SELF-ORGANIZATION IN BIOLOGICAL TISSUES: ANALYSIS OF ASYNCHRONOUS AND SYNCHRONOUS PERIODICITY, TURBULENCE AND SYNCHRONOUS CHAOS EMERGENT IN COUPLED CHAOTIC ARRAYS

Large discrete arrays of chaotic attractors, coupled by diffusion, organize into asynchronous periodic spiral waves, synchronous periodic bands, turbulent fields or synchronous chaos as a function of coupling strength and array size. Self-organization of periodic spirals in both two and three dimensional arrays of nonexcitable systems appears to require the early establishment of an antipodal phase relationship between the few cells that will form the vortex. Cells within or close to the vortex maintain low z amplitude, near limit cycle trajectories, with stable, well-defined phase relationships. In periodic banding structures, initial antipodal phase seeds evolve to isochrons that form nested periodic trajectories. The likelihood that biological systems are fundamentally oscillatory and chaotic is discussed.