Synchronization analysis of coupled fractional-order neural networks with time-varying delays

In this paper, the complete synchronization and Mittag-Leffler synchronization problems of a kind of coupled fractional-order neural networks with time-varying delays are introduced and studied. First, the sufficient conditions for a controlled system to reach complete synchronization are established by using the Kronecker product technique and Lyapunov direct method under pinning control. Here the pinning controller only needs to control part of the nodes, which can save more resources. To make the system achieve complete synchronization, only the error system is stable. Next, a new adaptive feedback controller is designed, which combines the Razumikhin-type method and Mittag-Leffler stability theory to make the controlled system realize Mittag-Leffler synchronization. The controller has time delays, and the calculation can be simplified by constructing an appropriate auxiliary function. Finally, two numerical examples are given. The simulation process shows that the conditions of the main theorems are not difficult to obtain, and the simulation results confirm the feasibility of the theorems

Exponential Synchronization of Memristive Neural Networks with Discrete and Distributed Time-Varying Delays via Event-Triggered Control

In this paper, we investigate the exponential synchronization problem of memristive neural networks (MNNs) with discrete and distributed time-varying delays under event-triggered control. An event-triggered controller with the static and dynamic event-triggering conditions is designed to improve the efficiency of resource utilization. By constructing a new Lyapunov function, some sufficient criteria are obtained to realize the exponential synchronization of considered drive-response MNNs under the designed event-triggered controller. In addition, the Zeno behavior will not occur by proving that the event-triggering interval has a positive lower bound under different event-triggering conditions. Finally, a numerical example is provided to prove the validity of our theoretical results

Fixed Point Results for Weak φ-Contractions in Cone Metric Spaces over Banach Algebras and Applications

By using a nontrivial proof method, the purpose of this paper is to obtain some fixed point results for weak φ-contractions in cone metric spaces over Banach algebras. Several examples and applications to the existence and uniqueness of a solution to two classes of equations are also given

Robustness Analysis of BAM Cellular Neural Network with Deviating Arguments of Generalized Type

By generating equivalent integral equations, we analyze the existence and uniqueness of solutions of bidirectional associative memory cellular neural network (BAMCNN) with deviating arguments firstly. Secondly, the question of robustness of stability (RoS) of BAMCNN with deviating argument is studied. Using the Gronwall inequality, we calculate the upper bounds of the interference intensities that can maintain the initial stability of system. The perturbed BAMCNN will maintain its original stability if the strength of one or more perturbations is less than the upper bounds that we calculated in this study. To demonstrate the validity of the conjectural values, a variety of numerical illustrations are provided

Hopf Bifurcation Analysis of a Predator-Prey Biological Economic System with Nonselective Harvesting

A modified predator-prey biological economic system with nonselective harvesting is investigated. An important mathematical feature of the system is that the economic profit on the predator-prey system is investigated from an economic perspective. By using the local parameterization method and Hopf bifurcation theorem, we analyze the Hopf bifurcation of the proposed system. In addition, the modified model enriches the database for the predator-prey biological economic system. Finally, numerical simulations illustrate the effectiveness of our results

Matrix Measure Approach for Stability and Synchronization of Complex-Valued Neural Networks with Deviating Argument

This paper concentrates on global exponential stability and synchronization for complex-valued neural networks (CVNNs) with deviating argument by matrix measure approach. The Lyapunov function is no longer required, and some sufficient conditions are firstly obtained to ascertain the addressed system to be exponentially stable under different activation functions. Moreover, after designing a suitable controller, the synchronization of two complex-valued coupled neural networks is realized, and the derived condition is easy to be confirmed. Finally, some numerical examples are given to demonstrate the superiority and feasibility of the presented theoretical analysis and results