Finite-Time and Fixed-Time Synchronization of Quaternion-Valued Neural Networks With/Without Mixed Delays: An Improved One-Norm Method

Exponential synchronization of quaternion-valued memristor-based Cohen-Grossberg neural networks with time-varying delays: norm method

In this paper, the exponential synchronization of quaternion-valued memristor-based Cohen-Grossberg neural networks with time-varying delays is discussed. By using the differential inclusion theory and the set-valued map theory, the discontinuous quaternion-valued memristor-based Cohen-Grossberg neural networks are transformed into an uncertain system with interval parameters. A novel controller is designed to achieve the control goal. With some inequality techniques, several criteria of exponential synchronization for quaternion-valued memristor-based Cohen-Grossberg neural networks are given. Different from the existing results using decomposition techniques, a direct analytical approach is used to study the synchronization problem by introducing an improved one-norm method. Moreover, the activation function is less restricted and the Lyapunov analysis process is simpler. Finally, a numerical simulation is given to prove the validity of the main results.

Fixed-Time Pinning Common Synchronization and Adaptive Synchronization for Delayed Quaternion-Valued Neural Networks

This article focuses on the fixed-time pinning common synchronization and adaptive synchronization for quaternion-valued neural networks with time-varying delays. First, to reduce transmission burdens and limit convergence time, a pinning controller which only controls partial nodes directly rather than the entire nodes is proposed based on fixed-time control theory. Then, by Lyapunov function approach and some inequalities techniques, fixed-time common synchronization criterion is established. Second, further to realize the self-regulation function of pinning controller, an adaptive pinning controller which can adjust automatically the control gains is developed, the desired fixed-time adaptive synchronization is achieved for the considered system, and the corresponding criterion is also derived. Finally, the availability of these results is tested by simulation example.

Preassigned-time projective synchronization of delayed fully quaternion-valued discontinuous neural networks with parameter uncertainties

This paper concerns with the preassigned-time projective synchronization issue for delayed fully quaternion-valued discontinuous neural networks involving parameter uncertainties through the non-separation method. Above all, based on the existing works, a new preassigned-time stability theorem is established. Subsequently, to realize the control goals, two types of novel and simple chattering-free quaternion controllers are designed, one without the power-law term and the other with a hyperbolic-tangent function. They are different from the existing common power-law controller and exponential controller. Thirdly, under the Filippov discontinuity theories and with the aid of quaternion inequality techniques, some novel succinct sufficient criteria are obtained to ensure the addressed systems to achieve the preassigned-time synchronization by using the preassigned-time stability theory. The preassigned settling time is free from any parameter and any initial value of the system, and can be preset according to the actual task demands. Particularly, unlike the existing results, the proposed control methods can effectively avoid the chattering phenomenon, and the time delay part is removed for simplicity. Additionally, the projection coefficient is generic quaternion-valued instead of real-valued or complex-valued, and some of the previous relevant results are extended. Lastly, numerical simulations are reported to substantiate the effectiveness of the control strategies, the merits of preassigned settling time, and the correctness of the acquired results.

Fixed-time and prescribed-time synchronization of quaternion-valued neural networks: A control strategy involving Lyapunov functions

A control strategy containing Lyapunov functions is proposed in this paper. Based on this strategy, the fixed-time synchronization of a time-delay quaternion-valued neural network (QVNN) is analyzed. This strategy is extended to the prescribed-time synchronization of the QVNN. Furthermore, an improved two-step switching control strategy is also proposed based on this flexible control strategy. Compared with some existing methods, the main method of this paper is a non-decomposition one, does not contain a sign function in the controller, and has better synchronization accuracy. Two numerical examples verify the above advantages.

Fixed-time synchronization of discontinuous competitive neural networks with time-varying delays

In this article, the fixed-time (FXT) synchronization of discontinuous competitive neural networks (CNNs) involving time-varying delays is investigated. Firstly, two kinds of discontinuous FXT control schemes are proposed and two forms of Lyapunov function are constructed based on p-norm and 1-norm to discuss the FXT synchronization of CNNs. By means of nonsmooth analysis and some inequality techniques, some simple criteria are obtained to achieve FXT synchronization and the upper bound of the settling time with less conservativeness is provided. Furthermore, the effect of time scale on FXT synchronization of CNNs is considered. Lastly, some numerical results for an example are provided to demonstrate the derived theoretical results.

Discrete analogue of impulsive recurrent neural networks with both discrete and finite distributive asynchronous time-varying delays

This paper studies the dynamical characteristics of discrete analogue of impulsive recurrent neural networks with both discrete and finite distributed asynchronous time-varying delays. Firstly, the discrete impulsive system of the corresponding continuous-time model is reformed by impulsive maps and semi-discrete method. Secondly, by employing a famous delay impulsive differential inequality, several novel sufficient conditions are derived to ensure the uniqueness of equilibrium point and its global exponential stability in Lagrange sense for the discussed discrete-time impulsive system. Meanwhile, it is illustrated that the discrete-time analogue retains the uniqueness of equilibrium point of the corresponding continuous-time model, and some corollaries follow. Finally, one example is given to demonstrate the validity of our obtained results.

Fixed/Preassigned-time synchronization of quaternion-valued neural networks via pure power-law control

The fixed-time synchronization and preassigned-time synchronization of quaternion-valued neural networks are concerned in this article. By developing fixed-time stability and proposing a pure power-law control scheme, some simple conditions are obtained to realize fixed-time synchronization of quaternion-valued neural networks and the upper bound of the synchronized time is provided. Furthermore, the preassigned-time synchronization of quaternion-valued neural networks is investigated based on pure power-law control design, where the synchronization time is preassigned in advance and the control gains are finite. Note that the designed controllers in this paper are the pure power-law forms, which are simpler and more effective compared with the traditional design composed of the linear part and power-law part. Eventually, an example is given to illustrate the feasibility and validity of the results obtained.