Haijun Jiang

Projective synchronization for fractional neural networks

In this paper, the global projective synchronization of fractional-order neural networks is investigated. First, a sufficient condition in the sense of Caputos fractional derivation to ensure the monotonicity of the continuous and differential functions and a new fractional-order differential inequality are derived, which play central roles in the investigation of the fractional adaptive control. Based on the preparation and some analysis techniques, some novel criteria are obtained to realize projective synchronization of fractional-order neural networks via combining open loop control and adaptive control. As some special cases, several control strategies are given to ensure the realization of complete synchronization, anti-synchronization and the stabilization of the addressed neural networks. Finally, an example with numerical simulations is given to show the effectiveness of the obtained results.

Finite-time synchronization for memristor-based neural networks with time-varying delays

Memristive network exhibits state-dependent switching behaviors due to the physical properties of memristor, which is an ideal tool to mimic the functionalities of the human brain. In this paper, finite-time synchronization is considered for a class of memristor-based neural networks with time-varying delays. Based on the theory of differential equations with discontinuous right-hand side, several new sufficient conditions ensuring the finite-time synchronization of memristor-based chaotic neural networks are obtained by using analysis technique, finite time stability theorem and adding a suitable feedback controller. Besides, the upper bounds of the settling time of synchronization are estimated. Finally, a numerical example is given to show the effectiveness and feasibility of the obtained results.

α-stability and α-synchronization for fractional-order neural networks

In this paper, a class of fractional-order neural networks is investigated. First, α-exponential stability is introduced as a new type of stability and some effective criteria are derived for such kind of stability of the addressed networks by handling a new fractional-order differential inequality. Based on the results, the existence and α-exponential stability of the equilibrium point are considered. Besides, the synchronization of fractional chaotic networks is also proposed. Finally, several examples with numerical simulations are given to show the effectiveness of the obtained results.

Boundedness and stability for nonautonomous cellular neural networks with delay

Abstract The Letter studies the nonautonomous delayed cellular neuraln networks systems. By applying Liapunov functional method, the ultimate boundedness, global exponential stability and the existence of periodic solutions are established. The results obtained in this Letter are new and useful.

Leader-following consensus of fractional-order multi-agent systems under fixed topology

The leader-following consensus problem of fractional-order multi-agent systems is considered. In the system, the dynamics of each agent and leader are nonlinear systems. The control of each agent using local information is designed and detailed analysis of the leader-following consensus is presented. The design technique is based on algebraic graph theory and Lyapunov method. Several simulation examples are presented as a proof of concept.

Finite-time synchronization of delayed neural networks with Cohen-Grossberg type based on delayed feedback control

This paper is concerned with finite-time synchronization for a class of delayed neural networks with Cohen-Grossberg type. Different from the existing related results, the time-delayed feedback strategy is utilized to investigate finite-time synchronization of delayed Cohen-Grossberg neural networks. By constructing Lyapunov functions and using differential inequalities, several new and effective criteria are derived to realize local and global synchronization in finite time of the addressed neural networks based on two different time-delayed feedback controllers. Besides, the upper bounds of the settling time of synchronization are estimated. Furthermore, as corollaries, some sufficient conditions are given to achieve finite-time synchronization of delayed cellular neural networks. Finally, some numerical examples are provided to verify the theoretical results established in this paper.

Exponential synchronization for reaction-diffusion networks with mixed delays in terms of p-norm via intermittent driving

In this paper, the globally exponential synchronization for a class of reaction-diffusion neural networks with Dirichlet boundary conditions and mixed delays is investigated based on periodically intermittent control. Some new and useful synchronization criteria in terms of p-norm are derived by introducing multi-parameters, using Lyapunov functional theory. Subsequently, a feasible region of the control parameters for each neuron is derived for the realization of exponential synchronization. Besides, according to the theoretical results, the influences of diffusion strengths and diffusion spaces on synchronization are analyzed and a very interesting fact is revealed that the synchronization of neural networks with reaction-diffusions is more easily realized than those of neural networks without reaction-diffusions. Finally, a reaction-diffusion chaotic network is given to demonstrate the effectiveness of the proposed control methods.

Original article: Exponential lag synchronization for delayed fuzzy cellular neural networks via periodically intermittent control

In this paper, lag synchronization for a class of delayed fuzzy cellular networks is investigated. By utilizing inequality technique, Lyapunov functional theory and the analysis method, some new and useful criteria of lag synchronization for the addressed networks are derived in terms of p-norm under a periodically intermittent controller. Finally, an example with simulation is given to show the effectiveness of the obtained results.

Finite-time synchronization for fuzzy cellular neural networks with time-varying delays

In this paper, finite-time synchronization for a class of fuzzy cellular neural networks with time-varying delays is investigated based on the finite-time stability theory. By applying the inequality technique and the analysis method, some new and useful criteria of finite-time synchronization for the addressed network are derived in terms of p-norm. Finally, two examples with their numerical simulations are given to show the feasibility and effectiveness of the developed synchronization method.

Existence and global exponential stability of periodic solution of memristor-based BAM neural networks with time-varying delays

In this paper, we investigate a class of memristor-based BAM neural networks with time-varying delays. Under the framework of Filippov solutions, boundedness and ultimate boundedness of solutions of memristor-based BAM neural networks are guaranteed by Chain rule and inequalities technique. Moreover, a new method involving Yoshizawa-like theorem is favorably employed to acquire the existence of periodic solution. By applying the theory of set-valued maps and functional differential inclusions, an available Lyapunov functional and some new testable algebraic criteria are derived for ensuring the uniqueness and global exponential stability of periodic solution of memristor-based BAM neural networks. The obtained results expand and complement some previous work on memristor-based BAM neural networks. Finally, a numerical example is provided to show the applicability and effectiveness of our theoretical results.