Synchronization of biological neural network systems with stochastic perturbations and time delays

With advances in biochemistry, molecular biology, and neurochemistry there has been impressive progress in the understanding of the molecular properties of anesthetic agents. However, despite these advances, we still do not understand how anesthetic agents affect the properties of neurons that translate into the induction of general anesthesia at the macroscopic level. There is extensive experimental verification that collections of neurons may function as oscillators and the synchronization of oscillators may play a key role in the transmission of information within the central nervous system. This may be particularly relevant to understand the mechanism of action for general anesthesia. In this paper, we develop a stochastic synaptic drive firing rate model for an excitatory and inhibitory cortical neuronal network in the face of system time delays and stochastic input disturbances. In addition, we provide sufficient conditions for global asymptotic and exponential mean-square synchronization for this model.     

Contraction-based model predictive control for stochastic nonlinear discrete-time systems with time-varying delays via multi-dimensional Taylor network

For stochastic nonlinear systems with time-varying delays, the existing robust control approaches are unnecessarily conservative in most practical scenarios. Within this context, a mathematically rigorous and computationally tractable tube-based model predictive control scheme is proposed in the framework of contraction theory. A contraction metric is systematically constructed via convex optimization by forming a differential LyapunovKrasovskii function on tangent space. It guarantees the perturbed actual solution trajectories to be contained within a robust positive invariant tube centered along the reference trajectories and results in an explicit exponential bound on the deviation. The application scenarios of the control contraction metric controller are extended from constant delay systems into time-varying delay systems thereby. Compared with the existing robust mechanism for time-delay systems based on min-max optimization formulation with a linear feedback controller, the proposed scheme greatly reduces the design conservativeness and yields a larger region of attraction. A sparse multi-dimensional Taylor network (MTN) is designed to parameterize the family of the geodesic. Compared to conventional NNs and MTN surrogates, sparse MTN features a more concise topology that enhances its computational efficiency conspicuously. Results of the numerical simulations verify the effectiveness of the proposed method.     

虚拟网络型产业技术学习理论框架初探

技术学习理论是解释发展中国家经济赶超的有力工具。传统的技术学习理论分析框架忽略了技术标准与知识产权因素,难以解释虚拟网络型产业的技术学习过程。本文分析了由技术标准和知识产权决定的虚拟网络型产业的三个特征:网络外部性、技术标准专利化和基于标准的竞争,提出了一个虚拟网络型产业技术学习的三维理论分析框架:国际贸易规则、全球技术演化和企业层面的技术学习模型,分别描述了国际贸易规则的变化,全球技术演化轨迹和企业的技术学习过程。     

A fault diagnosis in a nonlinear location network

In location problems, the out-transmission and in-transmission numbers are important indices to evaluate a directed network in which each edge is associated with a positive real number called the length of the edge and each vertex is associated with a positive real number call the weight of the vertex. The generalized indices of the out-transmission and in-transmission numbers are used in this paper. The indices are nonlinear functions of the distances between the vertices which represent the total cost or loss of service among the vertices. By a fault, we mean a change in the length of an edge. A fault diagnosis problem is discussed in a directed network in which the above indices are measurable at all times.     

Exponential synchronization of stochastic complex networks with multi-weights: A graph-theoretic approach

This paper concerns the exponential synchronization problem of stochastic complex networks with multiple weights (SCNMW). By the method of network split, SCNMW can be modelled as stochastic coupled systems driven by Brownian motion. By combining graph theory, Lyapunov stability theory and state feedback control technique, drive-response synchronization criteria of SCNMW have been obtained. Two kinds of exponential synchronization criteria are obtained, one is given with Lyapunov functions of vertex systems, and the other is shown with the coefficients of SCNMW. The obtained synchronization principles are closely related to the coupling strength of multiple sub-networks and the intensity of noise perturbation. Finally, a numerical example with some simulations is presented to illustrate the theoretical results.     

Stability and dissipative analysis for a class of stochastic system with time-delay

This paper deals with the stability and dissipative problem of a class of stochastic hybrid system. The system under study involves Markovian jump, impulsive effects and time delay, which are often encountered in practice and are the sources of instability. Our attention is focused on analysis of whether the stochastic hybrid system with time-delay is stochastically asymptotically stable and strictly (Q, S, R) dissipative. By introducing an extra artificial time instance, the equivalent system is obtained and the sufficient conditions are derived by using linear matrix inequality (LMI) techniques. The main results of this paper unify the existing results on H_∞ control.     

Model free adaptive iterative learning control for a class of nonlinear systems with randomly varying iteration lengths

This paper proposes a novel model free adaptive iterative learning control scheme for a class of unknown nonlinear systems with randomly varying iteration lengths. By applying the dynamic linearization technique along the iteration axis, such systems can be transformed into iteration-depended time varying linear systems. Then, an improved model free adaptive iterative learning control scheme can be constructed only using input and output data of the system. From the rigorous theoretical analysis, it is shown that the mathematical expectation of tracking errors converge to zero as iteration increases. This design does not require any dynamic information of the ILC systems and prior information of randomly varying iteration lengths. An illustrative example verifies the effectiveness of the proposed design.     

Consensus of second-order multi-agent systems with disturbances generated by nonlinear exosystems under switching topologies

In this paper, we consider the consensus of second-order multi-agent systems with exogenous disturbances generated by some nonlinear exosystems under switching topologies. Firstly, a dynamic gain technique based disturbance observer is proposed to estimate the disturbances generated by some nonlinear exosystems. Secondly, based on the proposed disturbance observer, consensus protocol is further proposed. A rigorous consensus analysis is performed. Finally, numerical simulation results are provided to show the effectiveness of the proposed results.     

Analyzing noise-induced tracking errors in control systems with saturation: A stochastic linearization approach

Noise Induced Tracking Error (NITE) refers to the tracking error of the mean of the output in feedback control systems with nonlinear instrumentation subject to zero-mean measurement noise. Most of the previous work rely on the stochastic averaging for NITE analysis, the validity of which requires that the bandwidth of the zero mean measurement noise is much higher than that of the system. This is because the results obtained by stochastic averaging are asymptotic with respect to the noise bandwidth. Due to the asymptotic nature of the analysis tool, it is not straightforward to provide a quantitative argument for high bandwidth. An alternative method in the literature that can analyze NITE is stochastic linearization for random input, which is analogous to the well known describing function approach for sinusoidal input. Unlike stochastic averaging, stochastic linearization is not an asymptotic approximation. Therefore, analysis can be carried out for any given noise bandwidth. We carry out NITE analysis using stochastic linearization for a class of LPNI systems that are prone to NITE; identify the system conditions under which the averaging analysis of NITE may yield inaccurate results for a finite noise bandwidth; and prove that the results from the two methods agree as the noise bandwidth approaches infinity. In addition, an existing NITE mitigation strategy is extended based on the proposed method. Numerical examples are given to illustrate the results.     

Inducing self-rotation of cells with natural and artificial melanin in a linearly polarized alternating current electric field

The phenomenon of self-rotation observed in naturally and artificially pigmented cells under an applied linearly polarized alternating current (non-rotating) electrical field has been investigated. The repeatable and controllable rotation speeds of the cells were quantified and their dependence on dielectrophoretic parameters such as frequency, voltage, and waveform was studied. Moreover, the rotation behavior of the pigmented cells with different melanin content was compared to quantify the correlation between self-rotation and the presence of melanin. Most importantly, macrophages, which did not originally rotate in the applied non-rotating electric field, began to exhibit self-rotation that was very similar to that of the pigmented cells, after ingesting foreign particles (e.g., synthetic melanin or latex beads). We envision the discovery presented in this paper will enable the development of a rapid, non-intrusive, and automated process to obtain the electrical conductivities and permittivities of cellular membrane and cytoplasm in the near future.     

Stability analysis of a class of stochastic differential delay equations with nonlinear impulsive effects

In this paper, we study stability of a class of stochastic differential delay equations with nonlinear impulsive effects. First, we establish the equivalent relation between the stability of this class of stochastic differential delay equations with impulsive effects and that of a corresponding stochastic differential delay equations without impulses. Then, some sufficient conditions ensuring various stabilities of the stochastic differential delay equations with impulsive effects are obtained. Finally, two examples are also discussed to illustrate the efficiency of the obtained results.     

Efficiency analysis of a filtering algorithm for discrete-time linear stochastic systems with polynomial measurements

A filtering algorithm is presented for discrete-time linear stochastic systems with polynomial measurements. The techniques to evaluate its efficiency are proposed. The algorithm performance is demonstrated by solving two navigation data processing problems, map-aided navigation using geophysical fields and single-beacon navigation for an autonomous underwater vehicle. The designed polynomial filter is compared to the extended Kalman filter, which is commonly used in practice. The simulation results reveal advantages of the polynomial algorithm. The obtained conclusions are reported.     

Threshold behavior in a stochastic delayed SIS epidemic model with vaccination and double diseases

In this paper, we investigate the threshold dynamics of a stochastic delayed SIS epidemic model with vaccination and double diseases which make the research more difficult. We establish sufficient conditions for extinction and persistence in the mean of the two diseases. We also obtain the threshold between persistence in the mean and extinction of the stochastic system. It is shown that: (i) time delay and environmental white noise have important effects on the persistence and extinction of the two diseases; (ii) the two diseases can coexist under certain conditions. Finally, some numerical simulations are provided to demonstrate the analytical results.     

Almost sure weak exponential stability with a certain decay function of semilinear stochastic evolutionequations

In this paper the weak exponential stability with decay function of sample path, which are given by mild solution to a class of semilinear stochastic evolution equations, are presented. The analyses consist in using exponential martingale formula, Lyapunov functional and some special inequalities derived for our stability purposes. Two examples are given to illustrate the theory.     

A novel event-triggered mechanism for networked cascade control system with stochastic nonlinearities and actuator failures

This paper deals with the event-triggered control for networked cascade control systems. Unlike conventional event-triggered schemes that predetermine a fixed threshold to reduce the data-releasing rate, this paper proposes a novel event-triggered mechanism (ETM) in an adaptive way. Under this ETM, it has the following merits: (1) the data-releasing rate remains at a lower level so as to save limited network bandwidth; (2) the reliability of control systems can be improved since the threshold of ETM is increased gradually with the elapse of time till the next event is generated. An integrated model of networked cascade control systems with consideration of stochastic nonlinearity, actuator failures and ETM is established. Sufficient conditions are obtained to ensure the mean-square stability and stabilization of networked cascade control systems. Finally, two examples are exploited to show the effectiveness of the proposed method.     

Behavior of a train of droplets in a fluidic network with hydrodynamic traps

The behavior of a droplet train in a microfluidic network with hydrodynamic traps in which the hydrodynamic resistive properties of the network are varied is investigated. The flow resistance of the network and the individual droplets guide the movement of droplets in the network. In general, the flow behavior transitions from the droplets being immobilized in the hydrodynamic traps at low flow rates to breaking up and squeezing of the droplets at higher flow rates. A state diagram characterizing these dynamics is presented. A simple hydrodynamic circuit model that treats droplets as fluidic resistors is discussed, which predicts the experimentally observed flow rates for droplet trapping in the network. This study should enable the rational design of microfuidic devices for passive storage of nanoliter-scale drops.     

Global sampled-data output feedback stabilization for a class of stochastic nonlinear systems with time-varying delay

This paper studies the global sampled-data output feedback stabilization problem for a class of stochastic nonlinear systems. The considered system is in non-strict feedback form with unknown time-varying delay. A state observer is introduced to estimate the unmeasured states. With the help of the backstepping method, a linear sampled-data output feedback controller is constructed. By choosing an appropriate Lyapunov–Krasoviskii functional and an allowable sampling period, it is shown that the stochastic system can be globally asymptotically stabilized in the mean square sense under the developed control scheme. Finally, two examples are presented to verify the effectiveness of the designed control scheme.     

Stability of stochastic neural networks of neutral type with Markovian jumping parameters: A delay-fractioning approach

This paper deals with the stochastically asymptotic stability in the mean square for a new class of stochastic neural networks of neutral type with both Markovian jump parameters and mixed time delays. The jumping parameters are modeled as a continuous-time, finite-state Markov chain. Based on the Lyapunov–Krasovskii functional, stochastic analysis theory and the delay-fractioning approach, the stochastically asymptotic stability of the considered neural network has been achieved by solving some linear matrix inequalities, which can be easily facilitated by using the standard numerical software. The obtained results are shown to be much less conservative via constructing a new Lyapunov–Krasovskii functional and the idea of “delay fractioning”. Finally, four numerical examples are provided to show the effectiveness of the proposed method.