Autogenous Formation of Spiral Waves by Coupled Chaotic Attractors

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Abstract
When large arrays of strange attractors are coupled diffusively through one of the variables, chaotic systems become periodic and form large archimedean spirals or concentric bands. This observation may have importance for many applications in the field of deterministic chaos and seems particularly relevant to the question of the formal temporal structure of the biological clock in metazoan organisms. In particular, although individual cellular oscillators, as manifested in the cell cycle, may have deep basins of attraction and appear to be more or less periodic, we suggest that cells oscillate with chaotic dynamics in the ultradian domain. Only when large aggregates of these cells are tightly coupled can a precise circadian clock emerge. For changing coupling strength or parameter values, period increase occurs through quantal or integral multiple increments of the fundamental. All calculations were implemented on a 386AT, using a Mercury MC6400 floating point processor.