Dynamical Systems and Complex Systems
A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "C2: Dynamical Systems".
Deadline for manuscript submissions: 20 August 2025 | Viewed by 347
Special Issue Editor
Special Issue Information
Dear Colleagues,
Dynamical and complex systems may sometimes refer to similar kinds of systems, considered either from the mathematical or application-oriented perspectives. In both viewpoints, the challenge is to tackle the interface between understanding the individual behavior of the constituent parts of the system and its collective behavior.
The mathematical analysis of dynamical systems has, from its origin, been intricately interwoven with the development of theoretical mechanics but has also developed various ramifications, ranging from completely integrable to ergodic or chaotic systems. Moreover, the interplay between continuous and discrete systems (maps) has proven to be an important research focus point. Recent advances in machine learning have also provided us with the opportunity to study dynamical systems not only from an analytical perspective but also from a data-driven viewpoint. On the other hand, understanding the dynamical behavior of various systems is an indispensable tool for the advancement of all kinds of neural network models which underlie many of the most recent artificial intelligence architectures.
The notion of complex systems usually refers, in a broad sense, to systems whose behavior is “complex” in the sense that it cannot be adequately understood from the properties of its individual components but which exhibit an emergent behavior. From a mathematical viewpoint, the challenge is to overcome this dichotomy between the “microscopic” and “macroscopic” behavior of a given system and, notwithstanding the many important developments in the past years and decades, there remain many questions to be answered.
The present Special Issue of Mathematics welcomes any paper which addresses, from a mathematical perspective, the interface and tension between the individual and collective behaviors of complex systems using the rich toolbox of dynamical systems analysis.
Dr. Andreas Henrici
Guest Editor
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Keywords
- dynamical systems
- complex systems
- ergodic systems
- chaotic systems
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