This article delves into the realm of computational bifurcation analysis, emphasizing the symbiotic relationship between theoretical foundations and computational methodologies. It elucidates how this synergy empowers researchers to effectively investigate and characterize the intricate behaviors exhibited by dynamical systems.
The authors employ a characteristic example of a continuous stirred tank reactor (CSTR) to illustrate their approach. Through a blend of analytical derivations and numerical simulations using the COCO software package, they showcase the identification and tracking of critical elements such as equilibria, periodic orbits, and bifurcation points.
The article further elaborates on a general methodology underpinning computational bifurcation analysis, encompassing stages of construction, initialization, adaptation, exploration, and interpretation. It underscores the importance of defining systems, numerical continuation algorithms, and bifurcation detection schemes.
By presenting a compelling case study and outlining a comprehensive methodology, the authors advocate for a synergistic approach to computational bifurcation analysis. This approach leverages theoretical insights to guide computational exploration and utilizes computational tools to validate and extend theoretical predictions, ultimately leading to a deeper understanding of complex dynamical systems.
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by Harry Dankow... at arxiv.org 11-04-2024
https://arxiv.org/pdf/2411.00735.pdfDeeper Inquiries