Results 251 to 260 of about 17,774,507 (277)

Global stabilization of planar homogeneous polynomial systems

Nonlinear Analysis: Theory, Methods & Applications, 1998
The 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, Jghima, Hamid, Outbib, Rachid   +2 more
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On the number of critical periods for planar polynomial systems

Nonlinear Analysis: Theory, Methods & Applications, 2008
The 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, Gasull, Armengol, da Silva, Paulo R.   +2 more
openaire   +3 more sources

On Lie's symmetries for planar polynomial differential systems

Nonlinearity, 2001
A 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., García, I. A., Giné, J.   +2 more
openaire   +2 more sources

Limit cycles of a class of planar polynomial differential systems

Mathematical Methods in the Applied Sciences, 2021
In this paper, we study the maximum number of limit cycles that can bifurcate from a linear center, when perturbed inside a class of planar polynomial differential systems of arbitrary degree n. Using averaging theory of first and second order, we estimate the maximum number of limit cycles that this class of systems can exhibit.
Nassima Debz, Amel Boulfoul, Abdelhak Berkane   +2 more
openaire   +1 more source

Computation of Lyapunov values for two planar polynomial differential systems

Applied Mathematics and Computation, 2008
The 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
openaire   +2 more sources

A STUDY ON THE EXISTENCE OF LIMIT CYCLES OF A PLANAR SYSTEM WITH THIRD-DEGREE POLYNOMIALS

International Journal of Bifurcation and Chaos, 2004
The 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
openaire   +3 more sources

Planar Polynomial Systems with Non-Algebraic Limit Cycles

AIP Conference Proceedings, 2009
In 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, George Maroulis, Theodore E. Simos   +2 more
openaire   +1 more source

NON-ALGEBRAIC LIMIT CYCLES FOR PARAMETRIZED PLANAR POLYNOMIAL SYSTEMS

International Journal of Mathematics, 2007
In 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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Global Dynamics of a Planar Polynomial Mechanical System

Journal of Advances in Civil and Mechanical Engineering
In 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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On the realization of limit cycles in planar polynomial systems

2017
Peer ...
openaire   +1 more source