The Kalman-Yakubovich-Popov lemma in a behavioural framework [PDF]
, 1997 The classical Kalman-Yakubovich-Popov Lemma provides a link between dissipativity of a system in state-space form and the solution to a linear matrix inequality.
Geest, Robert van der, Trentelman, Harry
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Reduction of Algebraic Parametric Systems by Rectification of their Affine Expanded Lie Symmetries [PDF]
, 2006 Lie group theory states that knowledge of a $m$-parameters solvable group of symmetries of a system of ordinary differential equations allows to reduce by $m$ the number of equations. We apply this principle by finding some \emph{affine derivations} that
G. Bluman +5 more
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Simple Equations Method and Non-Linear Differential Equations with Non-Polynomial Non-Linearity
Entropy, 2021 We discuss the application of the Simple Equations Method (SEsM) for obtaining exact solutions of non-linear differential equations to several cases of equations containing non-polynomial non-linearity. The main idea of the study is to use an appropriate
Nikolay K. Vitanov +1 more
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Computation, 2021 We discuss the Simple Equations Method (SEsM) for obtaining exact solutions of a class of nonlinear differential equations containing polynomial nonlinearities.
Nikolay K. Vitanov +2 more
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Limit cycles for generalized Kukles polynomial differential systems [PDF]
Nonlinear Analysis: Theory, Methods & Applications, 2011 We study the limit cycles of generalized Kukles polynomial differential systems using averaging theory of first and second order.
Llibre, Jaume, Mereu, Ana Cristina
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Integrability of Planar Polynomial Differential Systems through Linear Differential Equations
Rocky Mountain Journal of Mathematics, 2006 24 pages, no ...
Giacomini, H., Giné, J., Grau, M.
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Constructing the Lyapunov Function through Solving Positive Dimensional Polynomial System
Journal of Applied Mathematics, 2013 We propose an approach for constructing Lyapunov function in quadratic form of a differential system. First, positive polynomial system is obtained via the local property of the Lyapunov function as well as its derivative.
Zhenyi Ji +3 more
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Integrability of Stochastic Birth-Death processes via Differential Galois Theory [PDF]
, 2019 Stochastic birth-death processes are described as continuous-time Markov processes in models of population dynamics. A system of infinite, coupled ordinary differential equations (the so-called master equation) describes the time-dependence of the ...
Acosta-Humanez, Primitivo B. +2 more
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A new multistage technique for approximate analytical solution of nonlinear differential equations
Heliyon, 2020 The article introduces a new multistage technique for solving a polynomial system of nonlinear initial and boundary value problems of differential equations.
Saheed Ojo Akindeinde
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Polynomial Systems from Certain Differential Equations
Journal of Symbolic Computation, 1999 For the well-known Kukles system: \[ \dot x= y,\quad\dot y= -x+ a_{20}x^2+ a_{11}xy+ a_{02}y^2+ a_{30}x^3+ a_{21}x^2y+ a_{12}xy^2+ a_{03}y^3,\tag{1} \] \textit{I. S. Kukles} [Trudy tret'ego vsesojuzn. mat. S''ezda, Moskva, Ijuń-Ijul' 1956, 3, 81-91 (1958; Zbl 0089.06302)], \textit{L. A. Cherkas} [Differ. Equations 14, 1133-1138 (1978; Zbl 0423.34042)],
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