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ΠΠΈΠ½Π°ΠΌΠΈΡΠ΅ΡΠΊΠ°Ρ ΠΌΠΎΠ΄Π΅Π»Ρ ΡΠ°Π·Π²ΠΈΡΠΈΡ ΠΏΠΈΡΠΈΠ½Π³ΠΎΠ²ΠΎΠΉ ΡΠ°ΠΉΠ»ΠΎΠΎΠ±ΠΌΠ΅Π½Π½ΠΎΠΉ ΡΠ΅ΡΠΈ
In this work, the model of development of the P2P file exchange network organized by a torrent tracker is considered. The model is constructed on the basis of ordinary differential equations. The phase variables describing a status of a torrent tracker and the network organized by it (in first approximation is the number of the users of the tracker who are actively participate in information exchange, and the number of active torrents) are defined, the factors influencing the change of users number and the number of torrents are analyzed. On the basis of the analysis the system of differential equations, in first approximation describing evolution of the file exchange network organized by the torrent tracker β a hard dynamic model of evolution of the torrent tracker is written. Equilibrium points of hard model of evolution of the tracker are investigated, their possible quantity and type is described. All configurations of the general provision, possible in a hard model of evolution of the torrent tracker are described. The phase portrait of the hard model is represented. On the basis of the analysis of the hard model the system of differential equations describing evolution of a file exchange network with accounting of dependence of new users inflow intensity on a total quantity of potential audience of the torrent tracker, and also dependences of speed of torrents extinction on the number of users falling on one torrent β a soft dynamic model of evolution of a torrent tracker is written. Equilibrium points of a soft model of tracker evolution are investigated, their possible quantity and type is described. All configurations of the general provision, possible in a soft model of evolution of the torrent tracker are described. Phase portraits of each configuration are represented. The ratio of parameters necessary for the stability of the tracker a stable status is received. The influence of different administrative measures on a stock of the tracker stability in whole is analyzed. The need of support of torrents by administration at highly specialized torrent trackers with small potential audience is shown.Π Π΄Π°Π½Π½ΠΎΠΉ ΡΠ°Π±ΠΎΡΠ΅ ΡΠ°ΡΡΠΌΠ°ΡΡΠΈΠ²Π°Π΅ΡΡΡ ΠΌΠΎΠ΄Π΅Π»Ρ ΡΠ°Π·Π²ΠΈΡΠΈΡ ΠΏΠΈΡΠΈΠ½Π³ΠΎΠ²ΠΎΠΉ ΡΠ°ΠΉΠ»ΠΎΠΎΠ±ΠΌΠ΅Π½Π½ΠΎΠΉ ΡΠ΅ΡΠΈ, ΠΎΡΠ³Π°Π½ΠΈΠ·ΡΠ΅ΠΌΠΎΠΉ ΠΎΠ΄Π½ΠΈΠΌ ΡΠΎΡΡΠ΅Π½Ρ-ΡΡΠ΅ΠΊΠ΅ΡΠΎΠΌ. ΠΠΎΠ΄Π΅Π»Ρ ΠΏΠΎΡΡΡΠΎΠ΅Π½Π° Π½Π° ΠΎΡΠ½ΠΎΠ²Π΅ ΠΎΠ±ΡΠΊΠ½ΠΎΠ²Π΅Π½Π½ΡΡ
Π΄ΠΈΡΡΠ΅ΡΠ΅Π½ΡΠΈΠ°Π»ΡΠ½ΡΡ
ΡΡΠ°Π²Π½Π΅Π½ΠΈΠΉ. ΠΠΏΡΠ΅Π΄Π΅Π»Π΅Π½Ρ ΡΠ°Π·ΠΎΠ²ΡΠ΅ ΠΏΠ΅ΡΠ΅ΠΌΠ΅Π½Π½ΡΠ΅, ΠΎΠΏΠΈΡΡΠ²Π°ΡΡΠΈΠ΅ ΡΠΎΡΡΠΎΡΠ½ΠΈΠ΅ ΡΠΎΡΡΠ΅Π½ΡΡΡΠ΅ΠΊΠ΅ΡΠ° ΠΈ ΠΎΡΠ³Π°Π½ΠΈΠ·ΡΠ΅ΠΌΠΎΠΉ ΠΈΠΌ ΡΠ΅ΡΠΈ (Π² ΠΏΠ΅ΡΠ²ΠΎΠΌ ΠΏΡΠΈΠ±Π»ΠΈΠΆΠ΅Π½ΠΈΠΈ β ΡΡΠΎ ΠΊΠΎΠ»ΠΈΡΠ΅ΡΡΠ²ΠΎ ΠΏΠΎΠ»ΡΠ·ΠΎΠ²Π°ΡΠ΅Π»Π΅ΠΉ ΡΡΠ΅ΠΊΠ΅ΡΠ°, Π°ΠΊΡΠΈΠ²Π½ΠΎ ΡΡΠ°ΡΡΠ²ΡΡΡΠΈΡ
Π² ΠΈΠ½ΡΠΎΡΠΌΠ°ΡΠΈΠΎΠ½Π½ΠΎΠΌ ΠΎΠ±ΠΌΠ΅Π½Π΅, ΠΈ ΠΊΠΎΠ»ΠΈΡΠ΅ΡΡΠ²ΠΎ Π°ΠΊΡΠΈΠ²Π½ΡΡ
ΡΠ°Π·Π΄Π°Ρ), ΠΏΡΠΎΠ°Π½Π°Π»ΠΈΠ·ΠΈΡΠΎΠ²Π°Π½Ρ ΡΠ°ΠΊΡΠΎΡΡ, Π²Π»ΠΈΡΡΡΠΈΠ΅ Π½Π° ΠΈΠ·ΠΌΠ΅Π½Π΅Π½ΠΈΠ΅ ΠΊΠΎΠ»ΠΈΡΠ΅ΡΡΠ²Π° ΠΏΠΎΠ»ΡΠ·ΠΎΠ²Π°ΡΠ΅Π»Π΅ΠΉ ΠΈ ΠΊΠΎΠ»ΠΈΡΠ΅ΡΡΠ²Π° ΡΠ°Π·Π΄Π°Ρ. ΠΠ° ΠΎΡΠ½ΠΎΠ²Π΅ Π°Π½Π°Π»ΠΈΠ·Π° ΡΠ°Π·ΡΠ°Π±ΠΎΡΠ°Π½Π° ΡΠΈΡΡΠ΅ΠΌΠ° Π΄ΠΈΡΡΠ΅ΡΠ΅Π½ΡΠΈΠ°Π»ΡΠ½ΡΡ
ΡΡΠ°Π²Π½Π΅Π½ΠΈΠΉ, Π² ΠΏΠ΅ΡΠ²ΠΎΠΌ ΠΏΡΠΈΠ±Π»ΠΈΠΆΠ΅Π½ΠΈΠΈ ΠΎΠΏΠΈΡΡΠ²Π°ΡΡΠ°Ρ ΡΠ²ΠΎΠ»ΡΡΠΈΡ ΡΠ°ΠΉΠ»ΠΎΠΎΠ±ΠΌΠ΅Π½Π½ΠΎΠΉ ΡΠ΅ΡΠΈ, ΠΎΡΠ³Π°Π½ΠΈΠ·ΡΠ΅ΠΌΠΎΠΉ ΡΠΎΡΡΠ΅Π½Ρ-ΡΡΠ΅ΠΊΠ΅ΡΠΎΠΌ, β ΠΆΡΡΡΠΊΠ°Ρ Π΄ΠΈΠ½Π°ΠΌΠΈΡΠ΅ΡΠΊΠ°Ρ ΠΌΠΎΠ΄Π΅Π»Ρ ΡΠ²ΠΎΠ»ΡΡΠΈΠΈ ΡΠΎΡΡΠ΅Π½Ρ-ΡΡΠ΅ΠΊΠ΅ΡΠ°. ΠΡΡΠ»Π΅Π΄ΠΎΠ²Π°Π½Ρ ΠΎΡΠΎΠ±ΡΠ΅ ΡΠΎΡΠΊΠΈ ΠΆΡΡΡΠΊΠΎΠΉ ΠΌΠΎΠ΄Π΅Π»ΠΈ ΡΠ²ΠΎΠ»ΡΡΠΈΠΈ ΡΡΠ΅ΠΊΠ΅ΡΠ°, ΠΎΠΏΠΈΡΠ°Π½ΠΎ ΠΈΡ
Π²ΠΎΠ·ΠΌΠΎΠΆΠ½ΠΎΠ΅ ΠΊΠΎΠ»ΠΈΡΠ΅ΡΡΠ²ΠΎ ΠΈ ΡΠΈΠΏ. ΠΠΏΠΈΡΠ°Π½Ρ Π²ΡΠ΅ ΠΊΠΎΠ½ΡΠΈΠ³ΡΡΠ°ΡΠΈΠΈ ΠΎΠ±ΡΠ΅Π³ΠΎ ΠΏΠΎΠ»ΠΎΠΆΠ΅Π½ΠΈΡ, Π²ΠΎΠ·ΠΌΠΎΠΆΠ½ΡΠ΅ Π² ΠΆΡΡΡΠΊΠΎΠΉ ΠΌΠΎΠ΄Π΅Π»ΠΈ ΡΠ²ΠΎΠ»ΡΡΠΈΠΈ ΡΠΎΡΡΠ΅Π½Ρ-ΡΡΠ΅ΠΊΠ΅ΡΠ°. ΠΠ·ΠΎΠ±ΡΠ°ΠΆΡΠ½ ΡΠ°Π·ΠΎΠ²ΡΠΉ ΠΏΠΎΡΡΡΠ΅Ρ ΠΆΡΡΡΠΊΠΎΠΉ ΠΌΠΎΠ΄Π΅Π»ΠΈ. ΠΠ° ΠΎΡΠ½ΠΎΠ²Π΅ Π°Π½Π°Π»ΠΈΠ·Π° ΠΆΡΡΡΠΊΠΎΠΉ ΠΌΠΎΠ΄Π΅Π»ΠΈ ΠΏΠΎΠ»ΡΡΠ΅Π½Π° ΡΠΈΡΡΠ΅ΠΌΠ° Π΄ΠΈΡΡΠ΅ΡΠ΅Π½ΡΠΈΠ°Π»ΡΠ½ΡΡ
ΡΡΠ°Π²Π½Π΅Π½ΠΈΠΉ, ΠΎΠΏΠΈΡΡΠ²Π°ΡΡΠ°Ρ ΡΠ²ΠΎΠ»ΡΡΠΈΡ ΡΠ°ΠΉΠ»ΠΎΠΎΠ±ΠΌΠ΅Π½Π½ΠΎΠΉ ΡΠ΅ΡΠΈ Ρ ΡΡΡΡΠΎΠΌ Π·Π°Π²ΠΈΡΠΈΠΌΠΎΡΡΠΈ ΠΈΠ½ΡΠ΅Π½ΡΠΈΠ²Π½ΠΎΡΡΠΈ ΠΏΡΠΈΡΠΎΠΊΠ° Π½ΠΎΠ²ΡΡ
ΠΏΠΎΠ»ΡΠ·ΠΎΠ²Π°ΡΠ΅Π»Π΅ΠΉ ΠΎΡ ΠΎΠ±ΡΠ΅Π³ΠΎ ΠΊΠΎΠ»ΠΈΡΠ΅ΡΡΠ²Π° ΠΏΠΎΡΠ΅Π½ΡΠΈΠ°Π»ΡΠ½ΠΎΠΉ Π°ΡΠ΄ΠΈΡΠΎΡΠΈΠΈ ΡΠΎΡΡΠ΅Π½Ρ-ΡΡΠ΅ΠΊΠ΅ΡΠ°, Π° ΡΠ°ΠΊΠΆΠ΅ Π·Π°Π²ΠΈΡΠΈΠΌΠΎΡΡΠΈ ΡΠΊΠΎΡΠΎΡΡΠΈ Π²ΡΠΌΠΈΡΠ°Π½ΠΈΡ ΡΠ°Π·Π΄Π°Ρ ΠΎΡ ΠΏΡΠΈΡ
ΠΎΠ΄ΡΡΠ΅Π³ΠΎΡΡ Π½Π° ΠΎΠ΄Π½Ρ ΡΠ°Π·Π΄Π°ΡΡ ΠΊΠΎΠ»ΠΈΡΠ΅ΡΡΠ²Π° ΠΏΠΎΠ»ΡΠ·ΠΎΠ²Π°ΡΠ΅Π»Π΅ΠΉ β ΠΌΡΠ³ΠΊΠ°Ρ Π΄ΠΈΠ½Π°ΠΌΠΈΡΠ΅ΡΠΊΠ°Ρ ΠΌΠΎΠ΄Π΅Π»Ρ ΡΠ²ΠΎΠ»ΡΡΠΈΠΈ ΡΠΎΡΡΠ΅Π½Ρ-ΡΡΠ΅ΠΊΠ΅ΡΠ°. ΠΡΡΠ»Π΅Π΄ΠΎΠ²Π°Π½Ρ ΠΎΡΠΎΠ±ΡΠ΅ ΡΠΎΡΠΊΠΈ ΠΌΡΠ³ΠΊΠΎΠΉ ΠΌΠΎΠ΄Π΅Π»ΠΈ ΡΠ²ΠΎΠ»ΡΡΠΈΠΈ ΡΡΠ΅ΠΊΠ΅ΡΠ°, ΠΎΠΏΠΈΡΠ°Π½ΠΎ ΠΈΡ
Π²ΠΎΠ·ΠΌΠΎΠΆΠ½ΠΎΠ΅ ΠΊΠΎΠ»ΠΈΡΠ΅ΡΡΠ²ΠΎ ΠΈ ΡΠΈΠΏ. ΠΠΏΠΈΡΠ°Π½Ρ Π²ΡΠ΅ ΠΊΠΎΠ½ΡΠΈΠ³ΡΡΠ°ΡΠΈΠΈ ΠΎΠ±ΡΠ΅Π³ΠΎ ΠΏΠΎΠ»ΠΎΠΆΠ΅Π½ΠΈΡ, Π²ΠΎΠ·ΠΌΠΎΠΆΠ½ΡΠ΅ Π² ΠΌΡΠ³ΠΊΠΎΠΉ ΠΌΠΎΠ΄Π΅Π»ΠΈ ΡΠ²ΠΎΠ»ΡΡΠΈΠΈ ΡΠΎΡΡΠ΅Π½Ρ-ΡΡΠ΅ΠΊΠ΅ΡΠ°. ΠΠ·ΠΎΠ±ΡΠ°ΠΆΠ΅Π½Ρ ΡΠ°Π·ΠΎΠ²ΡΠ΅ ΠΏΠΎΡΡΡΠ΅ΡΡ ΠΊΠ°ΠΆΠ΄ΠΎΠΉ ΠΊΠΎΠ½ΡΠΈΠ³ΡΡΠ°ΡΠΈΠΈ. ΠΠΎΠ»ΡΡΠ΅Π½ΠΎ ΡΠΎΠΎΡΠ½ΠΎΡΠ΅Π½ΠΈΠ΅ ΠΏΠ°ΡΠ°ΠΌΠ΅ΡΡΠΎΠ², Π½Π΅ΠΎΠ±Ρ
ΠΎΠ΄ΠΈΠΌΠΎΠ΅ Π΄Π»Ρ ΡΡΡΠΎΠΉΡΠΈΠ²ΠΎΡΡΠΈ ΡΡΠ°Π±ΠΈΠ»ΡΠ½ΠΎΠ³ΠΎ ΡΠΎΡΡΠΎΡΠ½ΠΈΡ ΡΡΠ΅ΠΊΠ΅ΡΠ°. ΠΡΠΎΠ°Π½Π°Π»ΠΈΠ·ΠΈΡΠΎΠ²Π°Π½ΠΎ Π²Π»ΠΈΡΠ½ΠΈΠ΅ ΡΠ°Π·Π»ΠΈΡΠ½ΡΡ
Π°Π΄ΠΌΠΈΠ½ΠΈΡΡΡΠ°ΡΠΈΠ²Π½ΡΡ
ΠΌΠ΅Ρ Π½Π° Π·Π°ΠΏΠ°Ρ ΡΡΡΠΎΠΉΡΠΈΠ²ΠΎΡΡΠΈ ΡΡΠ΅ΠΊΠ΅ΡΠ° Π² ΡΠ΅Π»ΠΎΠΌ. ΠΠΎΠΊΠ°Π·Π°Π½Π° Π½Π΅ΠΎΠ±Ρ
ΠΎΠ΄ΠΈΠΌΠΎΡΡΡ ΠΏΠΎΠ΄Π΄Π΅ΡΠΆΠΊΠΈ ΡΠ°Π·Π΄Π°Ρ Π°Π΄ΠΌΠΈΠ½ΠΈΡΡΡΠ°ΡΠΈΠ΅ΠΉ Π½Π° ΡΠ·ΠΊΠΎΡΠΏΠ΅ΡΠΈΠ°Π»ΠΈΠ·ΠΈΡΠΎΠ²Π°Π½Π½ΡΡ
ΡΠΎΡΡΠ΅Π½Ρ-ΡΡΠ΅ΠΊΠ΅ΡΠ°Ρ
Ρ ΠΌΠ°Π»ΠΎΠΉ ΠΏΠΎΡΠ΅Π½ΡΠΈΠ°Π»ΡΠ½ΠΎΠΉ Π°ΡΠ΄ΠΈΡΠΎΡΠΈΠ΅ΠΉ