Almost anti-periodic solution of inertial neural networks model on time scales

In this work, since the importance of investigation of oscillators solutions, an methodology for proving the existence and stability of almost anti-periodic solutions of inertial neural networks model on time scales are discussed. By developing an approach based on differential inequality techniques coupled with Lyapunov function method. A numerical example is given for illustration.

Quasi-Projective Synchronization of Distributed-Order Recurrent Neural Networks

In this paper, the quasi-projective synchronization of distributed-order recurrent neural networks is investigated. Firstly, based on the definition of the distributed-order derivative and metric space theory, two distributed-order differential inequalities are obtained. Then, by employing the Lyapunov method, Laplace transform, Laplace final value theorem, and some inequality techniques, the quasi-projective synchronization sufficient conditions for distributed-order recurrent neural networks are established in cases of feedback control and hybrid control schemes, respectively. Finally, two numerical examples are given to verify the effectiveness of the theoretical results.

General decay projective synchronization of memristive competitive neural networks via nonlinear controller

In this paper, the general decay projective synchronization of a class of memristive competitive neural networks with time delay is studied. Firstly, a nonlinear feedback controller is designed, which does not require any knowledge about the activation functions. Then, some new and applicable conditions dependent on the Lyapunov function and the inequality techniques are obtained to guarantee the general decay projective synchronization of the considered systems under the developed controller. Unlike other forms of synchronization, projective synchronization can improve communication security due to the scaling constant’s unpredictability. In addition, the polynomial synchronization, asymptotical synchronization, and exponential synchronization can be seen as the special cases of the general decay projective synchronization. Finally, a numerical example is given to demonstrate the effectiveness of the proposed control scheme.

Dynamics of an Impulsive Stochastic Predator–Prey System with the Beddington–DeAngelis Functional Response

Taking impulsive effects into account, an impulsive stochastic predator–prey system with the Beddington–DeAngelis functional response is proposed in this paper. First, the impulsive system is transformed into an equivalent system without pulses. Then, by constructing suitable functionals and applying the extreme-value theory of quadratic functions, sufficient conditions on the existence of periodic Markovian processes are provided. The uniform continuity and global attractivity of solutions are also investigated. Additionally, we investigate the extinction and permanence in the mean of all species with the help of comparison methods and inequality techniques. Sufficient conditions on the existence and ergodicity of the stationary distribution of solutions for the autonomous and non-impulsive case are given. Finally, numerical simulations are performed to illustrate the main results.

Uniqueness and Stability Results on Non-local Stochastic Random Impulsive Integro-Differential Equations

The paper is concerned with stochastic random impulsive integro-differential equations with non-local conditions. The sufficient conditions guarantees uniqueness of mild solution derived using Banach fixed point theorem. Stability of the solution is derived by incorporating Banach fixed point theorem with certain inequality techniques.

Dynamic Analysis of a Model for Spruce Budworm Populations with Delay

A class of delayed spruce budworm population model is considered. Compared with previous studies, both autonomous and nonautonomous delayed spruce budworm population models are considered. By using the inequality techniques, continuation theorem, and the construction of suitable Lyapunov functional, we establish a set of easily verifiable sufficient conditions on the permanence, existence, and global attractivity of positive periodic solutions for the considered system. Finally, an example and its numerical simulation are given to illustrate our main results.

Global Exponential Stability and Periodicity of Nonautonomous Impulsive Neural Networks with Time-Varying Delays and Reaction-Diffusion Terms

In this paper, we investigate the global exponential stability and periodicity of nonautonomous cellular neural networks with reaction-diffusion, impulses, and time-varying delays. By establishing a new differential inequality for nonautonomous systems, using the properties of M-matrix and inequality techniques, some new sufficient conditions for the global exponential stability of the system are obtained. Moreover, sufficient conditions for the periodic solutions of the system are obtained by using the Poincare mapping and the fixed point theory. The validity and superiority of the main results are verified by numerical examples and simulations.

Finite-time synchronization for fuzzy inertial cellular neural networks with time-varying delays via integral inequality

This paper mainly considers the finite-time synchronization problem of fuzzy inertial cellular neural networks (FICNNs) with time-varying delays. By constructing the suitable Lyapunov functional, and using integral inequality techniques, several sufficient criteria have been proposed to ensure the finite-time synchronization for the addressed (FICNNs). Without applying the known finite-time stability theorem, which is widely used to solve the finite-time synchronization problems for (FICNNs). In this paper, the proposed method is relatively convenient to solve finite-time synchronization problem of the addressed system, this paper extends the research works on the finite-time synchronization of (FICNNs). Finally, numerical simulations illustrated verify the effectiveness of the proposed results.

Event-triggered Synchronization of Uncertain Delayed Generalized RDNNs

This paper investigates the exponential synchronization analysis of master–slave chaotic uncertain delayed generalized reaction-diffusion neural networks (GRDNNs) with event-triggered control scheme. A delay GRDNNs system model for the analysis is constructed by investigating the effect of the network transmission delay. By constructing a novel Lyapunov–Krasovskii functional and using a delay system approach for designing event-triggered controllers and some inequality techniques like Jensen’s inequality, Wirtinger’s inequality and Halanay’s inequality, the criteria are obtained for the event-triggered synchronization analysis and control synthesis of delayed GRDNNs. The synchronization criteria are formulated in terms of linear matrix inequalities. Finally, we conclude that the slave systems synchronize with the master systems. Two examples show the proposed theoretical results are feasible and effective.

Distributed adaptive event-triggered iterative learning controller based on a filtering network

This paper develops a distributed adaptive event-triggered iterative learning controller over a filtering network for a class of tracking control systems. The proposed distributed control method is more robust than centralized control in terms of node failure and transmission constraints. In view of the limited network bandwidth, adaptive event-triggered mechanisms (AETMs) have been considered in the network communication process. The proposed AETM is characterized by introducing the dynamic threshold parameter, which provides benefits in data scheduling. The existence of filters and controllers is analyzed by Lyapunov stability theory and linear matrix inequality techniques, and their parameters are finally obtained. Moreover, some simulation results on a numerical example and a irrigation canal are presented to show the applicability of the obtained results.