Cheng Hu

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.

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.

Exponential synchronization of Cohen-Grossberg neural networks via periodically intermittent control

In this paper, a class of Cohen-Grossberg neural networks with time-varying delays are studied by designing a periodically intermittent controller. Some novel and effective exponential synchronization criteria are derived by applying some analysis techniques. These results generalize a few previous known results and remove some restrictions on control width and time-delays. Finally, a chaotic Cohen-Grossberg neural network is represented to show the effectiveness and feasibility of our results.

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.

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.

Fixed-time stability of dynamical systems and fixed-time synchronization of coupled discontinuous neural networks

In this paper, the fixed-time stability of dynamical systems and the fixed-time synchronization of coupled discontinuous neural networks are investigated under the framework of Filippov solution. Firstly, by means of reduction to absurdity, a theorem of fixed-time stability is established and a high-precision estimation of the settling-time is given. It is shown by theoretic proof that the estimation bound of the settling time given in this paper is less conservative and more accurate compared with the classical results. Besides, as an important application, the fixed-time synchronization of coupled neural networks with discontinuous activation functions is proposed. By designing a discontinuous control law and using the theory of differential inclusions, some new criteria are derived to ensure the fixed-time synchronization of the addressed coupled networks. Finally, two numerical examples are provided to show the effectiveness and validity of the theoretical results.

Leader-following consensus of fractional-order multi-agent systems via adaptive pinning control

In this paper, the leader-following consensus problem of fractional-order multi-agent systems is considered via adaptive pinning control. The dynamics of leader and all followers with linear and nonlinear functions are investigated, respectively. We assume that the node should be pinned if its in-degree is less than its out-degree in the paper. Under this assumption and based on the stability theory of fractional-order differential systems, some leader-following consensus criteria are derived, which are easily obtained by matrix inequalities. 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 the Riccati inequality. Several simulation examples are presented to demonstrate the effectiveness of the proposed method.