Stability and pinning synchronization analysis of fractional order delayed Cohen–Grossberg neural networks with discontinuous activations

This article, we explore the asymptotic stability and asymptotic synchronization analysis of fractional order delayed Cohen–Grossberg neural networks with discontinuous neuron activation functions (FCGNNDDs). First, under the framework of Filippov theory and differ- ential inclusion theoretical analysis, the global existence of Filippov solution for FCGNNDDs is studied by means of the given growth condition. Second, by virtue of suitable Lyapunov functional, Young inequality and comparison theorem for fractional order delayed linear system, some global asymptotic stability conditions for such system is derived by limiting discontinuous neuron activations. Third, the global asymptotic synchronization condition for FCGNNDDs is obtained based on the pinning control. At last, two numerical simula- tions are given to verify the theoretical findings.N/

Exponential multistability of memristive Cohen-Grossberg neural networks with stochastic parameter perturbations

© 2020 Elsevier Ltd. All rights reserved. This manuscript is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International Licence http://creativecommons.org/licenses/by-nc-nd/4.0/.Due to instability being induced easily by parameter disturbances of network systems, this paper investigates the multistability of memristive Cohen-Grossberg neural networks (MCGNNs) under stochastic parameter perturbations. It is demonstrated that stable equilibrium points of MCGNNs can be flexibly located in the odd-sequence or even-sequence regions. Some sufficient conditions are derived to ensure the exponential multistability of MCGNNs under parameter perturbations. It is found that there exist at least (w+2) l (or (w+1) l) exponentially stable equilibrium points in the odd-sequence (or the even-sequence) regions. In the paper, two numerical examples are given to verify the correctness and effectiveness of the obtained results.Peer reviewe

New criteria on global Mittag-Leffler synchronization for Caputo-type delayed Cohen-Grossberg Inertial Neural Networks

Our focus of this paper is on global Mittag-Leffler synchronization (GMLS) of the Caputo-type Inertial Cohen-Grossberg Neural Networks (ICGNNs) with discrete and distributed delays. This model takes into account the inertial term as well as the two types of delays, which greatly reduces the conservatism with respect to the model. A change of variables transforms the $2\beta$ order inertial frame into $\beta$ order ordinary frame in order to deal with the effect of the inertial term. In the following steps, two novel types of delay controllers are designed for the purpose of reaching the GMLS. In conjunction with the novel controllers, utilizing differential mean-value theorem and inequality techniques, several criteria are derived to determine the GMLS of ICGNNs within the framework of Caputo-type derivative and calculus properties. At length, the feasibility of the results is further demonstrated by two simulation examples

Projective synchronization analysis for BAM neural networks with time-varying delay via novel control

In this paper, the projective synchronization of BAM neural networks with time-varying delays is studied. Firstly, a type of novel adaptive controller is introduced for the considered neural networks, which can achieve projective synchronization. Then, based on the adaptive controller, some novel and useful conditions are obtained to ensure the projective synchronization of considered neural networks. To our knowledge, different from other forms of synchronization, projective synchronization is more suitable to clearly represent the nonlinear systems’ fragile nature. Besides, we solve the projective synchronization problem between two different chaotic BAM neural networks, while most of the existing works only concerned with the projective synchronization chaotic systems with the same topologies. Compared with the controllers in previous papers, the designed controllers in this paper do not require any activation functions during the application process. Finally, an example is provided to show the effectiveness of the theoretical results

Synchronization of chaotic delayed systems via intermittent control and its adaptive strategy

In this paper the problem of synchronization for delayed chaotic systems is considered based on aperiodic intermittent control. First, delayed chaotic systems are proposed via aperiodic adaptive intermittent control. Next, to cut down the control gain, a new generalized intermittent control and its adaptive strategy is introduced. Then, by constructing a piecewise Lyapunov auxiliary function and making use of piecewise analysis technique, some effective and novel criteria are obtained to ensure the global synchronization of delayed chaotic systems by means of the designed control protocols. At the end, two examples with numerical simulations are provided to verify the effectiveness of the theoretical results proposed scheme

Mittag–Leffler synchronization for impulsive fractional-order bidirectional associative memory neural networks via optimal linear feedback control

In this paper, we are concerned with the synchronization scheme for fractional-order bidirectional associative memory (BAM) neural networks, where both synaptic transmission delay and impulsive effect are considered. By constructing Lyapunov functional, sufficient conditions are established to ensure the Mittag–Leffler synchronization. Based on Pontryagin’s maximum principle with delay, time-dependent control gains are obtained, which minimize the accumulative errors within the limitation of actuator saturation during the Mittag–Leffler synchronization. Numerical simulations are carried out to illustrate the feasibility and effectiveness of theoretical results with the help of the modified predictor-corrector algorithm and the forward-backward sweep method

Global Mittag-Leffler stability of Caputo fractional-order fuzzy inertial neural networks with delay

This paper deals with the global Mittag-Leffler stability (GMLS) of Caputo fractional-order fuzzy inertial neural networks with time delay (CFOFINND). Based on Lyapunov stability theory and global fractional Halanay inequalities, the existence of unique equilibrium point and GMLS of CFOFINND have been established. A numerical example is given to illustrate the effectiveness of our results

Stability analysis for delayed quaternion-valued neural networks via nonlinear measure approach

In this paper, the existence and stability analysis of the quaternion-valued neural networks (QVNNs) with time delay are considered. Firstly, the QVNNs are equivalently transformed into four real-valued systems. Then, based on the Lyapunov theory, nonlinear measure approach, and inequality technique, some sufficient criteria are derived to ensure the existence and uniqueness of the equilibrium point as well as global stability of delayed QVNNs. In addition, the provided criteria are presented in the form of linear matrix inequality (LMI), which can be easily checked by LMI toolbox in MATLAB. Finally, two simulation examples are demonstrated to verify the effectiveness of obtained results. Moreover, the less conservatism of the obtained results is also showed by two comparison examples