Stability analysis of recurrent neural networks with piecewise constant argument of generalized type

Mittag-Leffler stability of fractional-order quaternion-valued memristive neural networks with generalized piecewise constant argument

This paper studies the global Mittag-Leffler (M-L) stability problem for fractional-order quaternion-valued memristive neural networks (FQVMNNs) with generalized piecewise constant argument (GPCA). First, a novel lemma is established, which is used to investigate the dynamic behaviors of quaternion-valued memristive neural networks (QVMNNs). Second, by using the theories of differential inclusion, set-valued mapping, and Banach fixed point, several sufficient criteria are derived to ensure the existence and uniqueness (EU) of the solution and equilibrium point for the associated systems. Then, by constructing Lyapunov functions and employing some inequality techniques, a set of criteria are proposed to ensure the global M-L stability of the considered systems. The obtained results in this paper not only extends previous works, but also provides new algebraic criteria with a larger feasible range. Finally, two numerical examples are introduced to illustrate the effectiveness of the obtained results.

Strongly Unpredictable Oscillations of Hopfield-Type Neural Networks

In this paper, unpredictable oscillations in Hopfield-type neural networks is under investigation. The motion strongly relates to Poincaré chaos. Thus, the importance of the dynamics is indisputable for those problems of artificial intelligence, brain activity and robotics, which rely on chaos. Sufficient conditions for the existence and uniqueness of exponentially stable unpredictable solutions are determined. The oscillations continue the line of periodic and almost periodic motions, which already are verified as effective instruments of analysis and applications for image recognition, information processing and other areas of neuroscience. The concept of strongly unpredictable oscillations is a significant novelty of the present research, since the presence of chaos in each coordinate of the space state provides new opportunities in applications. Additionally to the theoretical analysis, we have provided strong simulation arguments, considering that all of the assumed conditions are fulfilled.

Global Exponential Stability of Cohen-Grossberg Neural Networks with Piecewise Constant Argument of Generalized Type and Impulses

In this letter, we consider a model of Cohen-Grossberg neural networks with piecewise constant argument of generalized type and impulses. Sufficient conditions ensuring the existence and uniqueness of solutions are obtained. Based on constructing a new differential inequality with piecewise constant argument and impulse and using the Lyapunov function method, we derive sufficient conditions ensuring the global exponential stability of equilibrium point, with approximate exponential convergence rate. An example is given to illustrate the validity and advantage of the theoretical results.