Finite-time synchronization for Cohen–Grossberg neural networks with mixed time-delays

Impulsive Memristive Cohen–Grossberg Neural Networks Modeled by Short Term Generalized Proportional Caputo Fractional Derivative and Synchronization Analysis

The synchronization problem for impulsive fractional-order Cohen–Grossberg neural networks with generalized proportional Caputo fractional derivatives with changeable lower limit at any point of impulse is studied. We consider the cases when the control input is acting continuously as well as when it is acting instantaneously at the impulsive times. We defined the global Mittag–Leffler synchronization as a generalization of exponential synchronization. We obtained some sufficient conditions for Mittag–Leffler synchronization. Our results are illustrated with examples.

Discrete Bidirectional Associative Memory Neural Networks of the Cohen–Grossberg Type for Engineering Design Symmetry Related Problems: Practical Stability of Sets Analysis

In recent years, artificial intelligence techniques have become fundamental parts of various engineering research activities and practical realizations. The advantages of the neural networks, as one of the main artificial intelligence methods, make them very appropriate for different engineering design problems. However, the qualitative properties of the neural networks’ states are extremely important for their design and practical performance. In addition, the variety of neural network models requires the formulation of appropriate qualitative criteria. This paper studies a class of discrete Bidirectional Associative Memory (BAM) neural networks of the Cohen–Grossberg type that can be applied in engineering design. Due to the nature of the proposed models, they are very suitable for symmetry-related problems. The notion of the practical stability of the states with respect to sets is introduced. The practical stability analysis is conducted by the method of the Lyapunov functions. Examples are presented to verify the proposed criteria and demonstrate the efficiency of the results. Since engineering design is a constrained processes, the obtained stability of the sets’ results can be applied to numerous engineering design tasks of diverse interest.

Recent Advances on Dynamical Behaviors of Coupled Neural Networks With and Without Reaction-Diffusion Terms

Recently, the dynamical behaviors of coupled neural networks (CNNs) with and without reaction-diffusion terms have been widely researched due to their successful applications in different fields. This article introduces some important and interesting results on this topic. First, synchronization, passivity, and stability analysis results for various CNNs with and without reaction-diffusion terms are summarized, including the results for impulsive, time-varying, time-invariant, uncertain, fuzzy, and stochastic network models. In addition, some control methods, such as sampled-data control, pinning control, impulsive control, state feedback control, and adaptive control, have been used to realize the desired dynamical behaviors in CNNs with and without reaction-diffusion terms. In this article, these methods are summarized. Finally, some challenging and interesting problems deserving of further investigation are discussed.

Synchronization of Fractional-Order Complex Chaotic Systems Based on Observers

By designing a state observer, a new type of synchronization named complex modified projective synchronization is investigated in a class of nonlinear fractional-order complex chaotic systems. Combining stability results of the fractional-order systems and the pole placement method, this paper proves the stability of fractional-order error systems and realizes complex modified projective synchronization. This method is so effective that it can be applied in engineering. Additionally, the proposed synchronization strategy is suitable for all fractional-order chaotic systems, including fractional-order hyper-chaotic systems. Finally, two numerical examples are studied to show the correctness of this new synchronization strategy.

Novel Finite-Time Synchronization Criteria for Inertial Neural Networks With Time Delays via Integral Inequality Method

In this paper, we are concerned with the finite-time synchronization of a class of inertial neural networks with time delays. Without applying some finite-time stability theorems, which are widely applied to studying the finite-time synchronization for neural networks, by constructing two Lyapunov functions and using integral inequality method, two sufficient conditions on the finite-time synchronization for a class of inertial neural networks with time delays are derived. Considering that the method and research results of the finite-time synchronization are different from some existing works, this paper extends the works on the finite-time synchronization of neural networks.