An Example of a Resonant Homoclinic Loop of Infinite Cyclicity
نویسندگان
چکیده
We describe a codimension-3 bifurcation surface in the space of C-smooth (r ≥ 3) dynamical systems (with phase space of dimension 4 or higher) having an attractive two-dimensional invariant manifold with an infinite sequence of periodic orbits of alternating stability which converge to a homoclinic loop. 2000 Math. Subj. Class. 37G20, 34C07, 34C37.
منابع مشابه
Bifurcations and Stability of Nondegenerated Homoclinic Loops for Higher Dimensional Systems
By using the foundational solutions of the linear variational equation of the unperturbed system along the homoclinic orbit as the local current coordinates system of the system in the small neighborhood of the homoclinic orbit, we discuss the bifurcation problems of nondegenerated homoclinic loops. Under the nonresonant condition, existence, uniqueness, and incoexistence of 1-homoclinic loop a...
متن کاملThe inverse integrating factor and the Poincaré map . ∗ Dedicated to Javier
This work is concerned with planar real analytic differential systems with an analytic inverse integrating factor defined in a neighborhood of a regular orbit. We show that the inverse integrating factor defines an ordinary differential equation for the transition map along the orbit. When the regular orbit is a limit cycle, we can determine its associated Poincaré return map in terms of the in...
متن کاملThe Inverse Integrating Factor and the Poincaré Map
This work is concerned with planar real analytic differential systems with an analytic inverse integrating factor defined in a neighborhood of a regular orbit. We show that the inverse integrating factor defines an ordinary differential equation for the transition map along the orbit. When the regular orbit is a limit cycle, we can determine its associated Poincaré return map in terms of the in...
متن کاملThe Twisting Bifurcations of Double Homoclinic Loops with Resonant Eigenvalues
and Applied Analysis 3 By the same process as in [32], which is based on the analysis of the Poincaré return map defined on some local transversal section of the double homoclinic loop Γ, we obtain the bifurcation equations as follows:
متن کاملVoltage Regulation of DC-DC Series Resonant Converter Operating in Discontinuous Conduction Mode: The Hybrid Control Approach
Dynamic modeling and control of dc-dc series resonant converter (SRC) especially when operating in discontinuous conduction mode (DCM) is still a challenge in power electronics. Due to semiconductors switching, SRC is naturally represented as a switched linear system, a class of hybrid systems. Nevertheless, the hybrid nature of the SRC is commonly neglected and it is modeled as a purely contin...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2005