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

A second-order ordinary differential equation with an essential nonlinearity and an external perturbation in the form of a continuous periodic function is studied. Nonlinearity is given by a symmetrical relay characteristic with hysteresis, dead zone, and saturation zones. The traversal of the chara...

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Bibliographic Details
Published in:Differential equations 2023-06, Vol.59 (6), p.726-740
Main Author: Yevstafyeva, V. V.
Format: Article
Language:English
Subjects:
Continuity (mathematics)
Difference and Functional Equations
Differential equations
Existence theorems
Hysteresis
Mathematics
Mathematics and Statistics
Nonlinearity
Ordinary Differential Equations
Partial Differential Equations
Periodic functions
Perturbation
Relay
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Summary:A second-order ordinary differential equation with an essential nonlinearity and an external perturbation in the form of a continuous periodic function is studied. Nonlinearity is given by a symmetrical relay characteristic with hysteresis, dead zone, and saturation zones. The traversal of the characteristic without entering the saturation zones is considered for some finite time and time commensurate with the period of the perturbation function. Conditions for the existence of an oscillating solution with a closed phase trajectory and four switching points during one traversal of the characteristic are obtained. Existence theorems for periodic solutions, including solutions with a symmetric trajectory, are proved. A numerical example is given.
ISSN:0012-2661
1608-3083
DOI:10.1134/S0012266123060022