No abstract

In this paper, we consider a class of delayed quaternion-valued cellular neural networks (DQVCNNs) with impulsive effects. By using a novel continuation theorem of coincidence degree theory, the existence of anti-periodic solutions for DQVCNNs is obtained with or without assuming that the activation functions are bounded. Furthermore, by constructing a suitable Lyapunov function, some sufficient conditions are derived to guarantee the global exponential stability of anti-periodic solutions for DQVCNNs. Our results are new and complementary to the known results even when DQVCNNs degenerate into real-valued or complex-valued neural networks. Finally, an example is given to illustrate the effectiveness of the obtained results. KEYWORDSanti-periodic solution, neural networks, quaternion, stabilitywhere q 0 , q 1 , q 2 , q 3 are real numbers and the elements i, j, and k obey the Hamilton's multiplication rules:In the past two decades, the theory of quaternion has been found a lot of applications in many fields such as such as attitude control, quantum mechanics, robotics, computer graphics, and so on. 26-30 Quaternion-valued neural networks (QVNNs), Math Meth Appl Sci. 2019;42:5-23.wileyonlinelibrary.com/journal/mma

No abstract

No abstract

In this paper, we are concerned with a class of competitive neural networks with multi‐proportional delays. By applying the Banach fixed point theorem and constructing suitable Lyapunov functions, we obtain new sufficient conditions for the global exponential stability to this class of neural networks, which are easily verifiable. Finally, two examples are given to illustrate the effectiveness of the obtained results.