Synchronization of coupled memristive competitive BAM neural networks with different time scales

Modeling biological memory network by an autonomous and adaptive multi-agent system

At the intersection of computation and cognitive science, graph theory is utilized as a formalized description of complex relationships description of complex relationships and structures, but traditional graph models are static, lack the dynamic and autonomous behaviors of biological neural networks, rely on algorithms with a global view. This study introduces a multi-agent system (MAS) model based on the graph theory, each agent equipped with adaptive learning and decision-making capabilities, thereby facilitating decentralized dynamic information memory, modeling and simulation of the brain's memory process. This decentralized approach transforms memory storage into the management of MAS paths, with each agent utilizing localized information for the dynamic formation and modification of these paths, different path refers to different memory instance. The model's unique memory algorithm avoids a global view, instead relying on neighborhood-based interactions to enhance resource utilization. Emulating neuron electrophysiology, each agent's adaptive learning behavior is represented through a microcircuit centered around a variable resistor. Using principles of Ohm's and Kirchhoff's laws, we validated the model's efficacy in memorizing and retrieving data through computer simulations. This approach offers a plausible neurobiological explanation for memory realization and validates the memory trace theory at a system level.

Complete synchronization of discrete-time fractional-order BAM neural networks with leakage and discrete delays

This paper concerns complete synchronization (CS) problem of discrete-time fractional-order BAM neural networks (BAMNNs) with leakage and discrete delays. Firstly, on the basis of Caputo fractional difference theory and nabla l-Laplace transform, two equations about the nabla sum are strictly proved. Secondly, two extended Halanay inequalities that are suitable for discrete-time fractional difference inequations with arbitrary initial time and multiple types of delays are introduced. In addition, through applying Caputo fractional difference theory and combining with inequalities gained from this paper, some sufficient CS criteria of discrete-time fractional-order BAMNNs with leakage and discrete delays are established under adaptive controller. Finally, one numerical simulation is utilized to certify the effectiveness of the obtained theoretical results.

Anti-periodic motion and mean-square exponential convergence of nonlocal discrete-time stochastic competitive lattice neural networks with fuzzy logic

This paper firstly establishes the discrete-time lattice networks for nonlocal stochastic competitive neural networks with reaction diffusions and fuzzy logic by employing a mix techniques of finite difference to space variables and Mittag-Leffler time Euler difference to time variable. The proposed networks consider both the effects of spatial diffusion and fuzzy logic, whereas most of the existing literatures focus only on discrete-time networks without spatial diffusion. Firstly, the existence of a unique ω-anti-periodic in distribution to the networks is addressed by employing Banach contractive mapping principle and the theory of stochastic calculus. Secondly, global exponential convergence in mean-square sense to the networks is discussed on the basis of constant variation formulas for sequences. Finally, an illustrative example is used to show the feasible of the works in the current paper with the help of MATLAB Toolbox. The work in this paper is pioneering in this regard and it has created a certain research foundations for future studies in this area.

Fixed/prescribed-time synchronization of BAM memristive neural networks with time-varying delays via convex analysis

The synchronization problem of bidirectional associative memory memristive neural networks (BAMMNNs) with time-varying delays plays an essential role in the implementation and application of neural networks. Firstly, under the framework of the Filippov's solution, the discontinuous parameters of the state-dependent switching are transformed by convex analysis method, which is different from most previous approaches. Secondly, based on Lyapunov function and some inequality techniques, several conditions for the fixed-time synchronization (FXTS) of the drive-response systems are obtained by designing special control strategies. Moreover, the settling time (ST) is estimated by the improved fixed-time stability lemma. Thirdly, the driven-response BAMMNNs are investigated to be synchronized within a prescribed time by designing new controllers based on the FXTS results, where ST is irrelevant to the initial values of BAMMNNs and the parameters of controllers. Finally, a numerical simulation is exhibited to verify the correctness of the conclusions.

Fixed/Predefined-time synchronization of memristor-based complex-valued BAM neural networks for image protection

This paper investigates the fixed-time synchronization and the predefined-time synchronization of memristive complex-valued bidirectional associative memory neural networks (MCVBAMNNs) with leakage time-varying delay. First, the proposed neural networks are regarded as two dynamic real-valued systems. By designing a suitable feedback controller, combined with the Lyapunov method and inequality technology, a more accurate upper bound of stability time estimation is given. Then, a predefined-time stability theorem is proposed, which can easily establish a direct relationship between tuning gain and system stability time. Any predefined time can be set as controller parameters to ensure that the synchronization error converges within the predefined time. Finally, the developed chaotic MCVBAMNNs and predefined-time synchronization technology are applied to image encryption and decryption. The correctness of the theory and the security of the cryptographic system are verified by numerical simulation.

Finite-Time Synchronization Analysis for BAM Neural Networks with Time-Varying Delays by Applying the Maximum-Value Approach with New Inequalities

In this paper, we consider the finite-time synchronization for drive-response BAM neural networks with time-varying delays. Instead of using the finite-time stability theorem and integral inequality method, by using the maximum-value method, two new criteria are obtained to ensure the finite-time synchronization for the considered drive-response systems. The inequalities in our paper, applied to obtaining the maximum-valued and designing the novel controllers, are different from those in existing papers.