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In this study, we developed a framework for achieving prescribed-time bipartite output consensus in nonlinear multi-agent systems by introducing a distributed observer approach. We propose a novel control protocol that utilizes a bipartite projective parameter and allows the settling time to be predetermined within a physically feasible range, independent of the system parameters and initial conditions. By using a time-varying scaling function (μ(t)), the prescribed time may not depend on initial conditions and system parameters and covers more complex, nonlinear multi-agent systems. State and disturbance observers are co-designed to estimate unmeasurable states and reject external perturbations. Sufficient conditions for scenarios regarding the presence of exogenous disturbances are established by using algebraic graph theory, nonlinear system theory, Lyapunov stability, and matrix theory. Finally, numerical simulations verify the effectiveness of the designed protocol and the correctness of the proposed theorem.

This study proposes two improved gradient descent parameter estimation algorithms for rational state-space models with time-delay. These two algorithms, based on intelligent search method and momentum method, can simultaneously estimate the time-delay and parameters without the matrix eigenvalue calculation in each iteration. Compared with the traditional gradient descent algorithm, the improved algorithms come with two advantages: having quicker convergence rates and less computational efforts, particularly meaningful for those large-scale systems. A simulated example is selected to illustrate the efficiency of the proposed algorithms.

In this study, two fractional-based stochastic gradient (FSG) algorithms for time-delayed auto-regressive exogenous (ARX) models are proposed. By combining momentum and adaptive methods, a momentum-based FSG and an adaptive-based FSG algorithms are developed. These two FSG algorithms have faster convergence rates when compared with the stochastic gradient algorithm. The mechanism of the convergence is proved in theory. Furthermore, two simulated examples are presented to illustrate the efficiency of the new proposed algorithms.

This study proposes a decomposition optimization-based expectation maximization algorithm for switching models. The identities of each sub-model are estimated in the expectation step, while the parameters are updated using the decomposition optimization method in the maximization step. Compared with the traditional expectation maximization algorithm and the gradient descent expectation maximization algorithm, the decomposition optimization-based expectation maximization algorithm avoids the matrix inversion and eigenvalue calculation; thus, it can be extended to complex nonlinear models and large-scale models. Convergence analysis and simulation examples are given to show the effectiveness of the proposed algorithm.

In this paper, the mean square asymptotic stability of stochastic Markovian jump neural networks with different time scales and randomly occurred nonlinearities is investigated. In terms of linear matrix inequality (LMI) approach and delay-partitioning projection technique, delay-dependent stability criteria are derived for the considered neural networks for cases with or without the information of the delay rates via new Lyapunov-Krasovskii functionals. We also obtain that the thinner the delay is partitioned, the more obviously the conservatism can be reduced. An example with simulation results is given to show the effectiveness of the proposed approach.

Diverse rhythms are generated by thousands of oscillators that somehow manage to operate synchronously. By using mathematical and computational modeling, we consider the synchronization and chaos control among chaotic oscillators coupled indirectly but through a quorum sensing mechanism. Some sufficient criteria for synchronization under quorum sensing are given based on traditional Lyapunov function method. The Melnikov function method is used to theoretically explain how to suppress chaotic Lorenz systems to different types of periodic oscillators in quorum sensing mechanics. Numerical studies for classical Lorenz and Rössler systems illustrate the theoretical results.

This paper is concerned with the stability problem for a class of impulsive neural networks model, which includes simultaneously parameter uncertainties, stochastic disturbances and two additive time-varying delays in the leakage term. By constructing a suitable Lyapunov–Krasovskii functional that uses the information on the lower and upper bound of the delay sufficiently, a delay-dependent stability criterion is derived by using the free-weighting matrices method for such Takagi–Sugeno fuzzy uncertain impulsive stochastic recurrent neural networks. The obtained conditions are expressed with linear matrix inequalities (LMIs) whose feasibility can be checked easily by MATLAB LMI Control toolbox. Finally, the theoretical result is validated by simulations.

Based on the seminal work of He and Li (J Econ Dyn Cont 36:973–987, 2012 ) on a financial market of heterogeneous beliefs and adaptive behavior, we further propose a model of five dimensional differential delay equations with time varying fundamental price. It is shown that not only the rational behavior of heterogeneous agents routes, but also the fluctuant fundamental price to market instability in continuous time. Oscillatory dynamics of the model are studied by analyzing the associated characteristic equation of the delay differential system. Numerical simulations indicate that the fluctuant fundamental price can obviously increases the financial market amplitude of vibration.

Taking the paper book loan data in Jiangnan University Library from 2002-2017 as example, this paper analyzed the change rules of book loan time series data, and established multiple seasonal ARIMA with Autoregressive conditional heteroscedasticity model in view of the complicated seasonal effect and long-term trend of the sequence caused by its randomness and human factors. According to Akaike Information Criterion (AIC) and the minimum relative error criterion, it selected the optimal ARIMA-ARCH model to fit the data and predict the prospect effectively. According to the forecast, the borrowing capacity would continue to decrease slowly in the future with yearly period, so as to provide valuable information to library managers.

As an important category of porous crystalline materials, metal‐organic frameworks (MOFs) have attracted extensive research interests owing to their unique structural features such as tunable pore structure and enormous surface area. Besides controlling the size, dimensionality, and composition of MOFs, further exploring the crystal‐phase‐dependent physicochemical properties is essential to improve their performances in various applications. Recently, great progress has been achieved in the phase engineering of nanomaterials (PEN), which provides an effective strategy to tune the functional properties of nanomaterials by modulating the arrangement of atoms. In this review, we adopt “phase” instead of “topology” to describe the crystal structure of MOFs and summarize the recent advances in phase engineering of MOFs. The two main strategies used to control the phase of MOFs, that is, phase‐controlled synthesis and phase transformation of MOFs, will be highlighted. The roles of various reaction parameters in controlling the crystal phase of MOFs are discussed. Then, the phase dependence of MOFs in various applications including luminescence, adsorption, and catalysis are introduced. Finally, some personal perspectives about the challenges and opportunities in this emerging field are presented. This review summarizes the recent progress in phase engineering of metal‐organic frameworks (MOFs), including the direct synthesis of MOFs with novel phases and phase transformation of MOFs. The phase dependence of MOFs in luminescence, adsorption, and catalysis is briefly discussed. Perspectives on challenges and opportunities in this emerging direction are also presented.