Mammalian Brain As a Network of Networks

Acknowledgements AZ, SG and AL acknowledge support from the Russian Science Foundation (16-12-00077). Authors thank T. Kuznetsova for Fig. 6.Peer reviewedPublisher PD

Robust Multimode Function Synchronization of Memristive Neural Networks with Parameter Perturbations and Time-Varying Delays

Publisher Copyright: IEEE Copyright: Copyright 2020 Elsevier B.V., All rights reserved.Currently, some works on studying complete synchronization of dynamical systems are usually restricted to its two special cases: 1) power-rate synchronization and 2) exponential synchronization. Therefore, how to give a generalization of these types of complete synchronization by the mathematical expression is an open question that needs to be urgently solved. To begin with, this article proposes multimode function synchronization by the mathematical expression for the first time, which is a generalization of exponential synchronization, power-rate synchronization, logarithmical synchronization, and so on. Moreover, two adaptive controllers are designed to achieve robust multimode function synchronization of memristive neural networks (MNNs) with mismatched parameters and uncertain parameters. Each adaptive controller includes function r(t) and update gain σ. By choosing different types of r(t), multiple types of complete synchronization, including power-rate synchronization and exponential synchronization can be obtained. And update gain σ can be used to adjust the speed of synchronization. Therefore, our results enlarge and strengthen the existing results. Two examples are put forward to verify the validity of our results.Peer reviewedFinal Accepted Versio

Adaptive Sliding Mode Control of Chaos in Permanent Magnet Synchronous Motor via Fuzzy Neural Networks

In this paper, based on fuzzy neural networks, we develop an adaptive sliding mode controller for chaos suppression and tracking control in a chaotic permanent magnet synchronous motor (PMSM) drive system. The proposed controller consists of two parts. The first is an adaptive sliding mode controller which employs a fuzzy neural network to estimate the unknown nonlinear models for constructing the sliding mode controller. The second is a compensational controller which adaptively compensates estimation errors. For stability analysis, the Lyapunov synthesis approach is used to ensure the stability of controlled systems. Finally, simulation results are provided to verify the validity and superiority of the proposed method

A Novel Disturbance Rejection Zeroing Neurodynamic Approach for Robust Synchronization of Chaotic Systems

Robust synchronization of chaotic systems becomes a hot topic in scientific and engineering fields because of the ubiquitous existence of time-variant external disturbances in complex application scenarios. In contrast with existing studies that the resultant synchronization error has a supremum or even diverges under the influence of time-variant external disturbances, this paper proposes a disturbance rejection zeroing neurodynamic (DRZN) approach and its related controller for the robust synchronization of chaotic systems against time-variant external disturbances. The controller designed by the proposed DRZN approach distinctively features the rejection of external disturbances with the generated synchronization error being convergence toward zero. Theoretical analyses guarantee that the DRZN approach and its related controller inherently possess robustness. Moreover, numerical studies including three examples substantiate the effectiveness of the proposed DRZN approach and its related controller for the synchronization of chaotic systems against the time-variant external disturbances. Comparisons with existing approaches, e.g., the conventional zeroing neurodynamic (CZN) approach and the linear-active control (LAC) approach, show the superiority of the proposed DRZN approach. Extensive tests further verify that the proposed DRZN approach possesses the outstanding anti-disturbance performance, and thus is suitable for the practical applications with time-variant external disturbances

Mathematical frameworks for oscillatory network dynamics in neuroscience

The tools of weakly coupled phase oscillator theory have had a profound impact on the neuroscience community, providing insight into a variety of network behaviours ranging from central pattern generation to synchronisation, as well as predicting novel network states such as chimeras. However, there are many instances where this theory is expected to break down, say in the presence of strong coupling, or must be carefully interpreted, as in the presence of stochastic forcing. There are also surprises in the dynamical complexity of the attractors that can robustly appear—for example, heteroclinic network attractors. In this review we present a set of mathemat- ical tools that are suitable for addressing the dynamics of oscillatory neural networks, broadening from a standard phase oscillator perspective to provide a practical frame- work for further successful applications of mathematics to understanding network dynamics in neuroscience

Parameter Identification and Hybrid Synchronization in an Array of Coupled Chaotic Systems with Ring Connection: An Adaptive Integral Sliding Mode Approach

This article presents an adaptive integral sliding mode control (SMC) design method for parameter identification and hybrid synchronization of chaotic systems connected in ring topology. To employ the adaptive integral sliding mode control, the error system is transformed into a special structure containing nominal part and some unknown terms. The unknown terms are computed adaptively. Then the error system is stabilized using integral sliding mode control. The controller of the error system is created that contains both the nominal control and the compensator control. The adapted laws and compensator controller are derived using Lyapunov stability theory. The effectiveness of the proposed technique is validated through numerical examples