title: ÐÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ðµ ÑÐ¸Ð½Ñ ÑÐ¾Ð½Ð¸Ð·Ð°ÑÐ¸Ð¸ ÑÑÐ¾Ñ Ð°ÑÑÐ¸ÑÐµÑÐºÐ¾Ð³Ð¾ Ð³ÐµÐ½ÐµÑÐ°ÑÐ¾ÑÐ° Ð½Ð° Ð¾ÑÐ½Ð¾Ð²Ðµ Ð½ÐµÑÑÐ°Ð±Ð¸Ð»ÑÐ½Ð¾Ð³Ð¾ Ð¾ÑÑÐ¸Ð»Ð»ÑÑÐ¾ÑÐ° Ð²ÑÐ¾ÑÐ¾Ð³Ð¾ Ð¿Ð¾ÑÑÐ´ÐºÐ° Ñ Ð³Ð¸ÑÑÐµÑÐµÐ·Ð¸ÑÐ½ÑÐ¼ ÑÐ»ÐµÐ¼ÐµÐ½ÑÐ¾Ð¼
title: Ð²ÑÐ¿ÑÑÐºÐ½Ð°Ñ ÐºÐ²Ð°Ð»Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¾Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð±Ð°ÐºÐ°Ð»Ð°Ð²ÑÐ°
titleType: Subtitle
title: Study of synchronization of a stochastic generator based on an unstable second order oscillator with a hysteresis element
Creators: name: Ð¨ÐµÐ»ÐºÐ¾Ð²ÐµÐ½ÐºÐ¾, ÐÐ°Ð²ÐµÐ»
Publisher: name: Ð¡Ð°Ð½ÐºÑ-ÐÐµÑÐµÑÐ±ÑÑÐ³ÑÐºÐ¸Ð¹ Ð¿Ð¾Ð»Ð¸ÑÐµÑÐ½Ð¸ÑÐµÑÐºÐ¸Ð¹ ÑÐ½Ð¸Ð²ÐµÑÑÐ¸ÑÐµÑ ÐÐµÑÑÐ° ÐÐµÐ»Ð¸ÐºÐ¾Ð³Ð¾
Year: 2024
Subjects: ÑÑÐ¾Ñ Ð°ÑÑÐ¸ÑÐµÑÐºÐ°Ñ Ð´Ð¸Ð½Ð°Ð¼Ð¸ÐºÐ°
Ð½ÐµÐ»Ð¸Ð½ÐµÐ¹Ð½ÑÐµ Ð´Ð¸Ð½Ð°Ð¼Ð¸ÑÐµÑÐºÐ¸Ðµ ÑÐ¸ÑÑÐµÐ¼Ñ
Ñ Ð°Ð¾Ñ
Ð°ÑÑÑÐ°ÐºÑÐ¾Ñ
Ð±Ð¸ÑÑÑÐºÐ°ÑÐ¸Ñ
ÑÐ¸Ð½Ñ ÑÐ¾Ð½Ð¸Ð·Ð°ÑÐ¸Ñ
Ð³Ð¸ÑÑÐµÑÐµÐ·Ð¸Ñ
Ð¼Ð¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ðµ
ÑÐºÑÐ¿ÐµÑÐ¸Ð¼ÐµÐ½ÑÐ°Ð»ÑÐ½ÑÐµ Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ñ
stochastic dynamics
nonlinear dynamic systems
chaos
attractor
bifurcation
synchronization
hysteresis
modeling
experimental studies

description: ÐÐ±ÑÐµÐºÑ Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ñ â Ð¿ÑÐ¾ÑÐµÑÑ ÑÐ¸Ð½ÑÑÐ¾Ð½Ð¸Ð·Ð°ÑÐ¸Ð¸ Ð´Ð²ÑÑ ÑÑÐ¾ÑÐ°ÑÑÐ¸ÑÐµÑÐºÐ¸Ñ Ð³ÐµÐ½ÐµÑÐ°ÑÐ¾ÑÐ¾Ð². Ð¦ÐµÐ»Ñ ÑÐ°Ð±Ð¾ÑÑ â Ð¿Ð¾Ð»ÑÑÐ¸ÑÑ Ð¸ Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°ÑÑ ÑÐ¸Ð½ÑÑÐ¾Ð½Ð¸Ð·Ð°ÑÐ¸Ñ Ð´Ð²ÑÑ ÑÑÐ¾ÑÐ°ÑÑÐ¸ÑÐµÑÐºÐ¸Ñ Ð³ÐµÐ½ÐµÑÐ°ÑÐ¾ÑÐ¾Ð². Ð ÑÐ¾Ð´Ðµ ÑÐ°Ð±Ð¾ÑÑ Ð±ÑÐ»Ð° ÑÑÐ°ÑÐµÐ»ÑÐ½Ð°Ñ Ð¸Ð·ÑÑÐµÐ½Ð° ÑÐµÐ¾ÑÐ¸Ñ ÑÑÐ¾ÑÐ°ÑÑÐ¸ÑÐµÑÐºÐ¾Ð¹ ÑÐ¸Ð½ÑÑÐ¾Ð½Ð¸Ð·Ð°ÑÐ¸Ð¸, Ð¿ÑÐ¾Ð°Ð½Ð°Ð»Ð¸Ð·Ð¸ÑÐ¾Ð²Ð°Ð½Ñ ÑÐ¾Ð²ÑÐµÐ¼ÐµÐ½Ð½ÑÐµ Ð¸ÑÑÐ¾ÑÐ½Ð¸ÐºÐ¸, Ð¿Ð¾Ð·Ð²Ð¾Ð»Ð¸Ð²ÑÐ¸Ðµ ÑÐ³Ð»ÑÐ±Ð¸ÑÑ Ð¿Ð¾Ð½Ð¸Ð¼Ð°Ð½Ð¸Ðµ Ð¿ÑÐ¾ÑÐµÑÑÐ¾Ð² ÑÑÐ¾ÑÐ°ÑÑÐ¸ÑÐµÑÐºÐ¾Ð¹ ÑÐ¸Ð½ÑÑÐ¾Ð½Ð¸Ð·Ð°ÑÐ¸Ð¸ Ð¸ Ð²ÑÑÐ²Ð¸ÑÑ Ð°ÐºÑÑÐ°Ð»ÑÐ½ÑÐµ Ð½Ð°Ð¿ÑÐ°Ð²Ð»ÐµÐ½Ð¸Ñ Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ð¹ Ð² Ð´Ð°Ð½Ð½Ð¾Ð¹ Ð¾Ð±Ð»Ð°ÑÑÐ¸. ÐÐ¿ÑÐµÐ´ÐµÐ»ÐµÐ½Ñ ÐºÐ»ÑÑÐµÐ²ÑÐµ Ð¿Ð°ÑÐ°Ð¼ÐµÑÑÑ, Ð²Ð»Ð¸ÑÑÑÐ¸Ðµ Ð½Ð° Ð¿ÐµÑÐµÑÐ¾Ð´ ÑÐ¸ÑÑÐµÐ¼Ñ Ð¾Ñ Ð½ÐµÑÑÐ°Ð±Ð¸Ð»ÑÐ½Ð¾Ð³Ð¾ Ðº ÑÑÐ°Ð±Ð¸Ð»ÑÐ½Ð¾Ð¼Ñ ÑÐ¾ÑÑÐ¾ÑÐ½Ð¸Ñ. Ð¡Ð¾Ð·Ð´Ð°Ð½Ð° ÐºÐ¾Ð¼Ð¿ÑÑÑÐµÑÐ½Ð°Ñ Ð¼Ð¾Ð´ÐµÐ»Ñ ÑÑÐ¾ÑÐ°ÑÑÐ¸ÑÐµÑÐºÐ¾Ð¹ ÑÐ¸Ð½ÑÑÐ¾Ð½Ð¸Ð·Ð°ÑÐ¸Ð¸, ÐºÐ¾ÑÐ¾ÑÐ°Ñ Ð¿Ð¾Ð·Ð²Ð¾Ð»Ð¸Ð»Ð° Ð¸Ð¼Ð¸ÑÐ¸ÑÐ¾Ð²Ð°ÑÑ Ð¿Ð¾Ð²ÐµÐ´ÐµÐ½Ð¸Ðµ ÑÐ¸ÑÑÐµÐ¼Ñ Ð¸ Ð¿ÑÐ¾Ð²ÐµÑÐ¸ÑÑ ÑÐµÐ¾ÑÐµÑÐ¸ÑÐµÑÐºÐ¸Ðµ Ð¿ÑÐµÐ´ÑÐºÐ°Ð·Ð°Ð½Ð¸Ñ. Ð ÐµÐ·ÑÐ»ÑÑÐ°ÑÑ Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ñ Ð¼Ð¾Ð³ÑÑ Ð½Ð°Ð¹ÑÐ¸ Ð¿ÑÐ¸Ð¼ÐµÐ½ÐµÐ½Ð¸Ðµ Ð² Ð¾Ð±Ð»Ð°ÑÑÐ¸ ÐºÑÐ¸Ð¿ÑÐ¾Ð³ÑÐ°ÑÐ¸Ð¸, Ð¾ÑÐ¾Ð±ÐµÐ½Ð½Ð¾ Ð² ÑÐ°Ð·ÑÐ°Ð±Ð¾ÑÐºÐµ Ð½Ð¾Ð²ÑÑ Ð¼ÐµÑÐ¾Ð´Ð¾Ð² ÑÐ¸ÑÑÐ¾Ð²Ð°Ð½Ð¸Ñ, Ð¾ÑÐ½Ð¾Ð²Ð°Ð½Ð½ÑÑ Ð½Ð° Ð¿ÑÐ¸Ð½ÑÐ¸Ð¿Ð°Ñ ÑÑÐ¾ÑÐ°ÑÑÐ¸ÑÐµÑÐºÐ¾Ð¹ ÑÐ¸Ð½ÑÑÐ¾Ð½Ð¸Ð·Ð°ÑÐ¸Ð¸. Ð­ÑÐ¾ Ð¼Ð¾Ð¶ÐµÑ Ð²ÐºÐ»ÑÑÐ°ÑÑ ÑÐ¾Ð·Ð´Ð°Ð½Ð¸Ðµ Ð±Ð¾Ð»ÐµÐµ Ð·Ð°ÑÐ¸ÑÐµÐ½Ð½ÑÑ ÑÐ¸ÑÑÐµÐ¼ Ð¿ÐµÑÐµÐ´Ð°ÑÐ¸ Ð¸Ð½ÑÐ¾ÑÐ¼Ð°ÑÐ¸Ð¸, ÑÐ¿Ð¾ÑÐ¾Ð±Ð½ÑÑ Ð¿ÑÐ¾ÑÐ¸Ð²Ð¾ÑÑÐ¾ÑÑÑ ÑÐ°Ð·Ð»Ð¸ÑÐ½ÑÐ¼ Ð²Ð¸Ð´Ð°Ð¼ Ð°ÑÐ°Ðº Ð¸ Ð¾Ð±ÐµÑÐ¿ÐµÑÐ¸Ð²Ð°ÑÑ Ð²ÑÑÐ¾ÐºÐ¸Ð¹ ÑÑÐ¾Ð²ÐµÐ½Ñ Ð±ÐµÐ·Ð¾Ð¿Ð°ÑÐ½Ð¾ÑÑÐ¸ Ð¿ÐµÑÐµÐ´Ð°Ð²Ð°ÐµÐ¼Ð¾Ð¹ Ð¸Ð½ÑÐ¾ÑÐ¼Ð°ÑÐ¸Ð¸. ÐÑÐ¿Ð¾Ð»ÑÐ·Ð¾Ð²Ð°Ð»Ð¸ÑÑ Ð¾ÑÐºÑÑÑÑÐµ Ð¾Ð±ÑÐ°Ð·Ð¾Ð²Ð°ÑÐµÐ»ÑÐ½ÑÐµ ÑÐµÑÑÑÑÑ, Ð¿ÑÐ¾Ð³ÑÐ°Ð¼Ð¼Ñ Ð¿Ð¾Ð¸ÑÐºÐ° Ð¸ Ð°Ð½Ð°Ð»Ð¸Ð·Ð° Ð¸Ð½ÑÐ¾ÑÐ¼Ð°ÑÐ¸Ð¸. ÐÑÐ¸Ð¼ÐµÐ½ÐµÐ½Ð¾ Ð¿ÑÐ¾Ð³ÑÐ°Ð¼Ð¼Ð½Ð¾Ðµ Ð¾Ð±ÐµÑÐ¿ÐµÑÐµÐ½Ð¸Ðµ: MicroCap, Multisim, Mathcad.
description: The objective of the work is to study and achieve synchronization of two stochastic generators. As a result of the research, thorough work was conducted to study the theory of stochastic synchronization, modern scientific works were analyzed, which allowed for a deeper understanding of the processes of stochastic synchronization and the identification of current research directions in this area. Key parameters influencing the systemâs transition from an unstable to a stable state were defined. A computer model of stochastic synchronization was created, which allowed for the simulation of the systemâs behavior and the verification of theoretical predictions. The results of the research can find application in the field of cryptography, especially in the development of new encryption methods based on the principles of stochastic synchronization. This may include creating more reliable encryption systems capable of withstanding various types of attacks and ensuring a high level of security for the transmitted information. Open educational resources, information search and analysis programs were used. The software applied includes MicroCap, Multisim, Mathcad.