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Axioms
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Modern Trends and Application of Decision-Making Theory, Stability and Control,...
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Modern Trends and Application of Decision-Making Theory, Stability and Control, 2nd Edition

A special issue of Axioms (ISSN 2075-1680). This special issue belongs to the section "Mathematical Analysis".

Deadline for manuscript submissions: 20 September 2026 | Viewed by 975

Special Issue Editors

Prof. Dr. Valentyn Sobchuk

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Guest Editor
Faculty of Mechanics and Mathematics, Taras Shevchenko National University of Kyiv, 4E Academician Glushkov Avenue, 03127 Kyiv, Ukraine
Interests: differential equations; information systems; dynamical systems; nonlinear dynamical systems; functional stability
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Oleksiy V. Kapustyan

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Guest Editor
Department of Integral and Differential Equations, Taras Shevchenko National University of Kyiv, 4E Glushkov Avenue, 03022 Kyiv, Ukraine
Interests: stability theory; control theory; approximation theory; information technologies
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

This Special Issue is a continuation of our previous Special Issue, titled “Modern Trends and Application of Decision-Making Theory, Stability and Control.” The present issue is devoted to recent advances in decision theory, stability theory, approximation theory, and control problems, as well as their interdisciplinary applications.

The growing interest in these topics is driven by the increasing complexity of modern mathematical models, which necessitate the use of information technologies, computer modeling, and simulation, along with the parallel development of both established and emerging theoretical approaches in these areas of mathematics.

In this Special Issue, we address problems related to Lyapunov stability and robust stability in evolutionary equations describing real-world phenomena; the existence and properties of limiting regimes and attracting sets in impulsive dynamical systems with mechanical applications; theoretical and practical aspects of approximation theory and numerical analysis; as well as optimal and adaptive control in nonlinear systems.

Our aim is to bring together contributions that reflect new trends and approaches in stability theory, approximation theory, control problems, and related topics.

Prof. Dr. Valentyn Sobchuk
Prof. Dr. Oleksiy V. Kapustyan
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 250 words) can be sent to the Editorial Office for assessment.

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. Axioms 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 2400 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

  • nonlinear system
  • stability
  • perturbation
  • impulsive system
  • approximation
  • numerical methods
  • control
  • operators
  • approximation methods
  • approximative properties
  • decision-making theory
  • machine learning
  • neural networks
  • large language models
  • computer use agents
  • GUI automation

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Related Special Issue

Published Papers (2 papers)

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15 pages, 328 KB  
Article
Preservation of Mean-Square Lyapunov Exponents for Nonautonomous Stochastic Evolution Equations
by Dmytro Shtefan, Oleksandr Stanzhytskyi and Svitlana Kushnirenko
Axioms 2026, 15(5), 307; https://doi.org/10.3390/axioms15050307 - 24 Apr 2026
Viewed by 240
Abstract
We study the long-time behavior of nonlinear stochastic evolution equations in a separable Hilbert space driven by a Q-Wiener process. The linear part of the equation is generated by a strongly continuous semigroup with an exponential dichotomy, which provides fixed rates of [...] Read more.
We study the long-time behavior of nonlinear stochastic evolution equations in a separable Hilbert space driven by a Q-Wiener process. The linear part of the equation is generated by a strongly continuous semigroup with an exponential dichotomy, which provides fixed rates of decay and growth. The nonlinear drift and diffusion terms are globally Lipschitz and become small as time tends to infinity. Our main result shows that under these conditions, the mean-square Lyapunov exponents of the nonlinear system coincide with those of the linear part. In other words, nonlinear stochastic perturbations that decay in time do not change the main growth or decay rates of solutions in the mean-square sense. This result provides simple and verifiable criteria ensuring that the long-time Lyapunov behavior of the nonlinear stochastic equation is fully determined by the linear semigroup, even in the presence of time-dependent stochastic perturbations. Full article
(This article belongs to the Special Issue Modern Trends and Application of Decision-Making Theory, Stability and Control, 2nd Edition)
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15 pages, 1117 KB  
Article
Application of Impulsive SIRQ Models for the Development of Forecasting and Cyberattack Mitigation Scenarios
by Valentyn Sobchuk, Vitalii Savchenko, Bohdan Stepanchenko and Halyna Haidur
Axioms 2026, 15(3), 229; https://doi.org/10.3390/axioms15030229 - 19 Mar 2026
Viewed by 385
Abstract
This paper proposes an impulsive SIRQ model for the analysis of computer network resilience against malware propagation and distributed denial-of-service (DDoS) attacks. The model extends classical epidemic frameworks by combining the continuous-time dynamics of malicious object spreading with discrete control actions corresponding to [...] Read more.
This paper proposes an impulsive SIRQ model for the analysis of computer network resilience against malware propagation and distributed denial-of-service (DDoS) attacks. The model extends classical epidemic frameworks by combining the continuous-time dynamics of malicious object spreading with discrete control actions corresponding to mass updates, node isolation, and access control policies. A qualitative analysis of the resulting system of impulsive differential equations is performed. The basic reproduction number R0, identified as a threshold parameter characterizing the intensity of attack propagation, and sufficient conditions for the global asymptotic stability of the infection-free state are established. It is shown that, under periodic impulsive control, the infection-free state can be stabilized with respect to the target population coordinates even when R0>1. An exponential decay estimate for the total active threat is derived, guaranteeing the asymptotic extinction of the infected and quarantined node populations. The proposed approach provides quantitative criteria for the effectiveness of impulsive cyber defense strategies and offers a theoretical foundation for the design of adaptive multi-layer protection systems for critical information infrastructures. Practical interpretation of the results illustrates the dependence of the critical impulsive control period on the model parameters and demonstrates the applicability of the approach to cybersecurity strategy design. Full article
(This article belongs to the Special Issue Modern Trends and Application of Decision-Making Theory, Stability and Control, 2nd Edition)
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