Analysis of Critical Behavior in Complex Systems
A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Complexity".
Deadline for manuscript submissions: 30 September 2026 | Viewed by 7
Special Issue Editor
Interests: complex systems; nonlinear system; data analysis; complex network; quantum network; neural network
Special Issues, Collections and Topics in MDPI journals
Special Issue Information
Dear Colleagues,
Critical state behavior is a fundamental feature of complex systems, characterized by heightened sensitivity to perturbations, nonlinear responses, and the emergence of large-scale collective phenomena. Such behavior appears across a wide range of natural, technological, and social systems, including climate and coastal systems, carbon and energy networks, brain dynamics, traffic systems, and quantum and communication networks. Despite significant progress, understanding how criticality emerges, evolves, and can be characterized remains a central challenge in complexity science.
Recent advances in complex network theory, higher-order and hypergraph representations, and data-driven artificial intelligence have opened new avenues for investigating critical states. By moving beyond traditional pairwise interactions and incorporating multi-layer, higher-order, and dynamical network structures, researchers can more accurately capture nonlinear couplings, multi-scale dependencies, and collective dynamics. At the same time, modern machine learning methods, such as graph neural networks, census-based and data assimilation models, and AI-driven inference techniques, enable the intelligent identification, prediction, and early warning of critical transitions.
This Special Issue aims to provide a multidisciplinary platform for theoretical, methodological, and applied studies that advance the analysis and intelligent characterization of critical state behavior in complex systems. Contributions addressing network-based modeling, higher-order dynamics, AI-assisted inference, and real-world applications are particularly encouraged.
Topics of interest include, but are not limited to, the following:
Complex systems and network modeling
- Complex and multi-layer networks;
- Higher-order and hypergraph network models;
- Network topology, geometry, and criticality.
Critical state analysis and dynamics
- Phase transitions and critical phenomena in networks;
- Cascading failures and systemic risk;
- Synchronization and nonlinear dynamics;
- Diffusion, spreading, and percolation near criticality.
Intelligent and data-driven methods
- Graph neural networks (GNNs);
- AI and machine learning for critical state detection;
- Data-driven inference and prediction;
- Model training and optimization for complex systems.
Dr. Gaogao Dong
Guest Editor
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. Entropy is an international peer-reviewed open access monthly 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
- complex system
- complex networks
- hypergraph network
- census model
- GNN
- AI
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