Mathematical Modeling of Symmetry in Collective Biological Dynamics

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Mathematics".

Deadline for manuscript submissions: 30 September 2025 | Viewed by 3376

Special Issue Editor

College of Science, Northwest A&F University, Yangling, China
Interests: dynamic analysis of complex systems; evolutionary game theory; swarm intelligence and dynamic feedback scenarios

Special Issue Information

Dear Colleagues,

The emergence of collective behavior within biological systems, from the synchronized movements of fish schools to intricate human social interactions, epitomizes the inherent complexity and symmetry in nature. This phenomenon, where simple individual-level rules manifest into complex and often symmetrical group dynamics, is the focus of our Special Issue. Herein, we delve into the mathematical foundations that elucidate the principles driving the emergence of collective behavior, emphasizing the transformative power of mathematical models in uncovering these principles, with a particular focus on symmetry analysis across various scales and contexts within biology.

We invite submissions of original research articles that employ mathematical modeling techniques, including symmetry analysis, to dissect the mechanisms underlying the emergence of collective behavior. Appropriate submission materials may belong to biomathematics, including, but not limited to, infectious disease dynamics and the emergence mechanism of collective cooperation. Our primary interest lies in models that clarify how local interactions among individuals culminate in the formation of global patterns and behaviors, particularly those exhibiting symmetry. Furthermore, we seek to understand how these emergent properties are modulated by environmental variables, evolutionary pressures, and internal group dynamics, with an emphasis on the role of symmetry in these processes.

This Special Issue aims to catalyze interdisciplinary collaboration, serving as a repository for the latest advancements in the mathematical modeling of collective behavior, with a special emphasis on symmetry analysis. By showcasing innovative methodologies and discoveries, we aspire to stimulate further research that enhances our comprehension of the complex and symmetrical dynamics which are responsible for these collective phenomena in the natural world.

Dr. Linjie Liu
Guest Editor

Manuscript Submission Information

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Keywords

  • collective behavior
  • mathematical modeling
  • biomathematics
  • emergent properties
  • symmetry analysis

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Published Papers (2 papers)

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Research

25 pages, 2721 KiB  
Article
Spatial Kinetic Modeling of Crowd Evacuation: Coupling Social Behavior and Infectious Disease Contagion
by Juan Pablo Agnelli, Claudio Armas and Damián A. Knopoff
Symmetry 2025, 17(1), 123; https://doi.org/10.3390/sym17010123 - 15 Jan 2025
Cited by 1 | Viewed by 911
Abstract
This paper introduces a kinetic model of crowd evacuation from a bounded domain, integrating social behavior and contagion dynamics. The model describes the spatial movement of individuals in a crowd, taking into account interactions with other people and the geometry of the environment. [...] Read more.
This paper introduces a kinetic model of crowd evacuation from a bounded domain, integrating social behavior and contagion dynamics. The model describes the spatial movement of individuals in a crowd, taking into account interactions with other people and the geometry of the environment. Interactions between healthy and infectious individuals can lead to disease transmission and are considered. The approach is grounded in the kinetic theory of active particles, where the activity variable represents both the infectious disease status of individuals (e.g., susceptible, infected) and the psychological state of pedestrians, including contagion awareness. Varying awareness levels influence individual behavior, leading to more cautious movement patterns, potentially reducing the overall infection rate. The performance of the model is evaluated through a series of numerical simulations. Different scenarios are examined to investigate the impact of awareness levels on pedestrian behavior, infectious disease spread, and evacuation times. Additionally, the effects of population immunization and individual contagion awareness are assessed to determine the most effective strategy for reducing infections. The results provide valuable insights into targeted strategies to mitigate contagion. Full article
(This article belongs to the Special Issue Mathematical Modeling of Symmetry in Collective Biological Dynamics)
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31 pages, 5524 KiB  
Article
Utilizing Potential Field Mechanisms and Distributed Learning to Discover Collective Behavior on Complex Social Systems
by Junqiao Zhang, Qiang Qu and Xuebo Chen
Symmetry 2024, 16(8), 1014; https://doi.org/10.3390/sym16081014 - 8 Aug 2024
Viewed by 1934
Abstract
This paper proposes the complex dynamics of collective behavior through an interdisciplinary approach that integrates individual cognition with potential fields. Firstly, the interaction between individual cognition and external potential fields in complex social systems is explored, integrating perspectives from physics, cognitive psychology, and [...] Read more.
This paper proposes the complex dynamics of collective behavior through an interdisciplinary approach that integrates individual cognition with potential fields. Firstly, the interaction between individual cognition and external potential fields in complex social systems is explored, integrating perspectives from physics, cognitive psychology, and social science. Subsequently, a new modeling method for the multidimensional potential field mechanism is proposed, aiming to reduce individual behavioral errors and cognitive dissonance, thereby improving system efficiency and accuracy. The approach uses cooperative control and distributed learning algorithms to simulate collective behavior, allowing individuals to iteratively adapt based on local information and collective intelligence. Simulations highlight the impact of factors such as individual density, noise intensity, communication radius, and negative potential fields on collective dynamics. For instance, in a high-density environment with 180 individuals, increased social friction and competition for resources significantly decrease collective search efficiency. Validation is achieved by comparing simulation results with existing research, showing consistency and improvements over traditional models. In noisy environments, simulations maintain higher accuracy and group cohesion compared to standard methods. Additionally, without communication, the Mean Squared Error (MSE) initially drops rapidly as individuals adapt but stabilizes over time, emphasizing the importance of communication in maintaining collective efficiency. The study concludes that collective behavior emerges from complex nonlinear interactions between individual cognition and potential fields, rather than being merely the sum of individual actions. These insights enhance the understanding of complex system dynamics, providing a foundation for future applications in adaptive urban environments and the design of autonomous robots and AI systems. Full article
(This article belongs to the Special Issue Mathematical Modeling of Symmetry in Collective Biological Dynamics)
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