By ΠΠ°ΡΠΊΠΎΡΠ΅Π² Π.Π.
ΠΠ°ΡΠΊΠΎΡΠ΅Π² Π.Π., 2025
ΠΠ½ΠΈΠ³Π° ΠΏΡΠ΅Π΄ΡΡΠ°Π²Π»ΡΠ΅Ρ ΡΠΎΠ±ΠΎΠΉ ΠΌΠ΅ΠΆΠ΄ΠΈΡΡΠΈΠΏΠ»ΠΈΠ½Π°ΡΠ½ΠΎΠ΅ ΠΈΡΡΠ»Π΅Π΄ΠΎΠ²Π°Π½ΠΈΠ΅ ΡΠΈΠ½Π΅ΡΠ³Π΅ΡΠΈΠΊΠΈ, ΠΌΠ°ΡΠ΅ΠΌΠ°ΡΠΈΡΠ΅ΡΠΊΠΈ ΠΈΠ½ΡΠ΅ΡΠΏΡΠ΅ΡΠΈΡΠΎΠ²Π°Π½Π½ΠΎΠ΅ ΡΠ΅ΡΠ΅Π· Π³ΠΈΠ±ΡΠΈΠ΄Π½ΡΠ΅ ΡΡΠ½ΠΊΡΠΈΠΈ ΠΏΠ΅ΡΠ²ΠΎΠ³ΠΎ ΠΈ Π²ΡΠΎΡΠΎΠ³ΠΎ ΡΠΎΠ΄Π°. ΠΡΠΈ ΡΡΠ½ΠΊΡΠΈΠΈ ΠΎΡΡΠ°ΠΆΠ°ΡΡ Π΄ΠΈΠ½Π°ΠΌΠΈΠΊΡ ΡΠΎΠ²ΡΠ΅ΠΌΠ΅Π½Π½ΠΎΠΉ ΡΠΏΠΎΡ ΠΈ Π±ΡΡΡΡΡΡ ΠΈΠ·ΠΌΠ΅Π½Π΅Π½ΠΈΠΉ. Π ΡΠ°Π±ΠΎΡΠ΅ ΡΠ°ΡΡΠΌΠ°ΡΡΠΈΠ²Π°ΡΡΡΡ ΠΌΠ°ΡΠ΅ΠΌΠ°ΡΠΈΡΠ΅ΡΠΊΠΈΠ΅ ΠΌΠΎΠ΄Π΅Π»ΠΈ Π½Π° ΠΎΡΠ½ΠΎΠ²Π΅ Π³ΠΈΠ±ΡΠΈΠ΄Π½ΡΡ ΡΡΠ½ΠΊΡΠΈΠΉ, ΠΎΡ Π²Π°ΡΡΠ²Π°ΡΡΠΈΠ΅ ΡΠ°ΠΊΠΈΠ΅ ΠΎΠ±Π»Π°ΡΡΠΈ, ΠΊΠ°ΠΊ ΡΠ΅ΠΎΡΠΈΡ ΠΊΠ°ΡΠ°ΡΡΡΠΎΡ, ΡΡΠ°ΠΊΡΠ°Π»ΡΠ½Π°Ρ Π³Π΅ΠΎΠΌΠ΅ΡΡΠΈΡ, ΡΠΊΠΎΠ½ΠΎΠΌΠΈΠΊΠ° ΠΈ ΡΠΎΡΠΈΠΎΠ»ΠΎΠ³ΠΈΡ. ΠΠΎΠΊΠ°Π·Π°Π½ΠΎ, ΠΊΠ°ΠΊ Π³ΠΈΠ±ΡΠΈΠ΄Π½ΡΠ΅ ΡΡΠ½ΠΊΡΠΈΠΈ ΠΌΠΎΠ΄Π΅Π»ΠΈΡΡΡΡ ΠΊΠ»ΡΡΠ΅Π²ΡΠ΅ ΠΊΠΎΠ½ΡΠ΅ΠΏΡΠΈΠΈ ΡΠΈΠ½Π΅ΡΠ³Π΅ΡΠΈΠΊΠΈ, Π²ΠΊΠ»ΡΡΠ°Ρ ΡΠ΅ΠΏΠ½ΡΠ΅ ΠΏΠ΅ΡΠ΅Ρ ΠΎΠ΄Ρ ΠΈ Π±ΠΈΡΡΡΠΊΠ°ΡΠΈΠΈ Π² ΡΠ΅Ρ Π½ΠΈΡΠ΅ΡΠΊΠΈΡ ΠΈ Π΅ΡΡΠ΅ΡΡΠ²Π΅Π½Π½ΡΡ ΡΠΈΡΡΠ΅ΠΌΠ°Ρ .
V.M. Markochev, 2025
This book offers an interdisciplinary exploration of synergetics, mathematically interpreted through hybrid functions of the first and second kind. These functions reflect the dynamics of the current era of rapid change. The work examines mathematical models based on hybrid functions, covering fields such as catastrophe theory, fractal geometry, economics, and sociology. It demonstrates how hybrid functions model key synergetic concepts, including chain transitions and bifurcations in technical and natural systems.