2024/01/04 by Louise Arno, Arno, Louise, Desmond Kabus +3
Computer Science · Neuroscience · #Biological Physics (physics.bio-ph) #Cellular Automata and Applications #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Medical Physics (physics.med-ph) #Neural dynamics and brain function #Nonlinear Dynamics and Pattern Formation #Pattern Formation and Solitons (nlin.PS)
paper · pdf · doi:10.48550/arxiv.2401.02571
openalex publication_date 2024/01/04 · openalex created_date 2024/01/13 · openalex updated_date 2026/07/28
Several excitable systems, such as the heart, self-organize into complex spatio-temporal patterns that involve wave collisions, wave breaks, and rotating vortices, of which the dynamics are incompletely understood. Recently, conduction block lines in two-dimensional media were recognized as phase defects, on which quasi-particles can be defined. These particles also form bound states, one of which corresponds to the classical phase singularity. Here, we relate the quasi-particles to the structure of the dynamical attractor in state space and extend the framework to three spatial dimensions. We reveal that 3D excitable media are governed by phase defect surfaces, i.e. branes, and three flavors of topologically preserved curves, i.e. strings: heads, tails, and pivot curves. We identify previously coined twistons as points of co-dimension three at the crossing of a head curve and a pivot curve. Our framework predicts splitting and branching phase defect surfaces that can connect multiple classical filaments, thereby proposing a new mechanism for the origin, perpetuation, and control of complex excitation patterns, including cardiac fibrillation.