Results 21 to 30 of about 10,383,907 (288)
Conserved- and zero-mean quadratic quantities in oscillatory systems
, 2005 We study quadratic functionals of the variables of a linear oscillatory system and their derivatives. We show that such functionals are partitioned in conserved quantities and in trivially- and intrinsic zero-mean quantities.
Willems, Jan C., Rapisarda, Paolo
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Symmetry of Quadratic Homogeneous Differential Systems
, 2008 10 ...
Nadjafikhah, Mehdi +1 more
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Demonstratio Mathematica, 2023 The classification of the phase portraits is one of the classical and difficult problems in the qualitative theory of polynomial differential systems in R2{{\mathbb{R}}}^{2}, particularly for quadratic systems.
Benterki Rebiha, Belfar Ahlam
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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, P. +7 more
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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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On positive-realness and stability of switched linear differential systems
, 2013 We present some results regarding the stability of switched linear differential systems (SLDS) in the behavioral framework. Positive-realness is studied as a sufficient condition for stability and some implications derived from the use of positive-real ...
Paolo Rapisarda +3 more
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Explicitly solvable systems of two autonomous first-order Ordinary Differential Equations with homogeneous quadratic right-hand sides [PDF]
Open Communications in Nonlinear Mathematical Physics, 2021 After tersely reviewing the various meanings that can be given to the property of a system of nonlinear ODEs to be solvable, we identify a special case of the system of two first-order ODEs with homogeneous quadratic right-hand sides which is explicitly ...
Francesco Calogero, Farrin Payandeh
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Rigid Polynomial Differential Systems with Homogeneous Nonlinearities
MathematicsPlanar differential systems whose angular velocity is constant are called rigid or uniform differential systems. The first rigid system goes back to the pendulum clock of Christiaan Huygens in 1656; since then, the interest for the rigid systems has been
Jaume Llibre
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Quadratic systems with two invariant real straight lines and an invariant parabola
Electronic Journal of Qualitative Theory of Differential EquationsAfter the linear differential systems in the plane the easiest ones are the quadratic polynomial differential systems. Due to their nonlinearity and also to their many applications these systems have been studied by many authors. Let QS denote the set of
Jaume Llibre, Huaxin Ou
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Higher-order linear lossless systems
, 2008 We define a lossless autonomous system as one having a quadratic differential form associated with it called the total energy, which obeys the property of positivity and which is conserved.
Rao, Shodhan, Rapisarda, Paolo
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