13 - Organized structures

Abstract

Even simple reaction–diffusion systems with unequal diffusions, flows, or autocatalytic systems may lead to multiple solutions and organized structures at stable and metastable states. Turing instabilities, which lead to pattern formations, demonstrate that transport processes such as diffusion, which ordinarily leads to uniform concentration in time, may cause unexpected differentiation and organization of species. Some examples of self-organization of diverse phenomena in biology are: spontaneous folding of proteins and other biomacromolecules, formation of lipid bilayer membranes, homeostasis (the self-maintaining nature of systems from the cell to the whole organism), morphogenesis, or how the living organism develops and grows, and flocking behavior (the formation of flocks by birds, schools of fish, etc.). The chapter briefly discusses some of the structured states in physical, chemical, and biological systems. When a system is sufficiently far from equilibrium, it may arrive at a bifurcation of states and move to ordered structures. Synergetics is concerned with the cooperation of individual parts of the system that produce macroscopic spatial and temporal structures, which are mainly dissipative. Bifurcation, instability, multiple solutions, and symmetry-breaking states are all related to each other.