Results 231 to 240 of about 155,898 (247)

Algebraic limit cycles in polynomial systems of differential equations

Journal of Physics A: Mathematical and Theoretical, 2007
Using elementary tools we construct cubic polynomial systems of differential equations with algebraic limit cycles of degrees 4, 5 and 6. We also construct a cubic polynomial system of differential equations having an algebraic homoclinic loop of degree 3. Moreover, we show that there are polynomial systems of differential equations of arbitrary degree
Jaume Llibre, Yulin Zhao
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Polynomial Vector Fields with Prescribed Algebraic Limit Cycles

Geometriae Dedicata, 2001
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Algebraical Limit Cycles of Polynomial Vector Fields on the Plane

Differential Equations, 2001
The existence of limit cycles of algebraic differential equations has been studied and their number has been estimated in numerous papers. In recent decades, much attention was paid to polynomial vector fields with invariant algebraic curves. The statement of the problem goes back to Darboux, Poincaré, and Erugin.
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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
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On the Number of Limit Cycles Bifurcating from the Bogdanov-Takens System with an Algebraic Switching Curve

International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
In this paper, we consider the bifurcation of limit cycles from the Bogdanov–Takens system with an algebraic switching curve under perturbations of piecewise smooth polynomials of degree [Formula: see text].
Jiaxin Wang, Liankun Zou
semanticscholar   +1 more source

Cubic planar differential systems with non-algebraic limit cycles enclosing a focus

International Journal of Dynamical Systems and Differential Equations, 2023
A. Bendjeddou, R. Cheurfa, Meryem Belattar   +2 more
semanticscholar   +1 more source

Control Barrier Function-Based Safety Filters: Characterization of Undesired Equilibria, Unbounded Trajectories, and Limit Cycles

arXiv.org
This paper focuses on safety filters designed based on Control Barrier Functions (CBFs): these are modifications of a nominal stabilizing controller typically utilized in safety-critical control applications to render a given subset of states forward ...
Pol Mestres, Yiting Chen, E. Dall’Anese, Jorge Cort'es   +3 more
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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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Coexistence of limit cycles and invariant algebraic curves for a Kukles system

Nonlinear Analysis: Theory, Methods & Applications, 2004
This paper deals with the so-called Kukles systems, \[ \dot x=-y,\qquad \dot y=f(x,y), \] \(f\) being a polynomial of degree \(d.\) Firstly, the authors study the number and distribution of invariant straight lines that this type of systems can have.
Chavarriga, J., Sáez, E., Szántó, I., Grau, M.   +3 more
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Semi Stable Limit Cycles in Dynamical Systems Via Algebraic Topological Approach

International Journal of Mathematical and Computer Sciences
Most phenomena in the natural and engineering fields are represented through dynamical systems composed of differential equations that incorporate parameters.
Ibrahim Jawarneh, Nesreen Alsharman
semanticscholar   +1 more source