Synchronization Of BAM Neural Networks Research Articles

New predefined-time stability results of impulsive systems with time-varying impulse strength and its application to synchronization of delayed BAM neural networks

In this paper, the predefined-time synchronization of BAM neural networks with hybrid impulsive effects and time-varying delays is explored. First, based on the improved Lyapunov function method, two novel predefined-time stability lemmas of impulsive dynamical systems are given, in which the derivative of Lyapunov function can be negative definite or indefinite. Second, different from previous studies on constant impulse strength, we consider the impulse strength as a time-varying function, which can take different values at different moments and allow for the coexistence of both stabilizing and destabilizing impulses simultaneously. Then, two novel controllers are designed, and some sufficient conditions are derived to ensure predefined-time synchronization of the established system. Finally, the effectiveness of the obtained criteria is verified by a numerical simulation. The results show that the synchronized time can be adjusted according to actual needs and does not depend on the initial values and parameters of the system.

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.

Nonlinear control scheme for general decay projective synchronization of delayed memristor-based BAM neural networks

In this paper, we have made an effort to investigate the general decay projective synchronization (GDPS) problem of a type of delayed memristor-based BAM neural networks. First, we introduced a type of novel nonlinear controller. Then, we derived some sufficient conditions ensuring the GDPS of considered networks by employing differential inclusion theory and using well-known Lyapunov functional method. Lastly, an example is given to show the correctness of obtained results. To the authors’ knowledge, the results derived in this paper are the only available ones on the projective synchronization of BAM neural networks, combining the three main factors, i.e., memristor, general decay and time-varying delays.