Search for Articles:
Title / Keyword
Author / Affiliation / Email
Journal
Article Type
 
 
Advanced Search
 
Section
Special Issue
Volume
Issue
Number
Page
 
3.5
2.4
Journals
Mathematics
Special Issues
Nonlinear Stochastic Dynamics and Control and Its Applications
share announcement

Nonlinear Stochastic Dynamics and Control and Its Applications

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

Deadline for manuscript submissions: closed (30 December 2023) | Viewed by 9027

Special Issue Editor

Dr. Konstantin Alexandrovich Rybakov

E-Mail Website
Guest Editor
Moscow Aviation Institute (National Research University), 125993 Moscow, Russia
Interests: stochastic control systems; application of statistical modeling methods

Special Issue Information

Dear Colleagues,

The goal of this Special Issue is to bring together theoretical and practical results with the aim of inspiring new ideas and solutions of existing and rising problems.

Nonlinear stochastic dynamics arises in many fields of science, such as mathematics, physics, engineering, economics and finance, biology and medicine, etc. Mathematical models of stochastic dynamical systems are becoming increasingly complex. They can include forward and backward stochastic difference, differential, integral, and integro-differential equations, including equations with fractional and partial derivatives.

There is a need for new methods of the analysis of nonlinear stochastic dynamic systems, for modern approaches to parametric optimization or optimal and suboptimal control, including methods based on metaheuristic optimization and machine learning. The problems of joint estimation and control have a notable place in theory, especially from an applied point of view. An important problem for researchers is the stability analysis of nonlinear stochastic dynamical systems.

An essential part of theory development is the solution of applied problems, which makes it possible to demonstrate the applicability of analysis and synthesis methods in various fields.

This Special Issue calls for high-quality research papers and surveys in the specified fields.

Dr. Konstantin Alexandrovich Rybakov
Guest Editor

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. Mathematics is an international peer-reviewed open access semimonthly 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

  • nonlinear stochastic dynamics
  • analysis and synthesis of stochastic systems
  • optimal control and stabilization
  • modeling stochastic systems
  • applications of stochastic systems

Published Papers (8 papers)

Download All Papers
Order results
Result details
Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:

Research

17 pages, 779 KiB  
Article
Effects of Small Random Perturbations in the Extended Glass–Kauffman Model of Gene Regulatory Networks
by Arcady Ponosov, Irina Shlykova and Ramazan I. Kadiev
Mathematics 2024, 12(8), 1223; https://doi.org/10.3390/math12081223 - 18 Apr 2024
Viewed by 437
Abstract
A mathematical justification of some basic structural properties of stochastically perturbed gene regulatory networks, including those with autoregulation and delay, is offered in this paper. By using the theory of stochastic differential equations, it is, in particular, shown how to control the asymptotic [...] Read more.
A mathematical justification of some basic structural properties of stochastically perturbed gene regulatory networks, including those with autoregulation and delay, is offered in this paper. By using the theory of stochastic differential equations, it is, in particular, shown how to control the asymptotic behavior of the diffusion terms in order to not destroy certain qualitative features of the networks, for instance, their sliding modes. The results also confirm that the level of randomness is gradually reduced if the gene activation times become much smaller than the time of interaction of genes. Finally, the suggested analysis explains why the deterministic numerical schemes based on replacing smooth, steep response functions by the simpler yet discontinuous Heaviside function, the well-known simplification algorithm, are robust with respect to uncertainties in data. The main technical difficulties of the analysis are handled by applying the uniform version of the stochastic Tikhonov theorem in singular perturbation analysis suggested by Yu. Kabanov and S. Pergamentshchikov. Full article
(This article belongs to the Special Issue Nonlinear Stochastic Dynamics and Control and Its Applications)
►▼ Show Figures

Figure 1

16 pages, 1564 KiB  
Article
Conditional Optimization of Algorithms for Estimating Distributions of Solutions to Stochastic Differential Equations
by Tatyana Averina
Mathematics 2024, 12(4), 586; https://doi.org/10.3390/math12040586 - 16 Feb 2024
Viewed by 444
Abstract
This article discusses an alternative method for estimating marginal probability densities of the solution to stochastic differential equations (SDEs). Two algorithms for calculating the numerical–statistical projection estimate for distributions of solutions to SDEs using Legendre polynomials are proposed. The root-mean-square error of this [...] Read more.
This article discusses an alternative method for estimating marginal probability densities of the solution to stochastic differential equations (SDEs). Two algorithms for calculating the numerical–statistical projection estimate for distributions of solutions to SDEs using Legendre polynomials are proposed. The root-mean-square error of this estimate is studied as a function of the projection expansion length, while the step of a numerical method for solving SDE and the sample size for expansion coefficients are fixed. The proposed technique is successfully verified on three one-dimensional SDEs that have stationary solutions with given one-dimensional distributions and exponential correlation functions. A comparative analysis of the proposed method for calculating the numerical–statistical projection estimate and the method for constructing the histogram is carried out. Full article
(This article belongs to the Special Issue Nonlinear Stochastic Dynamics and Control and Its Applications)
►▼ Show Figures

Figure 1

27 pages, 2098 KiB  
Article
Regime Tracking in Markets with Markov Switching
by Andrey Borisov
Mathematics 2024, 12(3), 423; https://doi.org/10.3390/math12030423 - 28 Jan 2024
Cited by 1 | Viewed by 699
Abstract
The object of the investigation is a model of the incomplete financial market. It includes a bank deposit with a known interest rate and basic risky securities. The instant interest rate and volatility are governed by a hidden market regime, represented by some [...] Read more.
The object of the investigation is a model of the incomplete financial market. It includes a bank deposit with a known interest rate and basic risky securities. The instant interest rate and volatility are governed by a hidden market regime, represented by some finite-state Markov jump process. The paper presents a solution to two problems. The first one consists of the characterization of the derivatives based on the existing market securities, which are valid to complete the considered market. It is determined that for the market completion, it is sufficient to add the number of derivatives equal to the number of possible market regimes. A generalization of the classic Black–Scholes equation, describing the evolution of the fair derivative price, is obtained along with the structure of a self-financing portfolio, replicating an arbitrary contingent claim in the market. The second problem consists of the online estimation of the market regime, given the observations of both the underlying and derivative prices. The available observations are either a combination of the time-discretized risky security prices or some high-frequency multivariate point processes associated with these prices. The paper presents the numerical algorithms of the market regime tracking for both observation types. The comparative numerical experiments illustrate the high quality of the proposed estimates. Full article
(This article belongs to the Special Issue Nonlinear Stochastic Dynamics and Control and Its Applications)
►▼ Show Figures

Figure 1

14 pages, 345 KiB  
Article
Feedback Stabilization Applied to Heart Rhythm Dynamics Using an Integro-Differential Method
by Asher Yahalom and Natalia Puzanov
Mathematics 2024, 12(1), 158; https://doi.org/10.3390/math12010158 - 3 Jan 2024
Viewed by 966
Abstract
In this paper, we applied a chaos control method based on integro-differential equations for stabilization of an unstable cardiac rhythm, which is described by a variation of the modified Van der Pol equation. Chaos control with this method may be useful for stabilization [...] Read more.
In this paper, we applied a chaos control method based on integro-differential equations for stabilization of an unstable cardiac rhythm, which is described by a variation of the modified Van der Pol equation. Chaos control with this method may be useful for stabilization of irregular heartbeat using a small perturbation. This method differs from other stabilization strategies by the absence of adjustable parameters and the lack of rough approximations in determining control functions whose control parameters are fixed by the properties of the unstable system itself. Full article
(This article belongs to the Special Issue Nonlinear Stochastic Dynamics and Control and Its Applications)
►▼ Show Figures

Figure 1

20 pages, 3302 KiB  
Article
Application of a Stochastic Extension of the Analytical Design of Aggregated Regulators to a Multidimensional Biomedical Object
by Svetlana Kolesnikova and Ekaterina Kustova
Mathematics 2023, 11(21), 4484; https://doi.org/10.3390/math11214484 - 30 Oct 2023
Viewed by 920
Abstract
The results of the application of the methods of the synergetic control theory to a high-dimensional immunology object with uncertainty in its descriptions are reported. The control here is the therapy treated as a problem for constructing an optimal cure program. The control [...] Read more.
The results of the application of the methods of the synergetic control theory to a high-dimensional immunology object with uncertainty in its descriptions are reported. The control here is the therapy treated as a problem for constructing an optimal cure program. The control object is presented in continuous and discrete forms, i.e., mathematical models given by a system of ordinary differential equations with a bounded disturbance and a system of stochastic difference equations, respectively. Two algorithms for deriving robust regulators applicable to a 10-dimensional nonlinear multi-loop system with unstable limit states, which models an immune response to the hepatitis B infection, are obtained. Analytical control design for a continuous model relies on the method of nonlinear adaptation on the target manifold. The second algorithm represents a stochastic extension of the method of analytical design of aggregated discrete regulators minimizing the variance of the target macro variable. The numerical simulation of the developed control systems indicates the performance of the designed control algorithms. The results of this study can be used as a component part of the mathematical tools of expert systems and decision support systems. Full article
(This article belongs to the Special Issue Nonlinear Stochastic Dynamics and Control and Its Applications)
►▼ Show Figures

Figure 1

23 pages, 382 KiB  
Article
Spectral Representations of Iterated Stochastic Integrals and Their Application for Modeling Nonlinear Stochastic Dynamics
by Konstantin Rybakov
Mathematics 2023, 11(19), 4047; https://doi.org/10.3390/math11194047 - 24 Sep 2023
Cited by 3 | Viewed by 1648
Abstract
Spectral representations of iterated Itô and Stratonovich stochastic integrals of arbitrary multiplicity, including integrals from Taylor–Itô and Taylor–Stratonovich expansions, are obtained by the spectral method. They are required for the implementation of numerical methods for solving Itô and Stratonovich stochastic differential equations with [...] Read more.
Spectral representations of iterated Itô and Stratonovich stochastic integrals of arbitrary multiplicity, including integrals from Taylor–Itô and Taylor–Stratonovich expansions, are obtained by the spectral method. They are required for the implementation of numerical methods for solving Itô and Stratonovich stochastic differential equations with high orders of mean-square and strong convergence. The purpose of such numerical methods is the modeling of nonlinear stochastic dynamics in many fields. This paper contains necessary theoretical results, as well as the results of numerical experiments. Full article
(This article belongs to the Special Issue Nonlinear Stochastic Dynamics and Control and Its Applications)
20 pages, 557 KiB  
Article
Stability of the Exponential Type System of Stochastic Difference Equations
by Leonid Shaikhet
Mathematics 2023, 11(18), 3975; https://doi.org/10.3390/math11183975 - 19 Sep 2023
Viewed by 697
Abstract
The method of studying the stability in the probability for nonlinear systems of stochastic difference equations is demonstrated on two systems with exponential and fractional nonlinearities. The proposed method can be applied to nonlinear systems of higher dimensions and with other types of [...] Read more.
The method of studying the stability in the probability for nonlinear systems of stochastic difference equations is demonstrated on two systems with exponential and fractional nonlinearities. The proposed method can be applied to nonlinear systems of higher dimensions and with other types of nonlinearity, both for difference equations and for differential equations with delay. Full article
(This article belongs to the Special Issue Nonlinear Stochastic Dynamics and Control and Its Applications)
►▼ Show Figures

Figure 1

21 pages, 1121 KiB  
Article
Application of a Novel Multi-Agent Optimization Algorithm Based on PID Controllers in Stochastic Control Problems
by Andrei Panteleev and Maria Karane
Mathematics 2023, 11(13), 2903; https://doi.org/10.3390/math11132903 - 28 Jun 2023
Cited by 1 | Viewed by 766
Abstract
The article considers the problem of finding the optimal on average control of the trajectories of continuous stochastic systems with incomplete feedback. This class of problems includes control problems in which the initial states are described by a given distribution law; random effects [...] Read more.
The article considers the problem of finding the optimal on average control of the trajectories of continuous stochastic systems with incomplete feedback. This class of problems includes control problems in which the initial states are described by a given distribution law; random effects on the control object are taken into account; and it is also assumed that information is available only about some coordinates of the state vector. As special cases, the problems of determining the optimal open-loop control and control with complete feedback in the presence of information about all state vector coordinates are considered. A method for parameterization of the control law based on expansions in various systems of basis functions is described. The problem of parametric optimization obtained is solved using a new metaheuristic multi-agent algorithm based on the use of extended PID (Proportional-Integral-Derivative) controllers to control the movement of agents. Solutions of three model examples of control of nonlinear continuous stochastic systems with interval constraints on the amount of control for all possible cases of state vector awareness are presented. Full article
(This article belongs to the Special Issue Nonlinear Stochastic Dynamics and Control and Its Applications)
►▼ Show Figures

Figure 1

Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:
 
Displaying articles 1-8
Back to TopTop