TY - JOUR

T1 - On One Type of Oscillating Solutions of a Second-Order Ordinary Differential Equation with a Three-Position Hysteresis Relay and a Perturbation

AU - Yevstafyeva, V.V.

AU - Kamachkin, A.M.

AU - Potapov, D.K.

N1 - Yevstafyeva, V.V., Kamachkin, A.M. & Potapov, D.K. On One Type of Oscillating Solutions of a Second-Order Ordinary Differential Equation with a Three-Position Hysteresis Relay and a Perturbation. Diff Equat 59, 153–167 (2023). https://doi.org/10.1134/S0012266123020015

PY - 2023

Y1 - 2023

N2 - A second-order ordinary differential equation with a three-position hysteresis relay characteristic and a periodic perturbation function is considered. The existence theorem is proved for an oscillatory solution with a complete traversal of the characteristic with a possible exit into its saturation zones in some finite time and with a closed phase trajectory of an arbitrary shape. Sufficient conditions for the existence of periodic solutions with arbitrary and symmetric phase trajectories are established, as well as conditions for the nonexistence of a periodic solution with a symmetric phase trajectory. Numerical examples are given.

AB - A second-order ordinary differential equation with a three-position hysteresis relay characteristic and a periodic perturbation function is considered. The existence theorem is proved for an oscillatory solution with a complete traversal of the characteristic with a possible exit into its saturation zones in some finite time and with a closed phase trajectory of an arbitrary shape. Sufficient conditions for the existence of periodic solutions with arbitrary and symmetric phase trajectories are established, as well as conditions for the nonexistence of a periodic solution with a symmetric phase trajectory. Numerical examples are given.

M3 - Article

VL - 59

SP - 153

EP - 167

JO - Differential Equations

JF - Differential Equations

SN - 0012-2661

IS - 2

ER -