Comparative exploration on bifurcation behavior for integer-order and fractional-order delayed BAM neural networks

In the present study, we deal with the stability and the onset of Hopf bifurcation of two type delayed BAM neural networks (integer-order case and fractional-order case). By virtue of the characteristic equation of the integer-order delayed BAM neural networks and regarding time delay as critical parameter, a novel delay-independent condition ensuring the stability and the onset of Hopf bifurcation for the involved integer-order delayed BAM neural networks is built. Taking advantage of Laplace transform, stability theory and Hopf bifurcation knowledge of fractional-order differential equations, a novel delay-independent criterion to maintain the stability and the appearance of Hopf bifurcation for the addressed fractional-order BAM neural networks is established. The investigation indicates the important role of time delay in controlling the stability and Hopf bifurcation of the both type delayed BAM neural networks. By adjusting the value of time delay, we can effectively amplify the stability region and postpone the time of onset of Hopf bifurcation for the fractional-order BAM neural networks. Matlab simulation results are clearly presented to sustain the correctness of analytical results. The derived fruits of this study provide an important theoretical basis in regulating networks

Recent Advances and Applications of Fractional-Order Neural Networks

This paper focuses on the growth, development, and future of various forms of fractional-order neural networks. Multiple advances in structure, learning algorithms, and methods have been critically investigated and summarized. This also includes the recent trends in the dynamics of various fractional-order neural networks. The multiple forms of fractional-order neural networks considered in this study are Hopfield, cellular, memristive, complex, and quaternion-valued based networks. Further, the application of fractional-order neural networks in various computational fields such as system identification, control, optimization, and stability have been critically analyzed and discussed

On the validity of memristor modeling in the neural network literature

An analysis of the literature shows that there are two types of non-memristive models that have been widely used in the modeling of so-called "memristive" neural networks. Here, we demonstrate that such models have nothing in common with the concept of memristive elements: they describe either non-linear resistors or certain bi-state systems, which all are devices without memory. Therefore, the results presented in a significant number of publications are at least questionable, if not completely irrelevant to the actual field of memristive neural networks

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

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

pth moment exponential stability of stochastic fuzzy Cohen–Grossberg neural networks with discrete and distributed delays

In this paper, stochastic fuzzy Cohen–Grossberg neural networks with discrete and distributed delays are investigated. By using Lyapunov function and the Ito differential formula, some sufficient conditions for the pth moment exponential stability of such stochastic fuzzy Cohen–Grossberg neural networks with discrete and distributed delays are established. An example is given to illustrate the feasibility of our main theoretical findings. Finally, the paper ends with a brief conclusion. Methodology and achieved results is to be presented