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Advances in the Analysis and Control of Nonlinear Dynamical Systems...
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Advances in the Analysis and Control of Nonlinear Dynamical Systems and Complex Phenomena

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

Deadline for manuscript submissions: 30 September 2026 | Viewed by 3192

Special Issue Editors

Dr. Gualberto Solís-Perales

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Guest Editor
Deptartamento de Electrónica, Centro Universitarios de Ciencias Exactas e Ingenierías, Universidad de Guadalajara, Guadalajara 44430, Mexico
Interests: control and synchronization of nonlinear systems; application of dynamic complex networks; control of fractional-order systems
Special Issues, Collections and Topics in MDPI journals
Dr. Adriana Aguilera-González

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Guest Editor
ESTIA Institute of Technology, University of Bordeaux, F-64210 Bidart, France
Interests: modeling and validation; fault detection and diagnosis; supervision; fault tolerant control; renewable energy; energy management systems; microgrids

Special Issue Information

Dear Colleagues,

The study and analysis of nonlinear dynamical systems is of high relevance in a vast area of science and engineering, due to its capacity to model complex phenomena in the real world. These systems, characterized by nonlinear interactions and often leading to unpredictable or chaotic behaviors, are presented in diverse areas such as robotics, networks of neurons, vehicular traffic, biological systems, fluid dynamics, energy microgrids, among others.

This Special Issue is dedicated to advances in the analysis and control of such systems, addressing both their theoretical foundations and practical applications. It includes contributions on nonlinear control techniques, mathematical modeling, complex network theory, machine learning strategies for dynamic systems, and control and prediction in nonlinear dynamical systems, such as weather patterns, biological systems, and power grids. Equally important, contributions exploring the emergence of complex phenomena—such as synchronization, bifurcations, and chaos—with the goal of enhancing control strategies and system design are also welcome.

We consider this Special Issue a valuable opportunity to showcase and discuss innovative advancements in the analysis and control of nonlinear systems and complex dynamical phenomena, fostering collaboration and knowledge exchange among researchers in the field.

Dr. Gualberto Solís-Perales
Dr. Adriana Aguilera-González
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

  • nonlinear dynamical systems
  • nonlinear control
  • complex phenomena
  • prediction and synchronization

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Published Papers (3 papers)

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Research

33 pages, 2243 KB  
Article
Nonlinear Smooth Sliding Mode Control Framework for a Tumor-Immune Dynamical System Under Combined Radio-Chemotherapy
by Muhammad Arsalan, Sadiq Muhammad and Muhammad Tariq Sadiq
Mathematics 2026, 14(3), 521; https://doi.org/10.3390/math14030521 - 1 Feb 2026
Viewed by 449
Abstract
Sliding mode control (SMC) is a robust nonlinear control framework that enforces system trajectories onto predefined manifolds, providing strong robustness guarantees against uncertainties. However, SMC inherently introduces unwanted transients or chattering in system state trajectories, which may cause issues especially for sensitive applications [...] Read more.
Sliding mode control (SMC) is a robust nonlinear control framework that enforces system trajectories onto predefined manifolds, providing strong robustness guarantees against uncertainties. However, SMC inherently introduces unwanted transients or chattering in system state trajectories, which may cause issues especially for sensitive applications such as regulation of drug administration. This paper proposes a multi-input smooth sliding mode control (MISSMC) strategy that combines radiotherapy and chemotherapy for a nonlinear tumor–immune dynamical system described by ordinary differential equations. The closed-loop system is first analyzed to establish key qualitative properties: all state variables remain positive and bounded, the sliding surfaces exhibit asymptotic convergence, and explicit analytical upper bounds on the cumulative therapy doses are derived under clinically motivated constraints. On this basis, a smooth hyperbolic-tangent sliding manifold and associated control law are designed to regulate the radiation and drug infusion rates. While the use of a hyperbolic-tangent smoothing function effectively suppresses chattering, it introduces a small steady-state error due to the presence of a boundary layer. To address this limitation, integral action is incorporated into the sliding surfaces, ensuring asymptotic convergence of tumor state and reducing residual steady-state error, while enhancing robustness against model uncertainties and parameter variations. Numerical simulations, based on a brain-tumor case study, show that the proposed smooth SMC markedly suppresses transient overshoots in both states and control inputs, while preserving effective tumor reduction. Compared with a conventional (non-smooth) SMC scheme, the MISSMC controller reduces baseline radiation and chemotherapy intensities on average by roughly 70%. Similarly, MISSMC lowers the overall cumulative doses on average by about 40%, without degrading the therapeutic outcome. The resulting integral smooth SMC framework therefore offers a rigorous nonlinear-systems approach to designing combined radio-chemotherapy protocols with guaranteed positivity, boundedness, and asymptotic stabilization of the closed-loop system, together with explicit bounds on the control inputs. Full article
(This article belongs to the Special Issue Advances in the Analysis and Control of Nonlinear Dynamical Systems and Complex Phenomena)
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20 pages, 506 KB  
Article
A Mathematical Model to Study the Role of Sterile Insect Technique in Crop Pest Control: Dynamics and Optimal Control Study
by Animesh Sinha, Jahangir Chowdhury, Aeshah A. Raezah and Fahad Al Basir
Mathematics 2025, 13(17), 2805; https://doi.org/10.3390/math13172805 - 1 Sep 2025
Viewed by 1285
Abstract
In this article, we propose and analyze a deterministic mathematical model that captures the dynamic interactions between crop biomass and pest populations under the influence of a biological control strategy, namely the sterile insect technique (SIT). The purpose of this study is to [...] Read more.
In this article, we propose and analyze a deterministic mathematical model that captures the dynamic interactions between crop biomass and pest populations under the influence of a biological control strategy, namely the sterile insect technique (SIT). The purpose of this study is to analyze the effectiveness of SIT as a biological pest control method and to understand how pest suppression influences the preservation and productivity of crops over time. The model incorporates four interacting biological populations, namely the crop biomass, female pests, male pests, and sterile male pests. The dynamics of the system are analyzed analytically and numerically. We determine the equilibrium points and their local and global stability. Stability change is found through Hopf bifurcation periodic solutions. It can be concluded from this study that this modeling framework with an optimal control strategy is highly useful in the context of sustainable agriculture that can reduce crop pests in a cost-effective manner. Full article
(This article belongs to the Special Issue Advances in the Analysis and Control of Nonlinear Dynamical Systems and Complex Phenomena)
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15 pages, 871 KB  
Article
Design of Stable Signed Laplacian Matrices with Mixed Attractive–Repulsive Couplings for Complete In-Phase Synchronization
by Gualberto Solis-Perales, Aurora Espinoza-Valdez, Beatriz C. Luna-Oliveros, Jorge Rivera and Jairo Sánchez-Estrada
Mathematics 2025, 13(17), 2741; https://doi.org/10.3390/math13172741 - 26 Aug 2025
Viewed by 1005
Abstract
Synchronization in complex networks mainly considers positive (attractive) couplings to guarantee network stability. However, in many real-world systems or processes, negative (repulsive) interactions exist, and this poses a challenging problem. In this proposal, we present an algorithm to design stable signed Laplacian matrices [...] Read more.
Synchronization in complex networks mainly considers positive (attractive) couplings to guarantee network stability. However, in many real-world systems or processes, negative (repulsive) interactions exist, and this poses a challenging problem. In this proposal, we present an algorithm to design stable signed Laplacian matrices with mixed attractive and repulsive couplings that ensure stability in both complete and in-phase synchronization. The main result is established through a constructive theorem that guarantees a single zero eigenvalue, while all other eigenvalues are negative, thereby preserving the diffusivity condition. The algorithm allows control over the spectral properties of the matrix by adjusting two parameters, which can be interpreted as a pole placement strategy from control theory. The approach is validated through numerical examples involving the synchronization of a network of chaotic Lorenz systems and a network of Kuramoto oscillators. In both cases, full synchronization is achieved despite the presence of negative couplings. Full article
(This article belongs to the Special Issue Advances in the Analysis and Control of Nonlinear Dynamical Systems and Complex Phenomena)
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