Results 151 to 160 of about 57,321 (196)

Generative models of cell dynamics: from Neural ODEs to flow matching. [PDF]

Commun Biol
Richter T, Wang W, Palma A, Theis FJ.
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Class of Perturbation Theories of Ordinary Differential Equations

Journal of Mathematical Physics, 1971
A class of perturbation theories of ordinary differential equations is studied in a systematic and rigorous way. This class contains the perturbation theory by Kruskal [J. Math. Phys. 3, 806 (1962)] and its generalization discussed by Coffey [J. Math. Phys.
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Regular Perturbation of Ordinary Differential Equations

2015
In this chapter we find asymptotic solutions of regularly perturbed equations and systems of equations, to which problems in mechanics are reduced. We consider Cauchy problems, problems for periodic solutions and boundary value problems.
S. M. Bauer, S. B. Filippov, A. L. Smirnov, P. E. Tovstik, R. Vaillancourt   +4 more
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Perturbations of Multipliers of Systems of Periodic Ordinary Differential Equations

Advances in Applied Mathematics and Mechanics, 2011
AbstractThe paper deals with periodic systems of ordinary differential equations (ODEs). A new approach to the investigation of variations of multipliers under perturbations is suggested. It enables us to establish explicit conditions for the stability and instability of perturbed systems.
Leonid Berezansky, Michael Gil’, Liora Troib   +2 more
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Lie equations for asymptotic solutions of perturbation problems of ordinary differential equations

Journal of Mathematical Physics, 2009
Lie theory is applied to perturbation problems of ordinary differential equations to construct approximate solutions and invariant manifolds according to the renormalization group approach of Iwasa and Nozaki [“A method to construct asymptotic solutions invariant under the renormalization group,” Prog. Theor. Phys. 116, 605 (2006)].
Chiba, Hayato, Iwasa, Masatomo
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Quasiperiodic Solutions of Functional Singularly Perturbed Linear Ordinary Higher-Order Differential Equations

Journal of Mathematical Sciences, 2020
Consider a system of differential equations \[ \varphi^{(1)}=\omega,\ \ \varepsilon a(\varphi)x^{(n+1)}+x^{(n)}+b_{1}(\varphi)x^{(n-1)}+\ldots+b_{n}(\varphi)x=f(\varphi),\tag{1} \] where \(\varphi \in \mathbb R^{m}\), \(\omega =(\omega_{1},\omega_{2},\ldots,\omega_{m})\) is a frequence basis, \(x\in \mathbb R\), \(f\in \mathcal T^{m}\) and \(\mathcal T^
Er'omenko, V. O., Aliluiko, A. M.
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Non-standard analysis and singular perturbations of ordinary differential equations

Russian Mathematical Surveys, 1984
This is a lively and interesting survey of a lively and interesting area of current research, namely the application of non-standard analysis to singular perturbation problems for ordinary differential equations. In particular, the authors discuss certain singular solutions (called ''ducks'') of nonlinear second-order equations depending on a small ...
Zvonkin, A. K., Shubin, M. A.
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Invariant manifolds of singularly perturbed ordinary differential equations

ZAMP Zeitschrift f�r angewandte Mathematik und Physik, 1985
Consider an autonomous system \[ (1)\quad dx/dt=f(x,y,\epsilon),\quad \epsilon dy/dt=g(x,y,\epsilon), \] where \(f: D\to {\mathbb{R}}^ m\), \(g: D\to {\mathbb{R}}^ n\), \(D=D_ 1\times D_ 2\times (-\epsilon_ 0,\epsilon_ 0)\) is a bounded domain in \({\mathbb{R}}^{m+n+1}\), and \(D_ 1\) is star shaped with \(C^{\nu +1}\) boundary, \(\nu\geq 1\).
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