Results 221 to 230 of about 6,408 (248)
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On Lie's symmetries for planar polynomial differential systems
Nonlinearity, 2001A function \(V(x,y)\) is called an inverse integrating factor for the planar system \[ \dot x=P(x,y), \quad\dot y=Q(x,y), \] if \[ P{\partial V \over \partial x}+Q{\partial V\over\partial y}=(P_x+Q_y) \cdot V \] holds. The authors investigate polynomial planar systems and give results concerning connections between the existence of polynomial inverse ...
Chavarriga, J. +2 more
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Global stabilization of planar homogeneous polynomial systems
Nonlinear Analysis: Theory, Methods & Applications, 1998The authors present a necessary and sufficient condition for global stabilization of a planar homogeneous polynomial system by use of continuous, but not necessarily homogeneous, state feedback.
Iggidr, Abderrahman +2 more
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On the number of critical periods for planar polynomial systems
Nonlinear Analysis: Theory, Methods & Applications, 2008The authors consider planar polynomial systems and get some lower bounds of critical periods for families of centers which are perturbations of the linear one. They present a method which lets them prove that there are polynomial centers of degree \(l\) with at least \(2[(l-2)/2]\) critical periods, moreover they study concrete families of potential ...
Cima, Anna +2 more
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Some properties of planar polynomial systems of even degree
Annali Di Matematica Pura Ed Applicata, 1992Let \(\dot x=P(x,y)\), \(\dot y=Q(x,y)\) be a planar polynomial system and let \(n=\max(\deg(P),\deg(Q))\). The authors show that, if \(n\) is even, then this system must have at least one unbounded trajectory. This implies that the system can have no global centers, that is, singular points \(p\in\mathbb{R}^ 2\) such that \(\mathbb{R}^ 2-\{p\}\) is ...
Massimo Villarini
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Computation of Lyapunov values for two planar polynomial differential systems
Applied Mathematics and Computation, 2008The computation of the focal values of an equilibrium point has important significance in the investigation of stability of a dynamical system. In this paper, the authors generalize the complex formulae for the computation of Lyapunov values of an equilibrium point of a planar polynomial system with a pair of purely imaginary eigenvalues.
J. Li, Y. Chen, W. Zhang, Y. Tian
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A STUDY ON THE EXISTENCE OF LIMIT CYCLES OF A PLANAR SYSTEM WITH THIRD-DEGREE POLYNOMIALS
International Journal of Bifurcation and Chaos, 2004The focus of the paper is mainly on the existence of limit cycles of a planar system with third-degree polynomial functions. A previously developed perturbation technique for computing normal forms of differential equations is employed to calculate the focus values of the system near equilibrium points. Detailed studies have been provided for a number
Maoan Han, Yiping Lin, Pei Yu
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Planar Polynomial Systems with Non-Algebraic Limit Cycles
AIP Conference Proceedings, 2009In this paper, we study the existence of the non‐algebraic limit cycles of the systems dxdt = Pn(x,y)+xRm(x,y) dydt = Qn(x,y)+yRm(x,y) where Pn(x,y), Qn(x,y) and Rm(x,y) are homogeneous polynomials of degrees n, n and m respectively with ...
Khalil I. T. Al-Dosary +2 more
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NON-ALGEBRAIC LIMIT CYCLES FOR PARAMETRIZED PLANAR POLYNOMIAL SYSTEMS
International Journal of Mathematics, 2007In this paper, we determine conditions for planar systems of the form [Formula: see text] where a, b and c are real constants, to possess non-algebraic limit cycles. This is done as an application of a former theorem gives description of the existence of the non-algebraic limit cycles of the family of systems: [Formula: see text] where Pn(x,y), Qn(x,y)
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On the period function of centers in planar polynomial hamiltonian systems of degree four
Qualitative Theory of Dynamical Systems, 2002Consider the plane Hamiltonian system \[ dx/dt=- \partial H(x,y)/\partial y,\quad dy/dt=\partial H(x,y)/\partial x \] where \(H(x,y)\) is a real polynomial in \(x,y\). Many authors studied problems like isochronicity, monotonicity or bifurcation of critical period of a nondegerate center of the system (a center is said to be nondegerate if the ...
Jarque, Xavier, Villadelprat, Jordi
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Global Dynamics of a Planar Polynomial Mechanical System
Journal of Advances in Civil and Mechanical EngineeringIn this paper, using a bifurcational geometric approach, we study the global dynamics and solve the problem on the maximum number and distribution of limit cycles in a planar polynomial Euler–Lagrange–Lienard type mechanical system.
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