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Special Issue "Memristor Cellular Nonlinear Networks: Theory and Applications"

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A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Engineering Mathematics".

Deadline for manuscript submissions: 31 May 2024 | Viewed by 5873

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Special Issue Editors

Prof. Dr. Angela Slavova

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Guest Editor

Mathematical Physics Department, Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Acad.G.Bonchev Str. 8, 1113 Sofia, Bulgaria
Interests: cellular neural networks; differential equations; modeling; numerical methods

Prof. Dr. Ronald Tetzlaff

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Guest Editor

Institute of Circuits and Systems, Technische Universität Dresden, 01062 Dresden, Germany
Interests: circuit theory; memristors; chaotic circuits; cellular neural networks (CNNs); deep learning; biomedical signal processing
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Special Issue Information

Dear colleagues,

Further development of memristor-based cellular nonlinear networks (MCNN), including conventional applications, is necessary from the point of view of the current market need for new nanoelectronic circuit architectures. MCNNs working on the edge of chaos can exhibit very complex behavior. The application of a new excitable medium in investigations to detect the global motion of excitable waves, and transferring this to the analysis of more complex systems such as brain networks and social networks, is particularly challenging.

In this Special Issue, the following topics will be covered:

- MCNNs operating on edge of chaos;
- Simulations of MCNNs operating on edge of chaos regime;
- Pattern formation in MCNN models;
- Simulation of MCNNs operating on edge of chaos regime;
- Applications of MCNNs.

Theoretical and simulation results for MCNNs will be in complete concordance, demonstrating that conventional, very large-scale integration technology could be an ideal medium for studying the complex behavior of different models.

Prof. Dr. Angela Slavova
Prof. Dr. Ronald Tetzlaff
Guest Editors

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Keywords

cellular nonlinear networks
memristor
local activity theory
edge of chaos
dynamical behavior
chaotic systems
patter formation.

Published Papers (4 papers)

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18 pages, 881 KiB

Open AccessFeature PaperArticle

Convergence of Neural Networks with a Class of Real Memristors with Rectifying Characteristics

and

Mathematics 2022, 10(21), 4024; https://doi.org/10.3390/math10214024 - 29 Oct 2022

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Abstract

The paper considers a neural network with a class of real extended memristors obtained via the parallel connection of an ideal memristor and a nonlinear resistor. The resistor has the same rectifying characteristic for the current as that used in relevant models in the literature to account for diode-like effects at the interface between the memristor metal and insulating material. The paper proves some fundamental results on the trajectory convergence of this class of real memristor neural networks under the assumption that the interconnection matrix satisfies some symmetry conditions. First of all, the paper shows that, while in the case of neural networks with ideal memristors, it is possible to explicitly find functions of the state variables that are invariants of motions, the same functions can be used as Lyapunov functions that decrease along the trajectories in the case of real memristors with rectifying characteristics. This fundamental property is then used to study convergence by means of a reduction-of-order technique in combination with a Lyapunov approach. The theoretical predictions are verified via numerical simulations, and the convergence results are illustrated via the applications of real memristor neural networks to the solution of some image processing tasks in real time. Full article

(This article belongs to the Special Issue Memristor Cellular Nonlinear Networks: Theory and Applications)

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13 pages, 431 KiB

Open AccessArticle

Bipartite Synchronization of Fractional-Order Memristor-Based Coupled Delayed Neural Networks with Pinning Control

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Mathematics 2022, 10(19), 3699; https://doi.org/10.3390/math10193699 - 09 Oct 2022

Cited by 3 | Viewed by 1180

Abstract

This paper investigates the bipartite synchronization of memristor-based fractional-order coupled delayed neural networks with structurally balanced and unbalanced concepts. The main result is established for the proposed model using pinning control, fractional-order Jensen’s inequality, and the linear matrix inequality. Further, new sufficient conditions are derived using the Lyapunov–Krasovskii functional with delay-dependent criteria. Finally, numerical simulations are provided including two numerical examples to show the effectiveness of the theoretical results. Full article

(This article belongs to the Special Issue Memristor Cellular Nonlinear Networks: Theory and Applications)

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11 pages, 2485 KiB

Open AccessEditor’s ChoiceArticle

Edge of Chaos in Memristor Cellular Nonlinear Networks

Angela Slavova

and

Ventsislav Ignatov

Mathematics 2022, 10(8), 1288; https://doi.org/10.3390/math10081288 - 12 Apr 2022

Cited by 2 | Viewed by 1412

Abstract

Information processing in the brain takes place in a dense network of neurons connected through synapses. The collaborative work between these two components (Synapses and Neurons) allows for basic brain functions such as learning and memorization. The so-called von Neumann bottleneck, which limits the information processing capability of conventional systems, can be overcome by the efficient emulation of these computational concepts. To this end, mimicking the neuronal architectures with silicon-based circuits, on which neuromorphic engineering is based, is accompanied by the development of new devices with neuromorphic functionalities. We shall study different memristor cellular nonlinear networks models. The rigorous mathematical analysis will be presented based on local activity theory, and the edge of chaos domain will be determined in the models under consideration. Simulations of these models working on the edge of chaos will show the generation of static and dynamic patterns. Full article

(This article belongs to the Special Issue Memristor Cellular Nonlinear Networks: Theory and Applications)

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Review

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19 pages, 3587 KiB

Open AccessReview

Memristor Cellular Nonlinear Networks

Angela Slavova

and

Ventsislav Ignatov

Mathematics 2023, 11(7), 1601; https://doi.org/10.3390/math11071601 - 26 Mar 2023

Viewed by 956

Abstract

This paper presents a review of the theory and applications of memristor cellular nonlinear networks. By mapping the physical processes to the memristive framework, all resistive switching devices can be modeled. The idea is to find a state variable that presents with high accuracy the important features of the system, its dynamics, and time evolution in response to the inputs of the memristor. In order to develop a new design of memristor-based cellular nonlinear networks (MCNN), new circuital and mathematical memristor models need to be introduced. In this way, implementation into new software packages for computer-aided integrated circuit realization can be achieved. Another challenging problem is studying the complex behavior of MCNN models by means of local activity theory and generalizing it for various test cases. An application of the hardware implementation of these models can be found in nanostructures. Full article

(This article belongs to the Special Issue Memristor Cellular Nonlinear Networks: Theory and Applications)

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