Nonlinear Dynamical Systems Interacting in Complex Networks

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E: Applied Mathematics".

Deadline for manuscript submissions: 31 October 2025 | Viewed by 271

Special Issue Editor


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Guest Editor
School of Complex Adaptive Systems, Arizona State University, Tempe, AZ 85281, USA
Interests: complex systems; network science; dynamical processes; gene regulatory networks; high energy physics; astrophysics

Special Issue Information

Dear Colleagues,

We stand at a pivotal moment in the study of complex systems, where an unprecedented wealth of data is refining our understanding of real-world network topology and establishing network science as one of the most powerful unifying tools for analyzing complex dynamics. Since the seminal discovery of the ubiquity of scale-free networks, it has become clear that these seemingly static topological patterns are far from arbitrary—they bear the imprint of underlying dynamical processes and the evolutionary histories that shape them, regardless of their respective domains.

Yet, the dynamism of networks extends far beyond their shifting topology. Many of the most complex systems they describe—such as social interactions and gene regulatory networks—operate on principles of preferential connectivity rather than simple physical links, often independent of spatial proximity. More than perhaps any other mathematical framework, networks provide a means to quantitatively study how physical interactions give rise to information processing.

Nowhere is this clearer than in gene regulatory networks, where biophysical processes translate raw molecular interactions into intricate systems of control and adaptation. Similar transformations are now unfolding in fields such as ecology, sociology, and economics, where the growing availability of data is driving a unified, quantitative understanding of their dynamics and evolutionary trajectories. As these disciplines increasingly adopt the common language of network science to integrate dynamical concepts more cohesively, we have an unprecedented opportunity to investigate physical, biological, and social interactions within a truly unified framework.

Dr. Enrico Borriello
Guest Editor

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Keywords

  • complex systems
  • network science
  • topology
  • scale-free networks
  • dynamical processes
  • gene regulatory networks
  • information processing
  • data science

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Published Papers (1 paper)

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Research

19 pages, 540 KiB  
Article
Exact Parametric and Semi-Analytical Solutions for the Rucklidge-Type Dynamical System
by Remus-Daniel Ene, Nicolina Pop and Rodica Badarau
Mathematics 2025, 13(13), 2052; https://doi.org/10.3390/math13132052 - 20 Jun 2025
Viewed by 167
Abstract
The behavior of the Rucklidge-type dynamical system was investigated, providing some semi-analytical solutions, in this paper. This system was analytically investigated by means of the Optimal Auxiliary Functions Method (OAFM) for two cases. An exact parametric solution was obtained. The effect of the [...] Read more.
The behavior of the Rucklidge-type dynamical system was investigated, providing some semi-analytical solutions, in this paper. This system was analytically investigated by means of the Optimal Auxiliary Functions Method (OAFM) for two cases. An exact parametric solution was obtained. The effect of the physical parameters was investigated on the asymptotic behaviors and damped oscillations of the solutions. Damped oscillations are essential for analyzing and designing various mechanical, biological, and electrical systems. Many of the applications involving these systems represent the main reason of this work. A comparison between the obtained results via the OAFM, the analytical solution obtained with the iterative method, and the corresponding numerical solution was performed. The accuracy of the analytical and corresponding numerical results is illustrated by graphical and tabular representations. Full article
(This article belongs to the Special Issue Nonlinear Dynamical Systems Interacting in Complex Networks)
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