and simulation results show the effectiveness of the tracking synchronization principle.     

Analysis of electric boundary condition effects on crack propagation in piezoelectric ceramics

There are three types of cracks: impermeable crack, permeable crack and conducting crack, with different electric boundary conditions on faces of cracks in piezoelectric ceramics, which poses difficulties in the analysis of piezoelectric fracture problems. In this paper, in contrast to our previous FEM formulation, the numerical analysis is based on the used of exact electric boundary conditions at the crack faces, thus the common assumption of electric impermeability in the FEM analysis is avoided. The crack behavior and elasto-electric fields near a crack tip in a PZT-5 piezoelectric ceramic under mechanical, electrical and coupled mechanical-electrical loads with different electric boundary conditions on crack faces are investigated. It is found that the dielectric medium between the crack faces will reduce the singularity of stress and electric displacement. Furthermore, when the permittivity of the dielectric medium in the crack gap is of the same order as that of the piezoelectric ceramic, the crack becomes a conducting crack, the applied electric field has no effect on the crack propagation. The project supported by the National Natural Science Foundation of China (19672026, 19891180)     

Remote synchronization in human cerebral cortex network with identical oscillators

Nonlinear Dynamics - Remote synchronization (RS) has recently received an increasing interest in the systems of nonidentical oscillators, but little attention has been paid to the systems of...     

Chaotic burst synchronization in heterogeneous small-world neuronal network with noise

Chaotic bursting is a fundamental behavior of neurons. In this paper, global and local burst synchronization is studied in a heterogeneous small-world neuronal network of non-identical Hindmarsh-Rose (HR) neurons with noise. It is found that the network can achieve global burst synchronization much more easily than phase synchronization and nearly complete synchronization. Moreover, local burst synchronized clusters have already formed before global burst synchronization happens. We study the effect of the shortcut-adding probability and the heterogeneity coefficient on local and global burst synchronization of the network and find that the introduction of shortcuts facilitates burst synchronization while the heterogeneity has little effect. Moreover, we study the spatiotemporal pattern of the network and find that there is an optimal coupling strength range in which the periodicity of the network is very apparent.     

Effects of time-periodic intercoupling strength on burst synchronization of a clustered neuronal network

In this paper, we investigate the effect of time-periodic intercoupling strength on burst synchronization of a clustered neuronal network. We mainly focus on discussing the effects of amplitude and frequency of the time-periodic intercoupling strength on burst synchronization. We found that by tuning the frequency, burst synchrony of the clustered neuronal network could change from higher synchronized states to low synchronized states, and vice versa. While for the amplitude, we surprisingly found that with increasing of the amplitude, burst synchrony of the clustered neuronal network is not always enhanced. We know that synchronization has close relationship with cognitive activities and brain disorders. Thus, our results could give us some useful insight on the important role of time-dependent couplings in neuronal systems.     

Zero-lag chaos synchronization properties in a hierarchical tree-type network consisting of mutually coupled semiconductor lasers

Nonlinear Dynamics - Chaos synchronization properties in a novel hierarchical tree-type optical network consisting of semiconductor lasers (SLs) are investigated numerically. In such network, each...     

Effect of the coupling matrix with a weight parameter on synchronization pattern in a globally coupled network

In this paper, effect of the coupling matrix with a weight parameter on synchronization pattern in a globally coupled network is investigated. On the basis of matrix theory, the threshold values of the coupling strength and the weight parameter for cluster synchronization have been obtained by utilizing the attractiveness criteria of the invariant synchronization manifold. It shows that cluster synchronization bifurcation comes forth, which concept is first put forward. That is to say, via changing the weight parameter and the coupling strength, the purpose of controlling the number of clusters is achieved, which provides a new idea for control the number of clusters in a network. Numerical simulations are given to demonstrate the theoretical results. In addition, the theoretical results and the numerical simulations also show that full synchronization may not be realized even if the network is globally coupled when there are some negative couplings.