Results 81 to 90 of about 1,285,867 (186)

Higher order branching of periodic orbits from polynomial isochrones

Electronic Journal of Differential Equations, 1999
We discuss the higher order local bifurcations of limit cycles from polynomial isochrones (linearizable centers) when the linearizing transformation is explicitly known and yields a polynomial perturbation one-form.
B. Toni
doaj  

Branching of periodic orbits from Kukles isochrones

Electronic Journal of Differential Equations, 1998
We study local bifurcations of limit cycles from isochronous (or linearizable) centers. The isochronicity has been determined using the method of Darboux linearization, which provides a birational linearization for the examples that we analyze.
B. Toni
doaj  

Attractive holomorphic limit cycles

Rendiconti di Matematica e delle Sue Applicazioni, 1995
This work deals with a problem which is, in a way, an opposite of the Reeb-Haefliger conjecture. The manifold \(X\) need not to be compact here, but it is assumed to be connected and to have a countable base. Holomorphic foliations on connected, complex manifolds are studied just like dynamical systems (thus limit sets, limit cycles, attractors etc ...
openaire   +2 more sources

Centres and limit cycles for an extended Kukles system

Electronic Journal of Differential Equations, 2007
We present conditions for the origin to be a centre for a class of cubic systems. Some of the centre conditions are determined by finding complicated invariant functions. We also investigate the coexistence of fine foci and the simultaneous bifurcation
Jane M. Pearson, Noel G. Lloyd, Joe M. Hill   +2 more
doaj  

The Solution of the Extended 16th Hilbert Problem for Some Classes of Piecewise Differential Systems

Mathematics
The limit cycles have a main role in understanding the dynamics of planar differential systems, but their study is generally challenging. In the last few years, there has been a growing interest in researching the limit cycles of certain classes of ...
Louiza Baymout, Rebiha Benterki, Jaume Llibre   +2 more
doaj   +1 more source

Limit cycles for discontinuous generalized Lienard polynomial differential equations

Electronic Journal of Differential Equations, 2013
We divide $\mathbb{R}^2$ into sectors $S_1,\dots ,S_l$, with $l>1$ even, and define a discontinuous differential system such that in each sector, we have a smooth generalized Lienard polynomial differential equation $\ddot{x}+f_i(x)\dot{x} +g_i(x)=0$,
Jaume Llibre, Ana Cristina Mereu
doaj  

Limit cycles in models of circular gene networks regulated by negative feedback loops. [PDF]

BMC Bioinformatics, 2020
Likhoshvai VA, Golubyatnikov VP, Khlebodarova TM.   +2 more
europepmc   +1 more source

Existence and stability of limit cycles in the model of a planar passive biped walking down a slope. [PDF]

Proc Math Phys Eng Sci, 2020
Makarenkov O.
europepmc   +1 more source

Multiple Limit Cycle Bifurcation Surfaces and Global Families of Multiple Limit Cycles

Journal of Differential Equations, 1995
``Sufficient conditions are given for the local existence of multiplicity-\(m\) limit cycle bifurcation surfaces, \(C_m\), of planar analytic systems depending on \(n\) parameters with \(n \geq m \geq 2\). In the generic case, the surfaces \(C_2\), \(C_3\), and \(C_4\) are the familiar saddle-node, cusp, and swallow-tail bifurcation surfaces ...
openaire   +2 more sources

Generalized Van der Pol equation and Hilbert's 16th problem

Electronic Journal of Differential Equations, 2014
In this article, we study the bifurcation of limit cycles from the harmonic oscillator $\dot{x}=y$, $\dot{y}=-x$ in the system $$ \dot{x}=y,\quad \dot{y}=-x+\varepsilon f(y)\big(1-x^2\big), $$ where $\varepsilon$ is a small positive parameter ...
Xenakis Ioakim
doaj