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Pattern generation in space and aspect. (English) Zbl 0576.92008
Summary: A survey is presented of theories for the generation and maintenance of spatial pattern in reaction-diffusion equations and their generalizations. Applications are selected from the biological sciences and physical chemistry. Special emphasis is placed on nonlocal interaction, as manifested by the inclusion of terms involving higher derivatives or integrals. It is stressed that traditional ideas of spatial pattern generation can usefully be extended to the study of pattern in general descriptive (”aspect”) variables, particularly in understanding ecological diversity and heterogeneity.
MSC:
92B05General biology and biomathematics
92D40Ecology
80A30Chemical kinetics (thermodynamic aspects)
92ExxChemistry
92CxxPhysiological, cellular and medical topics