This article considers a distributed adaptive control scheme for a class of second-order leader-following multiagent systems with only position information as output. An auxiliary network for the agent network is modeled to estimate the unmeasurable velocity information and make the output-based distributed adaptive control protocol effective. Under the distributed adaptive control scheme based on the auxiliary network model, several distributed synchronization criteria are established, and the corresponding convergence analysis is provided based on the stability theory. Finally, several simulation examples are provided to conform to the presented criteria.

This paper addresses the global stabilization of fractional-order memristor-based neural networks (FMNNs) with time delay. The voltage threshold type memristor model is considered, and the FMNNs are represented by fractional-order differential equations with discontinuous right-hand sides. Then, the problem is addressed based on fractional-order differential inclusions and set-valued maps, together with the aid of Lyapunov functions and the comparison principle. Two types of control laws (delayed state feedback control and coupling state feedback control) are designed. Accordingly, two types of stabilization criteria [algebraic form and linear matrix inequality (LMI) form] are established. There are two groups of adjustable parameters included in the delayed state feedback control, which can be selected flexibly to achieve the desired global asymptotic stabilization or global Mittag-Leffler stabilization. Since the existing LMI-based stability analysis techniques for fractional-order systems are not applicable to delayed fractional-order nonlinear systems, a fractional-order differential inequality is established to overcome this difficulty. Based on the coupling state feedback control, some LMI stabilization criteria are developed for the first time with the help of the newly established fractional-order differential inequality. The obtained LMI results provide new insights into the research of delayed fractional-order nonlinear systems. Finally, three numerical examples are presented to illustrate the effectiveness of the proposed theoretical results.

We propose a modified Fitzhugh-Nagumo neuron (MFNN) model. Based on this model, an integer-order MFNN system (case A) and a fractional-order MFNN system (case B) were investigated. In the presence of electromagnetic induction and radiation, memductance and induction can show a variety of distributions. Fractional-order magnetic flux can then be considered. Indeed, a fractional-order setting can be acceptable for non-uniform diffusion. In the case of an MFNN system with integer-order discontinuous magnetic flux, the system has chaotic and non-chaotic attractors. Dynamical analysis of the system shows the birth and death of period doubling, which is a sign of antimonotonicity. Such a behavior has not been studied previously in the dynamics of neurons. In an MFNN system with fractional-order discontinuous magnetic flux, different attractors such as chaotic and periodic attractors can be observed. However, there is no sign of antimonotonicity.

This paper is concerned with the existence and uniqueness of solutions for a coupled system of fractional differential equations with nonlocal and integral boundary conditions. The existence and uniqueness of solutions is established by Banach’s contraction principle, while the existence of solutio ns is derived by using Leray-Schauder’s alternative. The results are explained with the aid of examples. The case of nonlocal strip conditions is also discussed.

This letter focuses on lag synchronization control analysis for memristor-based coupled neural networks with parameter mismatches. Due to the parameter mismatches, lag complete synchronization in general cannot be achieved. First, based on the [Formula: see text]-measure method, generalized Halanay inequality, together with control algorithms, some sufficient conditions are obtained to ensure that coupled memristor-based neural networks are in a state of lag synchronization with an error. Moreover, the error level is estimated. Second, we show that memristor-based coupled neural networks with parameter mismatches can reach lag complete synchronization under a discontinuous controller. Finally, two examples are given to illustrate the effectiveness of the proposed criteria and well support theoretical results.