Homoclinic-doubling cascades

نویسندگان

  • Ale Jan Homburg
  • Hiroshi Kokubu
چکیده

Cascades of period-doubling bifurcations have attracted much interest from researchers of dynamical systems in the past two decades as it is one of the routes to onset of chaos. In this paper we consider routes to onset of chaos involving homoclinic-doubling bifurcations. ∗Partially supported by Grant-in-Aid for Scientific Research (No. 08740139), Ministry of Education, Science and Culture, Japan.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Universal scalings in homoclinic doubling cascades

We study a renormalization operator for families of one dimensional maps close to x 7! p + r(1 x ) 2 , 2 ( 1 2 ; 1). Such functions occur in the study of cascades of homoclinic doubling bifurcations in three dimensional di erential equations. For values of close to 1 2 , we prove the existence of a xed point of the renormalization operator, whose linearization at the xed point has two unstable ...

متن کامل

Homoclinic Tangencies near Cascades of Period Doubling Bifurcations

We consider perturbations of the Feigenbaum map in n dimensions. In the analytic topology we prove that the maps that are accumulated by period doubling bifurcations are approximable with homoclinic tangencies. We also develop a n-dimensional Feigenbaum theory in the Cr topology, for r large enough. We apply this theory to extend the result of approximation with homoclinic tangencies for Crmaps...

متن کامل

Period-Doubling Analysis and Chaos Detection Using Commercial Harmonic Balance Simulators - Microwave Theory and Techniques, IEEE Transactions on

Two of the most common phenomena leading to chaos are the period-doubling cascade and the formation of transverse homoclinic orbits. In this paper, a bifurcation analysis technique is presented for the prediction of both phenomena in microwave circuits. The fact that the technique is based on the use of commercial harmonic balance software constitutes a major advantage for the circuit designer....

متن کامل

Homoclinic Branch Switching: a Numerical Implementation of Lin's Method

We present a numerical method for branch switching between homoclinic orbits to equilibria of ODEs computed via numerical continuation. Starting from a 1-homoclinic orbit our method allows us to find and follow an N -homoclinic orbit, for any N > 1 (if it exists nearby). This scheme is based on Lin’s method and it is robust and reliable. The method is implemented in AUTO/HomCont. A system of or...

متن کامل

Synchronization of period-doubling oscillations in vascular coupled nephrons.

The mechanisms by which the individual functional unit (nephron) of the kidney regulates the incoming blood flow give rise to a number of nonlinear dynamic phenomena, including period-doubling bifurcations and intra-nephron synchronization between two different oscillatory modes. Interaction between the nephrons produces complicated and time-dependent inter-nephron synchronization patterns. In ...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 1997