Global Mittag-Leffler Synchronization for Fractional-Order BAM Neural Networks with Impulses and Multiple Variable Delays via Delayed-Feedback Control Strategy

Mittag‐Leffler state estimator design and synchronization analysis for fractional‐order BAM neural networks with time delays

“…Remark 3.12 Different from the control techniques in the earlier publications [9,48,51], adaptive feedback control (19) is more effective and the designer requirements of adaptive feedback controllers are very effortless. The sufficiently small control gains π j , ρ j , ε k and ϱ k of (19) would lead to small control inputs.…”

“…Since they have been fruitfully applied to the area of secure communication, fault diagnosis, biological systems, especially real world neural network models. Up to now, many authors investigate the various sorts of synchronization, such as exponential synchronization, Mittag-Leffler synchronization, Mittag-Leffler projective synchronization, asymptotic synchronization, finite time synchronization, projective synchronization, lag synchronization, quasiuniform synchronization and O(t −α )− synchronization, see Ref [6,8,21,19,25,26,40,46,48,49,51,52,55]. Lots of effective control strategies have been adopted to synchronize in fractional order neural networks, including linear feedback control, adaptive feedback control, impulsive control, sliding mode control, non-fragile control and so on.…”

“…For example, The authors of [9] studied the global Mittag-Leffler synchronization of fractional order delayed BAM neural networks by impulsive control and state feedback control. In [48], the authors discussed the finite time synchronization analysis of fractional order memristor based BAM neural networks with time delays via simple linear feedback controller and the global Mittag-Leffler synchronization of BAM neural networks under the delayed feedback control strategy was investigated in [51]. Under the impulsive controller, the authors [54], addressed the exponential synchronization of fractional order BAM neural networks with different impulsive effects by using Mittag-Leffler functions and average impulsive interval definitions.…”

“…In [6,9,15,45,51], the authors provided the definition of Mittag-Leffler stability and Mittag-Leffler synchronization of fractional-order neural networks. In [51], the authors presented the Mittag-Leffler synchronization of BAM neural networks. Motivated by these definitions, we introduce the definitions of Mittag-Leffler state estimator and adaptive Mittag-Leffler synchronization of FBNNs.…”

Hybrid Control Scheme for Projective Lag Synchronization of Riemann–Liouville Sense Fractional Order Memristive BAM NeuralNetworks with Mixed Delays

“…In reality, many real-world objects need to be described with the aid of fractional order models due to the fact that dynamics of fractional-order models are more correct than integer-order models. From the application point of view, for the electronic implementation of bidirectional associative memory (BAM) neural network model, many of the researchers attempted to update the normal capacitor by fractional capacitor; then, it creates the fractional order BAM neural network (FOBNNs) models [20][21][22][23][24]. In addition to that, time delays can impose complexity and restrictions in neural networks and the existence may lead to instability, chaos, and oscillation [25][26][27][28][29][30][31][32][33][34].…”