Results 21 to 30 of about 8,908 (255)
Bifurcations of a Homoclinic Orbit to Saddle-Center in Reversible Systems
Abstract and Applied Analysis, 2012 The bifurcations near a primary homoclinic orbit to a saddle-center are investigated in a 4-dimensional reversible system. By establishing a new kind of local moving frame along the primary homoclinic orbit and using the Melnikov functions, the existence
Zhiqin Qiao, Yancong Xu
doaj +1 more source
Homoclinic orbits on compact manifolds
Journal of Mathematical Analysis and Applications, 1991 Let \(M\) be a Riemannian manifold. Consider the differential equation \[ D_ t(x'(t))+\hbox{grad }V(x(t))=0,\leqno(1) \] where \(V\in C^ 2(M,{\mathbb{R}})\), \(x'\) is the derivative of the curve \(x(t)\) on \(M\), and \(D_ t(x')\) is the covariant derivative of \(x'\).
V. Benci, GIANNONI, Fabio
openaire +4 more sources
Bifurcation of Nongeneric Homoclinic Orbit Accompanied by Pitchfork Bifurcation
Abstract and Applied Analysis, 2014 The bifurcation of a nongeneric homoclinic orbit (i.e., the orbit comes from the equilibrium along the unstable manifold instead of the center manifold) connecting a nonhyperbolic equilibrium is investigated, and the nonhyperbolic equilibrium undergoes ...
Fengjie Geng, Song Li
doaj +1 more source
Resonant Homoclinic Flips Bifurcation in Principal Eigendirections
Abstract and Applied Analysis, 2013 A codimension-4 homoclinic bifurcation with one orbit flip and one inclination flip at principal eigenvalue direction resonance is considered. By introducing a local active coordinate system in some small neighborhood of homoclinic orbit, we get the ...
Tiansi Zhang, Xiaoxin Huang, Deming Zhu
doaj +1 more source
Моделирование и анализ информационных систем, 2015 We consider a finite-dimensional model of phase oscillators with inertia in the case of star configuration of coupling. The system of equations is reduced to a nonlinearly coupled system of pendulum equations.
V. N. Belykh +2 more
doaj +1 more source
Homoclinic orbit to a center manifold [PDF]
Calculus of Variations and Partial Differential Equations, 2003 Homoclinic orbit to a center manifold are obtained with a variational method.
openaire +3 more sources
Continuation of Homoclinic Orbits in Matlab [PDF]
, 2005 We have added the functionality for continuing homoclinic orbits to cl_matcont, a user-friendly matlab package for the study of dynamical systems and their bifurcations. It is now possible to continue homoclinic-to-hyperbolic-saddle and homoclinic-to-saddle-node orbits.
Willy Govaerts +3 more
openaire +3 more sources
Constructing the Second Order Poincaré Map Based on the Hopf-Zero Unfolding Method
Abstract and Applied Analysis, 2013 We investigate the Shilnikov sense homoclinicity in a 3D system and consider the dynamical behaviors in vicinity of the principal homoclinic orbit emerging from a third order simplified system.
Gen Ge, Wang Wei
doaj +1 more source
The Twisting Bifurcations of Double Homoclinic Loops with Resonant Eigenvalues
Abstract and Applied Analysis, 2013 The twisting bifurcations of double homoclinic loops with resonant eigenvalues are investigated in four-dimensional systems. The coexistence or noncoexistence of large 1-homoclinic orbit and large 1-periodic orbit near double homoclinic loops is given ...
Xiaodong Li +3 more
doaj +1 more source
Homoclinic orbits for Schrödinger systems
Michigan Mathematical Journal, 2003 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Schechter, Martin, Zou, Wenming
openaire +4 more sources