Can complex dynamics be understood through feedback circuits? This research explores how complex dynamics, specifically deterministic chaos, can be deciphered and understood through underlying logical structures like feedback circuits. Starting from the Rössler equations, the authors synthesize systems with similar steady states ab initio, demonstrating that chaotic dynamics are robust towards changes in nonlinearity and sign changes respecting feedback circuits. Using logical arguments, related systems with a single steady state are found. A variety of 3- and 4-d systems based on other combinations of feedback circuits and generating chaotic dynamics are described. The aim is to better understand the respective roles of feedback circuits and nonlinearity in deterministic chaos.
Published in the Journal of Biological Systems, this paper aligns with the journal's focus on systems-level approaches to understanding biological phenomena. By exploring how feedback circuits contribute to complex dynamics and deterministic chaos, the study contributes valuable insights into the behavior of biological systems, aligning with the journal's aim to integrate mathematical and computational approaches with biological research.