Results 221 to 230 of about 3,202,278 (248)

Bifurcations of subharmonic solutions in periodic perturbation of a hyperbolic limit cycle

Applied Mathematics and Mechanics (English Edition), 2002
Consider the planar periodically perturbed system \[ \dot x= f(x)+ \varepsilon g(t,x,\varepsilon,\delta),\quad x\in\mathbb{R}^2,\tag{1} \] where \(\varepsilon\in \mathbb{R}\), \(\delta\in \mathbb{R}^n\), \(f\) and \(g\) are \(C^3\)-functions and \(g\) is \(T\)-periodic in \(t\).
Han, Maoan, Gu, Shengshi
exaly   +3 more sources

A Limit Cycle in Plane Hyperbolic Curve Theory

Geometriae Dedicata, 2001
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
exaly   +3 more sources

Limit cycle bifurcations near a generalized homoclinic loop in piecewise smooth systems with a hyperbolic saddle on a switch line

Applied Mathematics and Computation, 2014
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Feng Liang, Shiping Lu, Lijun Wei
exaly   +4 more sources

Stable Hyperbolic Limit Cycles for a Class of Differential Systems

Russian Mathematics, 2021
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Hamizi, S. E., Boukoucha, R.
openaire   +2 more sources

Polynomial differential systems with hyperbolic limit cycles

Journal of Geometry and Physics, 2023
One of the main problems of the qualitative theory of the planar differential equations is the study their limit cycles. In this paper given an algebraic curve of degree n we characterize the planar polynomial differential systems of degree greater or equal than n which admit the ovals of the algebraic curve as hyperbolic limit cycles.
Llibre, Jaume, Valls, Clàudia
openaire   +3 more sources

Multiplicities of limit cycles appearing after perturbations of hyperbolic polycycles

Sbornik: Mathematics, 2023
The problem of the multiplicity of limit cycles appearing after a perturbation of a hyperbolic polycycle with generic set of characteristic numbers is considered. In particular, it is proved that the multiplicity of any limit cycle appearing after a perturbation in a smooth finite-parameter family does not exceed the number of separatrix connections ...
openaire   +1 more source

The number of limit cycles in planar systems and generalized Abel equations with monotonous hyperbolicity

Nonlinear Analysis: Theory, Methods & Applications, 2009
The paper gives a new criterion for the existence of at most two limit cycles for some families of planar vector fields. Its main hypothesis is given in terms of the monotonicity of one stability operator along the solutions of a suitable transversal vector field. This result is also applied to give a uniqueness of limit cycles result as well as to the
A. Guillamon, Sabatini, Marco
openaire   +3 more sources

Study on limit cycles near homoclinic loops and heteroclinic loops with hyperbolic saddles

Journal of Differential Equations
In the paper, the authors study the number of limit cycles near homoclinic and heteroclinic loops of near-Hamiltonian systems with hyperbolic saddles. They provide a new algorithm to calculate the coefficients of its asymptotic expansion of the first-order Melnikov function. An example is given to demonstrate the effectiveness of the new algorithm.
Hongwei Shi, Changjian Liu, Yanqin Xiong
openaire   +2 more sources

Local Robustness of Hyperbolic Limit Cycles

2005
Ulf T. Jönsson, Alexandre Megretski
openaire   +1 more source

The Hyperbolic-Parabolic Chemotaxis System for Vasculogenesis: Global Dynamics and Relaxation Limit Toward a Keller–Segel Model

SIAM Journal on Mathematical Analysis, 2023
Ling-Yun Shou, Timothée Crin-barat
exaly