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Advances in Differential Dynamical Systems with Applications to Economics and...
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Advances in Differential Dynamical Systems with Applications to Economics and Biology, 3rd Edition

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "C2: Dynamical Systems".

Deadline for manuscript submissions: 20 May 2026 | Viewed by 15099

Special Issue Editors

Prof. Dr. Mihaela Neamțu

E-Mail Website
Guest Editor
1. Faculty of Economics and Business Administration, West University of Timişoara, 300115 Timişoara, Romania
2. Institute for Advanced Environmental Research, West University of Timişoara, 300223 Timişoara, Romania
Interests: nonlinear dynamics; economic modeling; differential equations; stability analysis; biomathematics; numerical simulation; mathematical modeling
Special Issues, Collections and Topics in MDPI journals
Dr. Eva Kaslik

E-Mail Website
Guest Editor
1. Faculty of Mathematics and Computer Science, West University of Timișoara, 300223 Timişoara, Romania
2. Institute for Advanced Environmental Research, West University of Timişoara, 300223 Timişoara, Romania
Interests: dynamical systems; fractional-order differential equation; delay differential equations; mathematical modeling
Special Issues, Collections and Topics in MDPI journals
Dr. Anca Rădulescu

E-Mail Website
Guest Editor
Department of Mathematics, State University of New York at New Paltz, New Paltz, NY 12561, USA
Interests: dynamical systems; mathematical biology; computational neuroscience
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Nowadays, in order to study economic and biological processes, mathematical modeling is a very useful tool. In economics and biology, the delay between cause and effect is very often taken into consideration. Sometimes, it is more practical to add a distributed time delay because it illustrates the situation where delays arise in certain ranges of values for certain related probability distributions, taking into account the variables’ entire historical behavior. Moreover, fractional derivatives instead of integer-order derivatives may reflect the memory and the inherited properties of different systems. In terms of realistic conditions, stochastic perturbation framed by a stochastic differential delay system is used to explain the ambiguity about the context in which the system operates.

This Special Issue, titled “Advances in Differential Dynamical Systems with Applications to Economics and Biology, 3rd Edition”, as a follow-up to the successful first edition and second edition, focuses on the dynamical analysis of mathematical models arising from economics and biology and innovative developments in mathematical techniques for their applications. Submissions that involve interdisciplinary collaborations are welcome, as are recent advances in both discrete and continuous techniques and significant applications. Numerical simulations can be used to emphasize the theoretical findings. Finally, an economic or biological interpretation of the obtained results is desired.

Prof. Dr. Mihaela Neamțu
Dr. Eva Kaslik
Dr. Anca Rădulescu
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. 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

  • dynamical systems
  • time delay
  • stability
  • bifurcation analysis in economic and biological systems
  • chaotic behavior
  • population dynamics
  • reaction–diffusion systems
  • economic dynamics
  • fractional order systems
  • numerical methods
  • numerical simulations

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Published Papers (6 papers)

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11 pages, 723 KB  
Article
A Conceptual Model for Growth by Capital–Education Investments
by Ferdinand Verhulst
Mathematics 2026, 14(5), 747; https://doi.org/10.3390/math14050747 - 24 Feb 2026
Viewed by 259
Abstract
In a first approximation, economic growth depends on capital investments and on investments in education and innovation. The macro-economic model introduced here will specifiy aggregate output as determined by aggregate supply of capital and education investment. We will consider the effectiveness of education [...] Read more.
In a first approximation, economic growth depends on capital investments and on investments in education and innovation. The macro-economic model introduced here will specifiy aggregate output as determined by aggregate supply of capital and education investment. We will consider the effectiveness of education including its quality for the growth of the National Product. It is surprising that small changes in the quality of education have a considerable long-term impact on economic growth. Secondly, we consider the positive and negative influences of chaotic fluctuations of capital investments caused by hype cycles or erratic policies. Finally, we introduce a continuous control by consumption on education investments. In this three-dimensional macro-economic model, a tipping point exists where an increase in consumption affecting the amount of education and innovation leads to a decline in economic growth. Full article
(This article belongs to the Special Issue Advances in Differential Dynamical Systems with Applications to Economics and Biology, 3rd Edition)
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17 pages, 2176 KB  
Article
Turing Instability of Hopf Bifurcation Periodic Solutions and Stability Analysis in a Diffusive Forest Kinematic Model
by Jiahui You, Yuhang Hu, Wenyu Zhang and Mi Wang
Mathematics 2026, 14(3), 481; https://doi.org/10.3390/math14030481 - 29 Jan 2026
Viewed by 396
Abstract
In this paper, we investigate the asymptotic behavior of solutions to a diffusive forest kinematic model, which describes the interactions among young trees, old trees, and airborne seeds. Our study focuses on the stability of the positive equilibrium, the occurrence of Hopf bifurcation [...] Read more.
In this paper, we investigate the asymptotic behavior of solutions to a diffusive forest kinematic model, which describes the interactions among young trees, old trees, and airborne seeds. Our study focuses on the stability of the positive equilibrium, the occurrence of Hopf bifurcation yielding spatially homogeneous periodic solutions, and the subsequent Turing instability induced by diffusion in these periodic states. The analysis highlights that the juvenile tree mortality rate, represented by a quadratic function of mature tree density, plays a central dynamical role. Specifically, the parameter corresponding to the mature tree density at which juvenile mortality is minimized serves as a key Hopf bifurcation parameter. This indicates that the system’s transition to periodic solutions and later to diffusion-driven pattern formation can be effectively regulated through this parameter. From an ecological perspective, these results suggest that forest management strategies capable of indirectly influencing factors related to this critical parameter could help control the emergence of spatial patterns, such as forest patches. Furthermore, the functional form of the mortality rate offers a useful foundation for future studies examining how different assumptions regarding tree interaction morphology may influence ecosystem patterning. Full article
(This article belongs to the Special Issue Advances in Differential Dynamical Systems with Applications to Economics and Biology, 3rd Edition)
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33 pages, 3010 KB  
Article
The Predator-Prey Model of Tax Evasion: Foundations of a Dynamic Fiscal Ecology
by Miroslav Gombár, Nella Svetozarovová and Štefan Tóth
Mathematics 2026, 14(2), 337; https://doi.org/10.3390/math14020337 - 19 Jan 2026
Viewed by 355
Abstract
Tax evasion is a dynamic process reflecting continuous interaction between taxpayers and regulatory institutions rather than a static deviation from fiscal equilibrium. This study introduces a predator-prey model of tax evasion that translates the Lotka-Volterra framework from biology into budgetary dynamics. The model [...] Read more.
Tax evasion is a dynamic process reflecting continuous interaction between taxpayers and regulatory institutions rather than a static deviation from fiscal equilibrium. This study introduces a predator-prey model of tax evasion that translates the Lotka-Volterra framework from biology into budgetary dynamics. The model captures the feedback between the volume of tax evasion and the intensity of regulation, incorporating nonlinearity, implicit reactive lag, and adaptive response. Theoretical derivation and numerical simulation identify three dynamic regimes—stable equilibrium, limit-cycle oscillation, and instability—that arise through a Hopf bifurcation. Bifurcation maps in the (r, a), (r, b), and (r, c) parameter spaces reveal how control efficiency, institutional inertia, and behavioral feedback jointly determine fiscal stability. Results show that excessive enforcement may destabilize the system by inducing regulatory fatigue, while weak control enables exponential growth in evasion. The model provides a dynamic analytical tool for evaluating fiscal policy efficiency and identifying stability thresholds. Its findings suggest that adaptive, feedback-based regulation is essential for maintaining long-term tax discipline. The study contributes to closing the research gap by providing a unified dynamic framework linking micro-behavioral decision-making with macro-fiscal stability, offering a foundation for future empirical calibration and behavioral extensions of fiscal systems. Full article
(This article belongs to the Special Issue Advances in Differential Dynamical Systems with Applications to Economics and Biology, 3rd Edition)
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51 pages, 2311 KB  
Article
The Similarity Between Epidemiologic Strains, Minimal Self-Replicable Siphons, and Autocatalytic Cores in (Chemical) Reaction Networks: Towards a Unifying Framework
by Florin Avram, Rim Adenane, Lasko Basnarkov and Andras Horvath
Mathematics 2026, 14(1), 23; https://doi.org/10.3390/math14010023 - 21 Dec 2025
Viewed by 571
Abstract
Motivation: We aim to study the boundary stability and persistence of positive odes in mathematical epidemiology models by importing structural tools from chemical reaction networks. This is largely a review work, which attempts to congregate the fields of mathematical epidemiology (ME), and [...] Read more.
Motivation: We aim to study the boundary stability and persistence of positive odes in mathematical epidemiology models by importing structural tools from chemical reaction networks. This is largely a review work, which attempts to congregate the fields of mathematical epidemiology (ME), and chemical reaction networks (CRNs), based on several observations. We started by observing that epidemiologic strains, defined as disjoint blocks in either the Jacobian on the infected variables, or as blocks in the next generating matrix (NGM), coincide in most of the examples we studied, with either the set of critical minimal siphons or with the set of minimal autocatalytic sets (cores) in an underlying CRN. We leveraged this to provide a definition of the disease-free equilibrium (DFE) face/infected set as the union of either all minimal siphons, or of all cores (they always coincide in our examples). Next, we provide a proposed definition of ME models, as models which have a unique boundary fixed point on the DFE face, and for which the Jacobian of the infected subnetwork admits a regular splitting, which allows defining the famous next generating matrix. We then define the interaction graph on minimal siphons (IGMS), whose vertices are minimal siphons, and whose edges indicate the existence of reactions producing species in one siphon from species in another. When this graph is acyclic, we say the model exhibits an Acyclic Minimal Siphon Decomposition (AMSD). For AMSD models whose minimal siphons partition the infection species, we show that the NGM is block triangular after permutation, which implies the classical max structure of the reproduction number R0 for multi-strain models. In conclusion, using irreversible reaction networks, minimal siphons and acyclic siphon decompositions, we provide a natural bridge from CRN to ME. We implement algorithms to compute IGMS and detect AMSD in our Epid-CRN Mathematica package (which already contain modules to identify minimal siphons, criticality, drainability, self-replicability, etc.). Finally, we illustrate on several multi-strain ME examples how the block structure induced by AMSD, and the ME reproduction functions, allow expressing boundary stability and persistence conditions by comparing growth numbers to 1, as customary in ME. Note that while not addressing the general Persistence Conjecture mentioned in the title, our work provides a systematic method for deriving boundary instability conditions for a significant class of structured models. Full article
(This article belongs to the Special Issue Advances in Differential Dynamical Systems with Applications to Economics and Biology, 3rd Edition)
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25 pages, 657 KB  
Article
Bitcoin Price Regime Shifts: A Bayesian MCMC and Hidden Markov Model Analysis of Macroeconomic Influence
by Vaiva Pakštaitė, Ernestas Filatovas, Mindaugas Juodis and Remigijus Paulavičius
Mathematics 2025, 13(10), 1577; https://doi.org/10.3390/math13101577 - 10 May 2025
Cited by 3 | Viewed by 11467
Abstract
Bitcoin’s role in global finance has rapidly expanded with increasing institutional participation, prompting new questions about its linkage to macroeconomic variables. This study thoughtfully integrates a Bayesian Markov Chain Monte Carlo (MCMC) covariate selection process within homogeneous and non-homogeneous Hidden Markov Models (HMMs) [...] Read more.
Bitcoin’s role in global finance has rapidly expanded with increasing institutional participation, prompting new questions about its linkage to macroeconomic variables. This study thoughtfully integrates a Bayesian Markov Chain Monte Carlo (MCMC) covariate selection process within homogeneous and non-homogeneous Hidden Markov Models (HMMs) to analyze 16 macroeconomic and Bitcoin-specific factors from 2016 to 2024. The proposed method integrates likelihood penalties to refine variable selection and employs a rolling-window bootstrap procedure for 1-, 5-, and 30-step-ahead forecasting. Results indicate a fundamental shift: while early Bitcoin pricing was primarily driven by technical and supply-side factors (e.g., halving cycles, trading volume), later periods exhibit stronger ties to macroeconomic indicators such as exchange rates and major stock indices. Heightened volatility aligns with significant events—including regulatory changes and institutional announcements—underscoring Bitcoin’s evolving market structure. These findings demonstrate that integrating Bayesian MCMC within a regime-switching model provides robust insights into Bitcoin’s deepening connection with traditional financial forces. Full article
(This article belongs to the Special Issue Advances in Differential Dynamical Systems with Applications to Economics and Biology, 3rd Edition)
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19 pages, 389 KB  
Article
On the Existence and Uniqueness of Solutions for Neutral-Type Caputo Fractional Differential Equations with Iterated Delays: Hyers–Ulam–Mittag–Leffler Stability
by Ekaterina Madamlieva and Mihail Konstantinov
Mathematics 2025, 13(3), 484; https://doi.org/10.3390/math13030484 - 31 Jan 2025
Cited by 4 | Viewed by 1256
Abstract
This study investigates nonlinear Caputo-type fractional differential equations with iterated delays, focusing on the neutral type. Initially formulated by D. Bainov and the second author of the current paper between 1972 and 1978, these superneutral equations have been extensively studied in scholarly inquiry. [...] Read more.
This study investigates nonlinear Caputo-type fractional differential equations with iterated delays, focusing on the neutral type. Initially formulated by D. Bainov and the second author of the current paper between 1972 and 1978, these superneutral equations have been extensively studied in scholarly inquiry. The present research seeks to reinvigorate interest in such delays within sophisticated frameworks of differential equations, particularly those involving fractional calculus. The primary objectives are to thoroughly examine neutral-type fractional differential equations with iterated delays and provide novel insights into their existence and uniqueness by applying Bielecki’s and Chebyshev’s norms for solution constraints analysis. Additionally, this work establishes Hyers–Ulam–Mittag–Leffler stability for these equations. Full article
(This article belongs to the Special Issue Advances in Differential Dynamical Systems with Applications to Economics and Biology, 3rd Edition)
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