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: 24 December 2025 | Viewed by 1041

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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
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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

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Keywords

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

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Published Papers (2 papers)

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Research

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 422
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
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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 420
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
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