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Mathematics
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Memristor Cellular Nonlinear Networks: Theory and Applications
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Memristor Cellular Nonlinear Networks: Theory and Applications

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

Deadline for manuscript submissions: closed (31 May 2024) | Viewed by 8832

Special Issue Editors

Prof. Dr. Angela Slavova

E-Mail Website
Guest Editor
Institute of Mechanics, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., Bl. 4, Sofia 1113, Bulgaria
Interests: cellular neural networks; differential equations; modeling; numerical methods
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Ronald Tetzlaff

E-Mail Website
Guest Editor
Institute of Circuits and Systems, TUD, Dresden University of Technology, 01062 Dresden, Germany
Interests: circuit theory; memristors; chaotic circuits; nonlinear dynamics; AI; machine learning; cellular neural networks; biomedical signal processing
Special Issues, Collections and Topics in MDPI journals

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.

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

Manuscript Submission Information

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Keywords

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

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Published Papers (4 papers)

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Research

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18 pages, 881 KiB  
Article
Convergence of Neural Networks with a Class of Real Memristors with Rectifying Characteristics
by Mauro Di Marco, Mauro Forti, Riccardo Moretti, Luca Pancioni and Alberto Tesi
Mathematics 2022, 10(21), 4024; https://doi.org/10.3390/math10214024 - 29 Oct 2022
Viewed by 1699
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 [...] Read more.
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  
Article
Bipartite Synchronization of Fractional-Order Memristor-Based Coupled Delayed Neural Networks with Pinning Control
by P. Babu Dhivakaran, A. Vinodkumar, S. Vijay, S. Lakshmanan, J. Alzabut, R. A. El-Nabulsi and W. Anukool
Mathematics 2022, 10(19), 3699; https://doi.org/10.3390/math10193699 - 9 Oct 2022
Cited by 6 | Viewed by 1692
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 [...] Read more.
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  
Article
Edge of Chaos in Memristor Cellular Nonlinear Networks
by Angela Slavova and Ventsislav Ignatov
Mathematics 2022, 10(8), 1288; https://doi.org/10.3390/math10081288 - 12 Apr 2022
Cited by 3 | Viewed by 1979
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 [...] Read more.
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  
Review
Memristor Cellular Nonlinear Networks
by Angela Slavova and Ventsislav Ignatov
Mathematics 2023, 11(7), 1601; https://doi.org/10.3390/math11071601 - 26 Mar 2023
Cited by 1 | Viewed by 1702
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 [...] Read more.
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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