Results 261 to 270 of about 10,383,907 (288)
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Bifurcation of Limit Cycles for a Perturbed Piecewise Quadratic Differential Systems
Acta Mathematica Sinica, English Series, 2022zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ji, Gui Lin +2 more
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On the geometric structure of the class of planar quadratic differential systems
Qualitative Theory of Dynamical Systems, 2002This is a well-written article which uses a geometric approach in the study of real quadratic planar differential systems, i.e., systems of two first-order quadratic ordinary differential equations with real coefficients that have a vector field. The interest is in the global theory.
Roussarie, Robert, Schlomiuk, Dana
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On Differential Systems with Quadratic Impulses and Their Applications to Lagrangian Mechanics
SIAM Journal on Control and Optimization, 1993Summary: This paper is concerned with the basic dynamics and a class of variational problems for control systems of the form (E) \(\dot x=f(t,x,u)+ g(t,x,u)\dot u+ h(t,x,u)\dot u^ 2\). These systems have impulsive character, due to the presence of the time derivative \(\dot u\) of the control.
Alberto Bressan, RAMPAZZO, FRANCO
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SOME BIFURCATION DIAGRAMS FOR LIMIT CYCLES OF QUADRATIC DIFFERENTIAL SYSTEMS
International Journal of Bifurcation and Chaos, 2001Concrete numerical examples of quadratic differential systems having three limit cycles surrounding one singular point are shown. In case another finite singular point also exists, a (3, 1) distribution of limit cycles is also obtained. This is the highest number of limit cycles known to occur in a quadratic differential system so far.
H. S. Y. Chan +2 more
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Blow-up solutions of quadratic differential systems
Journal of Mathematical Sciences, 2008zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Baris, J., Baris, P., Ruchlewicz, B.
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A Differential Equation System for Equality-Constrained Quadratic Programming
2009 Fifth International Conference on Natural Computation, 2009This paper presents a differential system which involves the first order derivatives of problem functions for solving equality-constrained quadratic problem. Local minimizers to the optimization problems are proved to be asymptotically stable equilibrium points of the differential system.
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The Geometry of Quadratic Differential Systems with a Weak Focus of Third Order
Canadian Journal of Mathematics, 2004AbstractIn this article we determine the global geometry of the planar quadratic differential systems with a weak focus of third order. This class plays a significant role in the context of Hilbert's 16-th problem. Indeed, all examples of quadratic differential systems with at least four limit cycles, were obtained by perturbing a system in this family.
Llibre, Jaume, Schlomiuk, Dana
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On the geometry in the neighborhood of infinity of quadratic differential systems with a weak focus
Qualitative Theory of Dynamical Systems, 2001The authors study the phase portraits near infinity of quadratic vector fields which have a finite critical point that is a weak focus. The global phase portrait of these quadratic vector fields in the whole Poincaré sphere, but just when the weak focus has order three, has been already studied by \textit{J. C. Artés} and \textit{J.
Schlomiuk, Dana, Pal, Janos
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A Resolution Method for Riccati Differential Systems Coupled in Their Quadratic Terms
SIAM Journal on Mathematical Analysis, 1988The paper deals with a system of two Riccati differential equations coupled in their quadratic terms. Systems of this kind arise in singular and hybrid systems control, reduced order compensator design, and nonzero sum differential games. An algebraic transformation is performed, leading to a more convenient form of the system; then the successive ...
Jodar, L., Abou-Kandil, H.
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On Stability Cones for Quadratic Systems of Differential Equations
Journal of Dynamical and Control Systems, 2005New sufficient conditions of conditional stability of the trivial solution of a system of quadratic ordinary differential equations are obtained. For the homogeneous system the domain of unlocal stability is also found (it is a cone). This domain is then used for design of piecewise linear (discontinuous) control laws on output for a bilinear control ...
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