On limit cycles of piecewise differential systems formed by arbitrary linear systems and a class of quadratic systems [PDF]
Mathematica Bohemica, 2023 We study the continuous and discontinuous planar piecewise differential systems separated by a straight line and formed by an arbitrary linear system and a class of quadratic center.
Aziza Berbache
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Analytic integrability of quadratic–linear polynomial differential systems [PDF]
Ergodic Theory and Dynamical Systems, 2009 AbstractFor the quadratic–linear polynomial differential systems with a finite singular point, we classify the ones which have a global analytic first integral, and provide the explicit expression of their first integrals.
Llibre, Jaume, Valls, Clàudia
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Fundamental response in the vibration control of buildings subject to seismic excitation with ATMD
Selecciones Matemáticas, 2023 The linear quadratic regulator for vibration systems subject to seismic excitations is discussed in his own physical newtonian space as a second-order linear differential system with matrix coefficients.
Fidel Jara Huanca +2 more
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Phase Portraits of Families VII and VIII of the Quadratic Systems
Axioms, 2023 The quadratic polynomial differential systems in a plane are the easiest nonlinear differential systems. They have been studied intensively due to their nonlinearity and the large number of applications.
Laurent Cairó, Jaume Llibre
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New lower bound for the Hilbert number in piecewise quadratic differential systems [PDF]
Journal of Differential Equations, 2018 We study the number of limit cycles bifurcating from a piecewise quadratic system. All the differential systems considered are piecewise in two zones separated by a straight line.
L. C. Da Cruz +2 more
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Adaptive Control of Differentially Private Linear Quadratic Systems [PDF]
2021 IEEE International Symposium on Information Theory (ISIT), 2021 In this paper, we study the problem of regret minimization in reinforcement learning (RL) under differential privacy constraints. This work is motivated by the wide range of RL applications for providing personalized service, where privacy concerns are becoming paramount.
Chowdhury, Sayak Ray +2 more
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Stability of the Planar Quadratic Systems from the Ring-Theoretic Viewpoint
Mathematics, 2022 We show that the classical result on the stability of the origin in a quadratic planar system of ODEs can be formulated using either matrix theory or via its associated real and complex Marcus algebra.
Borut Zalar, Matej Mencinger
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Synthesis of dissipative systems using quadratic differential forms: Part I [PDF]
IEEE Transactions on Automatic Control, 2002 In this second part of this paper, we discuss several important special cases of the problem solved in Part I. These are: disturbance attenuation and passivation, the full information case, the filtering problem, and the case that the to-be-controlled plant is given in input–state–output representation.
Trentelman, H.L., Willems, Jan C.
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On the number of limit cycles for a class of discontinuous quadratic differential systems [PDF]
, 2016 The present paper is devoted to the study of the maximum number of limit cycles bifurcated from the periodic orbits of the quadratic isochronous center $\dot{x}=-y+\frac{16}{3}x^{2}-\frac{4}{3}y^{2},\dot{y}=x+\frac{8}{3}xy$ by the averaging method of ...
Xiuli Cen, Shimin Li, Yulin Zhao
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Linear Hamiltonian behaviors and bilinear differential forms [PDF]
, 2004 We study linear Hamiltonian systems using bilinear and quadratic differential forms. Such a representation-free approach allows us to use the same concepts and techniques to deal with systems isolated from their environment and with systems subject to ...
Rapisarda, Paolo, Trentelman, Harry L.
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