Complex Networks and Dynamical Systems

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

Deadline for manuscript submissions: 30 November 2024 | Viewed by 513

Special Issue Editors


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Guest Editor
College of Science, Northeast Forestry University, Harbin, China
Interests: complex systems; control theory; stochastic differential equations; stability; synchronization

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Guest Editor
Department of Mathematics, Southwest Jiaotong University, Chengdu, China
Interests: networked control system; stochastic differential equations
Special Issues, Collections and Topics in MDPI journals

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Guest Editor
Faculty of Science, Qingdao University of Technology, Qingdao, China
Interests: network control systems; the dynamic property of stochastic differential equations

Special Issue Information

Dear Colleagues:

With the development of science and technology, complex networks can be seen everywhere in the real world. Examples include the Internet, social networks, neural networks, and many others. In recent years, complex networks have attracted the attention of scholars in many fields including mathematics, biology, engineering and sociology. How to model actual complex networks and study their dynamic behavior is a very interesting and important topic in the field of complex network research. In mathematics, complex networks are usually described by differential or difference equations. In addition, practical applications depend on its dynamic properties such as stability, synchronization, periodicity, etc.

In this Special Issue of Axioms, we aim to explore the latest research and developments in dynamic properties of complex network control systems described by differential or difference equations. We will feature high-quality papers that cover a range of topics, including stability, synchronization and consistency of complex networks.

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

  1. Dynamic behaviors of complex networks in the real world and their applications;
  2. Dynamic properties of different complex dynamical networks.

I look forward to receiving your contributions.

Dr. Shang Gao
Dr. Chunmei Zhang
Prof. Dr. Ying Guo
Guest Editors

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Keywords

  • complex networks
  • stability
  • white noise
  • telegraph noise
  • stochastic systems
  • control theory
  • synchronization
  • periodicity

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Published Papers (1 paper)

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Research

14 pages, 375 KiB  
Article
The Stability of a Predator–Prey Model with Cross-Dispersal in a Multi-Patch Environment
by Keyao Xu, Keyu Peng and Shang Gao
Axioms 2024, 13(11), 783; https://doi.org/10.3390/axioms13110783 - 13 Nov 2024
Viewed by 307
Abstract
This paper investigates the stability of predator–prey models within multi-patch environments, with a particular focus on the influence of cross-dispersion across patches. We apply Kirchhoff’s matrix tree theorem and Liapunov’s method to derive criteria related to the cross-dispersion topology, thus solving the challenge [...] Read more.
This paper investigates the stability of predator–prey models within multi-patch environments, with a particular focus on the influence of cross-dispersion across patches. We apply Kirchhoff’s matrix tree theorem and Liapunov’s method to derive criteria related to the cross-dispersion topology, thus solving the challenge of determining global asymptotic stability conditions. The method incorporates realistic ecological interactions and spatial heterogeneity, offering a framework for stability analysis. Our findings demonstrate that an appropriate level of cross-dispersion can effectively mitigate oscillations and foster convergence toward equilibrium. Two numerical examples validate these theoretical results and demonstrate the feasibility and effectiveness of the model across multiple patches. Full article
(This article belongs to the Special Issue Complex Networks and Dynamical Systems)
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