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Dynamics in Complex Neural Networks

A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Complexity".

Deadline for manuscript submissions: closed (31 May 2021) | Viewed by 7478

Special Issue Editors


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Guest Editor
Department of Mathematics, University of Texas at San Antonio, One UTSA Circle, San Antonio, TX 78249, USA
Interests: applied mathematics; dynamical systems; differential equations; qualitative properties (almost periodicity, invariant manifolds, asymptotic properties, stability); impulsive perturbations; delays; fractional differential equations; neural networks; economic models
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Complex neural network systems are essential tools investigated and applied by academic researchers and industry. Recent advances in computer sciences, robotics, and mathematics have introduced new technologies and expanded the opportunities for neural network applications. Knowledge and understanding of these technologies have led to the development of new models, novel methods, and extending the existing techniques for analysis of the neural network dynamics.

Original research articles that will contribute to the development of the theory of complex neural network systems are invited. The focus will be on models as well as methods that explore aspects of dynamics in complex neural networks. Experimental and applied research results are also welcomed. Potential topics of the Special Issue include but are not limited to:

  • Stability theory and strategies;
  • Control theory;
  • Extended stability strategies;
  • Delayed neural networks;
  • Impulsive neural networks;
  • Fractional-order neural networks;
  • Cohen–Grossberg neural networks;
  • Reaction–diffusion neural networks;
  • Biological neural network models;
  • Bifurcation strategies;
  • Entropy in complex neural networks;
  • Asymptotic behavior;
  • Applications in science and engineering.

Dr. Ivanka Stamova
Dr. Gani Stamov
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Entropy is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • dynamics
  • complex neural networks
  • fractional calculus
  • impulsive effects
  • delays
  • entropy effects
  • mathematics of computing

Published Papers (3 papers)

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13 pages, 7835 KiB  
Article
Information Bottleneck Analysis by a Conditional Mutual Information Bound
by Taro Tezuka and Shizuma Namekawa
Entropy 2021, 23(8), 974; https://doi.org/10.3390/e23080974 - 29 Jul 2021
Cited by 2 | Viewed by 2186
Abstract
Task-nuisance decomposition describes why the information bottleneck loss I(z;x)βI(z;y) is a suitable objective for supervised learning. The true category y is predicted for input x using latent variables z. [...] Read more.
Task-nuisance decomposition describes why the information bottleneck loss I(z;x)βI(z;y) is a suitable objective for supervised learning. The true category y is predicted for input x using latent variables z. When n is a nuisance independent from y, I(z;n) can be decreased by reducing I(z;x) since the latter upper bounds the former. We extend this framework by demonstrating that conditional mutual information I(z;x|y) provides an alternative upper bound for I(z;n). This bound is applicable even if z is not a sufficient representation of x, that is, I(z;y)I(x;y). We used mutual information neural estimation (MINE) to estimate I(z;x|y). Experiments demonstrated that I(z;x|y) is smaller than I(z;x) for layers closer to the input, matching the claim that the former is a tighter bound than the latter. Because of this difference, the information plane differs when I(z;x|y) is used instead of I(z;x). Full article
(This article belongs to the Special Issue Dynamics in Complex Neural Networks)
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18 pages, 331 KiB  
Article
Fractional Lotka-Volterra-Type Cooperation Models: Impulsive Control on Their Stability Behavior
by Rohisha Tuladhar, Fidel Santamaria and Ivanka Stamova
Entropy 2020, 22(9), 970; https://doi.org/10.3390/e22090970 - 31 Aug 2020
Cited by 9 | Viewed by 2242
Abstract
We present a biological fractional n-species delayed cooperation model of Lotka-Volterra type. The considered fractional derivatives are in the Caputo sense. Impulsive control strategies are applied for several stability properties of the states, namely Mittag-Leffler stability, practical stability and stability with respect [...] Read more.
We present a biological fractional n-species delayed cooperation model of Lotka-Volterra type. The considered fractional derivatives are in the Caputo sense. Impulsive control strategies are applied for several stability properties of the states, namely Mittag-Leffler stability, practical stability and stability with respect to sets. The proposed results extend the existing stability results for integer-order nspecies delayed Lotka-Volterra cooperation models to the fractional-order case under impulsive control. Full article
(This article belongs to the Special Issue Dynamics in Complex Neural Networks)
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18 pages, 1920 KiB  
Article
Design and Practical Stability of a New Class of Impulsive Fractional-Like Neural Networks
by Gani Stamov, Ivanka Stamova, Anatoliy Martynyuk and Trayan Stamov
Entropy 2020, 22(3), 337; https://doi.org/10.3390/e22030337 - 15 Mar 2020
Cited by 10 | Viewed by 2263
Abstract
In this paper, a new class of impulsive neural networks with fractional-like derivatives is defined, and the practical stability properties of the solutions are investigated. The stability analysis exploits a new type of Lyapunov-like functions and their derivatives. Furthermore, the obtained results are [...] Read more.
In this paper, a new class of impulsive neural networks with fractional-like derivatives is defined, and the practical stability properties of the solutions are investigated. The stability analysis exploits a new type of Lyapunov-like functions and their derivatives. Furthermore, the obtained results are applied to a bidirectional associative memory (BAM) neural network model with fractional-like derivatives. Some new results for the introduced neural network models with uncertain values of the parameters are also obtained. Full article
(This article belongs to the Special Issue Dynamics in Complex Neural Networks)
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