Abstract
One-dimensional Fibonacci numbers and their applications are actively used in various fields of mathematics, computer technology and computer science, biology and economics. The article presents the results of the study of additive series of two-dimensional hyperbolic numbers with Fibonacci coordinates. Particular attention is paid to the matrix representation of such hyperbolic Fibonacci numbers. Some applications of new additive sequences in the field of genetic biomechanics are shown, including the laws of morphogenesis of phyllotaxis and the basic psychophysical law of Weber-Fechner. The important role of hyperbolic numbers in the modeling of biological phenomena is noted. The described results lead to new applications of Fibonacci numbers in various fields of science and technology.
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