scholarly journals On the Response of Autonomous Sweeping Processes to Periodic Perturbations

2015 ◽  
Vol 24 (4) ◽  
pp. 551-563 ◽  
Author(s):  
Mikhail Kamenskii ◽  
Oleg Makarenkov
Keyword(s):  
Periodic Perturbations ◽  
Sweeping Processes

scholarly journals On Periodic Perturbations of Asymmetric Duffing–Van-der-Pol Equation

2014 ◽  
Vol 24 (05) ◽  
pp. 1450061 ◽  
Author(s):  
Albert D. Morozov ◽  
Olga S. Kostromina
Keyword(s):  
Saddle Point ◽  
Limit Cycles ◽  
Small Neighborhood ◽  
Integrable Equation ◽  
Van Der Pol Equation ◽  
Van Der Pol ◽  
Periodic Perturbations ◽  
Autonomous Equation ◽  
Nonautonomous Equation ◽  
Time Periodic

Time-periodic perturbations of an asymmetric Duffing–Van-der-Pol equation close to an integrable equation with a homoclinic "figure-eight" of a saddle are considered. The behavior of solutions outside the neighborhood of "figure-eight" is studied analytically. The problem of limit cycles for an autonomous equation is solved and resonance zones for a nonautonomous equation are analyzed. The behavior of the separatrices of a fixed saddle point of the Poincaré map in the small neighborhood of the unperturbed "figure-eight" is ascertained. The results obtained are illustrated by numerical computations.

Optimal Control Involving Sweeping Processes

2018 ◽  
Vol 27 (2) ◽  
pp. 523-548 ◽  
Author(s):  
M. d. R. de Pinho ◽  
M. M. A. Ferreira ◽  
G. V. Smirnov
Keyword(s):  
Optimal Control ◽  
Sweeping Processes

scholarly journals Stabilization of periodic sweeping processes and asymptotic average velocity for soft locomotors with dry friction

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Giovanni Colombo ◽  
Paolo Gidoni ◽  
Emilio Vilches
Keyword(s):  
Periodic Solution ◽  
Asymptotic Stability ◽  
Periodic Solutions ◽  
Finite Time ◽  
Dry Friction ◽  
Average Velocity ◽  
Well Posedness ◽  
Asymptotic Velocity ◽  
Sweeping Processes

<p style='text-indent:20px;'>We study the asymptotic stability of periodic solutions for sweeping processes defined by a polyhedron with translationally moving faces. Previous results are improved by obtaining a stronger <inline-formula><tex-math id="M1">\begin{document}$ W^{1,2} $\end{document}</tex-math></inline-formula> convergence. Then we present an application to a model of crawling locomotion. Our stronger convergence allows us to prove the stabilization of the system to a running-periodic (or derivo-periodic, or relative-periodic) solution and the well-posedness of an average asymptotic velocity depending only on the gait adopted by the crawler. Finally, we discuss some examples of finite-time versus asymptotic-only convergence.</p>

scholarly journals Multiple solutions for periodic perturbations of a delayed autonomous system near an equilibrium

2019 ◽  
Vol 18 (4) ◽  
pp. 1695-1709
Author(s):  
Pablo Amster ◽  
◽  
Mariel Paula Kuna ◽  
Gonzalo Robledo ◽  
Keyword(s):  
Multiple Solutions ◽  
Autonomous System ◽  
Periodic Perturbations
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