TY - JOUR

T1 - Oscillating Solutions of a Second-Order Ordinary Differential Equation with a Three-Position Hysteresis Relay without Entering the Saturation Zones

AU - Yevstafyeva, V.V.

PY - 2023/6/1

Y1 - 2023/6/1

N2 - Abstract: A second-order ordinary differential equation with an essential nonlinearity and anexternal perturbation in the form of a continuous periodic function is studied. Nonlinearity isgiven by a symmetrical relay characteristic with hysteresis, dead zone, and saturation zones. Thetraversal of the characteristic without entering the saturation zones is considered for some finitetime and time commensurate with the period of the perturbation function. Conditions for theexistence of an oscillating solution with a closed phase trajectory and four switching points duringone traversal of the characteristic are obtained. Existence theorems for periodic solutions,including solutions with a symmetric trajectory, are proved. A numerical example is given.

AB - Abstract: A second-order ordinary differential equation with an essential nonlinearity and anexternal perturbation in the form of a continuous periodic function is studied. Nonlinearity isgiven by a symmetrical relay characteristic with hysteresis, dead zone, and saturation zones. Thetraversal of the characteristic without entering the saturation zones is considered for some finitetime and time commensurate with the period of the perturbation function. Conditions for theexistence of an oscillating solution with a closed phase trajectory and four switching points duringone traversal of the characteristic are obtained. Existence theorems for periodic solutions,including solutions with a symmetric trajectory, are proved. A numerical example is given.

UR - https://www.mendeley.com/catalogue/244975fe-5370-3819-94d6-984a15dc2889/

U2 - 10.1134/s0012266123060022

DO - 10.1134/s0012266123060022

M3 - Article

VL - 59

SP - 726

EP - 740

JO - Differential Equations

JF - Differential Equations

SN - 0012-2661

IS - 6

ER -