In 1998, Artés, Kooij and Llibre proved that there exist 44 structurally stable topologically distinct phase portraits modulo limit cycles, and in 2018 Artés, Llibre and Rezende showed the existence of at least 204 (at most 211) structurally unstable ...
Joan Artés, Marcos Mota, Alex Rezende
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Analytic integrability of quadratic–linear polynomial differential systems [PDF]
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
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 Bernoulli quadratic polynomial differential systems
In this article we study a new class of quadratic polynomial differential systems. We classify all global phase portraits in the Poincare disk of Bernoulli quadratic polynomial differential systems in R^2. For more information see https://ejde.math.txstate.edu/Volumes/2020/48/abstr ...
Llibre, Jaume +2 more
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Mean-field linear-quadratic stochastic differential games in an infinite horizon [PDF]
This paper is concerned with two-person mean-field linear-quadratic non-zero sum stochastic differential games in an infinite horizon. Both open-loop and closed-loop Nash equilibria are introduced.
Xunjing Li, Jingtao Shi, J. Yong
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Linear quadratic control of backward stochastic differential equation with partial information [PDF]
In this paper, we study an optimal control problem of linear backward stochastic differential equation (BSDE) with quadratic cost functional under partial information.
Guangchen Wang, Wencan Wang, Zhiguo Yan
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New lower bound for the Hilbert number in piecewise quadratic differential systems [PDF]
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]
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 NONLINEAR DYNAMICAL SYSTEM MOTION UNDER CONSTANTLY ACTING PERTURBATIONS [PDF]
We consider the motion of a mechanical system with several degrees of freedom near zero of the phase space of states under conditions of constantly acting small perturbations. The generalized forces are represented in the dynamic equations by homogeneous
V. G. Melnikov +3 more
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On limit cycles of piecewise differential systems formed by arbitrary linear systems and a class of quadratic systems [PDF]
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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