Advances in Nonlinear Dynamics: Theory and Application

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

Deadline for manuscript submissions: 31 July 2026 | Viewed by 708

Special Issue Editor


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Guest Editor
Interdisciplinary Lab for Mathematical Ecology & Epidemiology, University of Alberta, Edmonton, AB, Canada
Interests: nonlinear dynamics; ecological modelling

Special Issue Information

Dear Colleagues,

Nonlinear dynamics has emerged as a powerful tool to analyze the mathematics of complex systems in the real world. Further, the advances in analytical methods, computational techniques, and interdisciplinary applications have significantly broadened the scope of this field. Therefore, having a deep understanding of the research area and the gaps would help us move forward in this field.

The Special Issue aims to attract the recent trends in the modelling, analysis and application of nonlinear dynamics to reveal the complex dynamics of the natural systems. It aims to collect articles focused on mathematical modelling of complex systems, stability analysis, bifurcation theory, and their applications across diverse scientific and engineering domains. The theme aligns with the scope of the journal by integrating the theoretical advancements with the practical applications.

In this Special Issue, original research articles and reviews are welcome. Research areas may include (but are not limited to) the following:

  • Advances in analytical methods in nonlinear dynamical systems;
  • Data-driven approaches to nonlinear systems;
  • Mathematical modelling of ecological systems;
  • Bifurcation theory, tipping points and regime shifts;
  • Extreme events;
  • Climate Network modelling;
  • Chaotic systems.

We look forward to receiving your contributions.

Dr. Pranali Roy Chowdhury
Guest Editor

Manuscript Submission Information

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Keywords

  • mathematical modelling
  • complex systems
  • bifurcation
  • data-driven dynamics
  • chaotic systems

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Published Papers (1 paper)

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Research

17 pages, 665 KB  
Article
Investigating Uniform Stability of Fractional-Order Complex-Valued Stochastic Neural Networks with Impulses via a Direct Method
by Jianglian Xiang, Tiantian Tang and Xiaoli Huang
Axioms 2026, 15(1), 17; https://doi.org/10.3390/axioms15010017 - 26 Dec 2025
Cited by 2 | Viewed by 365
Abstract
This paper focuses on exploring the existence and uniqueness of solutions for a specific type of impulsive fractional-order complex-valued stochastic neural network within the complex domain, a topic hitherto undocumented. The combination of fractional order, stochastic nature, complex values, and impulses allows the [...] Read more.
This paper focuses on exploring the existence and uniqueness of solutions for a specific type of impulsive fractional-order complex-valued stochastic neural network within the complex domain, a topic hitherto undocumented. The combination of fractional order, stochastic nature, complex values, and impulses allows the model to seize memory-related, noise-resilient, phase-sensitive, and discontinuous dynamics. These dynamics are crucial for applications in neuroscience, signal processing, engineering control, and time-series prediction. In contrast to more simplistic models, this framework provides greater fidelity when simulating real-world systems and wider applicability without the need for redundant component splitting, thus justifying the requirement for such a comprehensive model. Leveraging the contraction mapping principle and contradiction, sufficient conditions are deduced to guarantee the existence and uniform stability (in the distribution sense) of solutions for the impulsive fractional-order complex-valued stochastic neural networks under study. Finally, a numerical example is presented to illustrate the feasibility and precision of our findings. Full article
(This article belongs to the Special Issue Advances in Nonlinear Dynamics: Theory and Application)
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