Bifurcations and Stability in Networked, Ecological, and Biological Systems

Nonlinear dynamical systems provide a mathematical framework for understanding phase transitions, oscillatory behavior, pattern formation, resilience, and the emergence of complex structures across biological, ecological, physical, and technological settings. Bifurcation theory and stability analysis remain central to identifying qualitative changes in system behavior, while chaos-control methods offer strategies for regulating irregular or unpredictable dynamics. However, the increasing complexity of real-world systems raises important questions concerning how delays, network interactions, multiple temporal and spatial scales, and uncertainty influence transitions, stability, and resilience. Recent research has extended classical approaches, including Hopf and transcritical bifurcation analysis, to delay differential equations, networked systems, multi-scale models, and coupled biological processes. These developments have produced new insights into pattern formation, disease dynamics involving within-host processes, ecological variability, and the control of chaotic behavior. Nevertheless, theoretical and computational challenges remain in linking local stability properties to global dynamics, characterizing tipping points in interconnected systems, and designing robust control strategies under uncertainty. Further investigation is needed to integrate mathematical theory with applications and to clarify how complex systems can transition between stability, oscillation, and chaos.This Research Topic aims to advance the mathematical analysis and application of bifurcation, stability, and chaos-control methods in complex nonlinear systems. It will address how qualitative changes in dynamics arise, how resilience and instability can be detected, and how oscillatory, chaotic, or emergent patterns can be understood and regulated. Contributions may develop new analytical, computational, or data-informed methods; establish theoretical results for deterministic or uncertain systems; or demonstrate the relevance of these approaches to biological, ecological, and other real-world phenomena.To gather further insights into bifurcation, stability, resilience, and chaos control in complex dynamical systems, we welcome articles addressing, but not limited to, the following themes:- Classical and codimension-two bifurcations, including Hopf and transcritical bifurcations- Stability, asymptotic behavior, and global dynamics of nonlinear systems- Delay differential equations and systems with memory- Bifurcation and pattern formation in complex networks- Synchronization, consensus, and collective dynamics- Chaos detection, prediction, and control- Multi-scale and multistable dynamical systems- Disease dynamics, including within-host and between-host processes- Ecological modelling, resilience, and tipping points- Uncertainty quantification and stochastic dynamical systems- Mathematical models of biological and physical processes- Analytical, numerical, and data-driven approaches to nonlinear dynamics Topic editors: Khalid Hattaf, Fahad Al Basir Source: https://www.frontiersin.org/research-topics/85074/bifurcations-and-stability-in-networked-ecological-and-biological-systems