2025/01/07 by Franco Bagnoli, Michele Baia, Bagnoli, Franco +5
Computer Science · Engineering · Mathematics · #Cellular Automata and Applications #Chaotic Dynamics (nlin.CD) #FOS: Physical sciences #Mathematical Dynamics and Fractals #Slime Mold and Myxomycetes Research
paper · pdf · doi:10.48550/arxiv.2501.12398
openalex publication_date 2025/01/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
We investigate the synchronization dynamics in a chain of coupled chaotic maps organized in a single-parent family tree, whose properties can be captured considering each parent node connected to two children, one of which also serves as the parent for the subsequent node. Our analysis focuses on two distinct synchronization behaviors: parent-child synchronization, defined by the vanishing distance between successive nodes along the chain, and sibling synchronization, corresponding to the convergence of the states of two child nodes. Our findings reveal significant differences in these two type of synchronization mechanisms, which are closely associated with the probability distribution of the state of parent node. Theoretical analysis and simulations with the logistic map support our findings. We further investigate numerical aspects of the implementation corresponding to cases for which the simulated regimes differ from the theoretically predicted one due to computational finite accuracy. We perform a detailed study on how instabilities are numerically suppressed or amplified along the chain. In some cases, a properly adjusted computational scheme can solve this problem.