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On Quasiperiodic Perturbations of Ordinary Differential Equations [PDF]
, 1991 In this work we study several topics concerning quasi-periodic time-dependent perturbations of ordinary differential equations. This kind of equations appear as models in many applied problems of Celestial Mechanics, and we have used, as an illustration, the study of the behaviour near the equilateral libration points of the real Earth-Moon system. Let
Jorba i Monte, Àngel
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Averaging for ordinary differential equations perturbed by a small parameter [PDF]
Mathematica Bohemica, 2016 In averaging theory, it is well known that the solutions to a nonautonomous ordinary differential equation of the form \[ x'(t)=f(t/\varepsilon,x(t)) \] are well approximated by solutions of the autonomous equation \[ y'(t)=f^0(y(t)), \] where the right-hand side \(f^0\) is given by \[ f^0(x)=\lim_{T\to\infty}\frac{1}{T}\int_0^T f(\tau,x)\,\mathrm{d ...
Mustapha Lakrib +2 more
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Transversal homoclinics in nonlinear systems of ordinary differential equations
Electronic Journal of Qualitative Theory of Differential Equations, 2000 Bifurcation of transversal homoclinics is studied for a pair of ordinary differential equations with periodic perturbations when the first unperturbed equation has a manifold of homoclinic solutions and the second unperturbed equation is vanishing.
Michal Fečkan
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Least Square Homotopy Perturbation Method for Ordinary Differential Equations [PDF]
Journal of Mathematics, 2021 In this study, a new modification of the homotopy perturbation method (HPM) is introduced for various order boundary value problems (BVPs). In this modification, HPM is hybrid with least square optimizer and named as the least square homotopy perturbation method (LSHPM). The proposed scheme is tested against various linear and nonlinear BVPs (second to
Mubashir Qayyum, Imbsat Oscar
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Extended Differential Aggregations in Process Algebra for Performance and Biology [PDF]
Electronic Proceedings in Theoretical Computer Science, 2014 We study aggregations for ordinary differential equations induced by fluid semantics for Markovian process algebra which can capture the dynamics of performance models and chemical reaction networks. Whilst previous work has required perfect symmetry for
Max Tschaikowski, Mirco Tribastone
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Universe, 2022 We investigate electromagnetic, gravitational, and plasma-related perturbations to the first order on homogeneous and hypersurface orthogonal locally rotationally symmetric (LRS) class II spacetimes.
Philip Semrén
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Asymptotic behavior of solutions of a system of nonlinear differential equations with small parameter [PDF]
E3S Web of Conferences, 2023 The present paper addresses a qualitative pattern of the behavior of solutions of a system of ordinary differential equations when small parameter tends to zero at a finite amount of time where slow variable passes through a certain point that ...
Petelina Vera
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Strict and non-strict inequalities for implicit first order causal differential equations
Electronic Journal of Qualitative Theory of Differential Equations, 2011 In this paper, some fundamental differential inequalities for the implicit perturbations of nonlinear first order ordinary causal differential equations have been established.
Bapurao Dhage
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Parametric Perturbation Problems in Ordinary Differential Equations [PDF]
Transactions of the American Mathematical Society, 1976 The asymptotic behavior of solutions of a nonlinear differential equation that arises through a nonlinear parametric perturbation of a linear system of differential equations is discussed. Fundamental hypotheses include the admissibility of a pair of Banach spaces for the linear system.
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Sparse inference and active learning of stochastic differential equations from data
Scientific Reports, 2022 Automatic machine learning of empirical models from experimental data has recently become possible as a result of increased availability of computational power and dedicated algorithms. Despite the successes of non-parametric inference and neural-network-
Yunfei Huang +3 more
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