Results 1 to 10 of about 9,325 (173)
Homoclinic Orbits In Slowly Varying Oscillators [PDF]
SIAM Journal on Mathematical Analysis, 1987 We obtain existence and bifurcation theorems for homoclinic orbits in three-dimensional flows that are perturbations of families of planar Hamiltonian systems. The perturbations may or may not depend explicitly on time.
Holmes, Philip, Wiggins, Stephen
core +3 more sources
Scarring by homoclinic and heteroclinic orbits [PDF]
Physical Review Letters, 2006 In addition to the well known scarring effect of periodic orbits, we show here that homoclinic and heteroclinic orbits, which are cornerstones in the theory of classical chaos, also scar eigenfunctions of classically chaotic systems when associated ...
A. M. Ozorio de Almeida +7 more
core +3 more sources
Bifurcation of big periodic orbits through symmetric homoclinics, application to Duffing equation [PDF]
Journal of Mahani Mathematical Research, 2023 We consider a planar symmetric vector field that undergoes a homoclinic bifurcation. In order to study the existence of exterior periodic solutions of the vector field around broken symmetric homoclinic orbits, we investigate the existence of fixed ...
Liela Soleimani, Omid RabieiMotlagh
doaj +1 more source
Mathematics, 2021 The existence of homoclinic orbits or heteroclinic cycle plays a crucial role in chaos research. This paper investigates the existence of the homoclinic orbits to a saddle-focus equilibrium point in several classes of three-dimensional piecewise affine ...
Yanli Chen, Lei Wang, Xiaosong Yang
doaj +1 more source
Dynamics of a plant-herbivore model with a chemically-mediated numerical response
Mathematics in Applied Sciences and Engineering, 2021 A system of two ordinary differential equations is proposed to model chemically-mediated interactions between plants and herbivores by incorporating a toxin-modified numerical response.
Lin Wang, James Watmough, Fang Yu
doaj +1 more source
Homoclinic orbits to invariant tori near a homoclinic orbit to center–center–saddle equilibrium [PDF]
Physica D: Nonlinear Phenomena, 2005 We consider a perturbation of an integrable Hamiltonian vector field with three degrees of freedom with a center–center–saddle equilibrium having a homoclinic orbit or loop. With the help of a Poincaré map (chosen based on the unperturbed homoclinic loop), we study the homoclinic intersections between the stable and unstable manifolds associated to ...
Koltsova, Oksana +3 more
openaire +2 more sources
Heteroclinic Connections between Periodic Orbits in Planar Restricted Circular Three Body Problem - Part II [PDF]
, 2004 We present a method for proving the existence of symmetric periodic, heteroclinic or homoclinic orbits in dynamical systems with the reversing symmetry.
Wilczak, D., Zgliczynski, P.
core +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 +3 more sources
Homoclinic Bifurcations in Planar Piecewise-Linear Systems
Discrete Dynamics in Nature and Society, 2013 The problem of homoclinic bifurcations in planar continuous piecewise-linear systems with two zones is studied. This is accomplished by investigating the existence of homoclinic orbits in the systems.
Bin Xu, Fenghong Yang, Yun Tang, Mu Lin
doaj +1 more source
Complex dynamics of a sub-quadratic Lorenz-like system
Open Physics, 2023 Motivated by the generic dynamical property of most quadratic Lorenz-type systems that the unstable manifolds of the origin tending to the stable manifold of nontrivial symmetrical equilibria forms a pair of heteroclinic orbits, this technical note ...
Li Zhenpeng +5 more
doaj +1 more source