On the Robust Stability of Stationary Solutions to a Class of Mathieu-Type Equations

We consider a class of nonlinear ordinary differential equations of the second order with parameters. We establish conditions for perturbations of the coefficients of the equations under which the zero solution is asymptotically stable. Estimates for attraction sets of the zero solution and estimate...

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Bibliographic Details
Published in:Lobachevskii journal of mathematics 2023-03, Vol.44 (3), p.883-895
Main Authors: Demidenko, G. V., Myagkikh, K. S.
Format: Article
Language:English
Subjects:
Algebra
Analysis
Estimates
Geometry
Mathematical analysis
Mathematical Logic and Foundations
Mathematics
Mathematics and Statistics
Nonlinear differential equations
Perturbation
Probability Theory and Stochastic Processes
Robustness
Stability
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Summary:We consider a class of nonlinear ordinary differential equations of the second order with parameters. We establish conditions for perturbations of the coefficients of the equations under which the zero solution is asymptotically stable. Estimates for attraction sets of the zero solution and estimates of the stabilization rate of solutions at infinity are obtained. Using these results, theorems on the robust stability of stationary solutions are proven.
ISSN:1995-0802
1818-9962
DOI:10.1134/S1995080223030113