# American Institute of Mathematical Sciences

• Previous Article
Qualitative analysis of periodic oscillations of an earth satellite with magnetic attitude stabilization
• DCDS Home
• This Issue
• Next Article
The diffusion time of the connecting orbit around rotation number zero for the monotone twist maps
April  2000, 6(2): 275-292. doi: 10.3934/dcds.2000.6.275

## Symbolic dynamics in nondifferentiable system originating in R-L-Diode driven circuit

 1 Department of Electrical Engineering, Ecole Nationale d'Ingenieurs Tunis, Tunis II University, BP 37, 1002 Tunis Belvedere, Tunisia

Received  September 1998 Revised  October 1999 Published  January 2000

In this paper, we will study a simple, piecewise linear model which mimics the transformation in a chaotic electrical circuit: R-L-Diode driven by a sinusoïdal voltage source. This map leads to a complicated chaotic structure, with infinitly many distinct, prime homoclinic points. We prove here that there are infinitly many distinct homoclinic points. Their dynamical classification is not completely understood. They are derived through a nonlinear ($-+$) map, built with piecewise linear pieces. To different two sequences, should correspond two distinct prime homoclinic points. We have derived, we believe, the basic phenomena leading to the complicated dynamics.
Citation: Safya Belghith. Symbolic dynamics in nondifferentiable system originating in R-L-Diode driven circuit. Discrete & Continuous Dynamical Systems - A, 2000, 6 (2) : 275-292. doi: 10.3934/dcds.2000.6.275
 [1] Jose S. Cánovas, Tönu Puu, Manuel Ruiz Marín. Detecting chaos in a duopoly model via symbolic dynamics. Discrete & Continuous Dynamical Systems - B, 2010, 13 (2) : 269-278. doi: 10.3934/dcdsb.2010.13.269 [2] Fryderyk Falniowski, Marcin Kulczycki, Dominik Kwietniak, Jian Li. Two results on entropy, chaos and independence in symbolic dynamics. Discrete & Continuous Dynamical Systems - B, 2015, 20 (10) : 3487-3505. doi: 10.3934/dcdsb.2015.20.3487 [3] Marian Gidea, Yitzchak Shmalo. Combinatorial approach to detection of fixed points, periodic orbits, and symbolic dynamics. Discrete & Continuous Dynamical Systems - A, 2018, 38 (12) : 6123-6148. doi: 10.3934/dcds.2018264 [4] Steven T. Piantadosi. Symbolic dynamics on free groups. Discrete & Continuous Dynamical Systems - A, 2008, 20 (3) : 725-738. doi: 10.3934/dcds.2008.20.725 [5] Victoria Rayskin. Homoclinic tangencies in $R^n$. Discrete & Continuous Dynamical Systems - A, 2005, 12 (3) : 465-480. doi: 10.3934/dcds.2005.12.465 [6] Zhihong Xia. Homoclinic points and intersections of Lagrangian submanifold. Discrete & Continuous Dynamical Systems - A, 2000, 6 (1) : 243-253. doi: 10.3934/dcds.2000.6.243 [7] Jim Wiseman. Symbolic dynamics from signed matrices. Discrete & Continuous Dynamical Systems - A, 2004, 11 (2&3) : 621-638. doi: 10.3934/dcds.2004.11.621 [8] George Osipenko, Stephen Campbell. Applied symbolic dynamics: attractors and filtrations. Discrete & Continuous Dynamical Systems - A, 1999, 5 (1) : 43-60. doi: 10.3934/dcds.1999.5.43 [9] Michael Hochman. A note on universality in multidimensional symbolic dynamics. Discrete & Continuous Dynamical Systems - S, 2009, 2 (2) : 301-314. doi: 10.3934/dcdss.2009.2.301 [10] Wenqiang Zhao. Smoothing dynamics of the non-autonomous stochastic Fitzhugh-Nagumo system on $\mathbb{R}^N$ driven by multiplicative noises. Discrete & Continuous Dynamical Systems - B, 2019, 24 (8) : 3453-3474. doi: 10.3934/dcdsb.2018251 [11] Ting Yang. Homoclinic orbits and chaos in the generalized Lorenz system. Discrete & Continuous Dynamical Systems - B, 2017, 22 (11) : 0-0. doi: 10.3934/dcdsb.2019210 [12] Flaviano Battelli, Michal Fečkan. On the existence of solutions connecting IK singularities and impasse points in fully nonlinear RLC circuits. Discrete & Continuous Dynamical Systems - B, 2017, 22 (8) : 3043-3061. doi: 10.3934/dcdsb.2017162 [13] Wenxiang Sun, Yun Yang. Hyperbolic periodic points for chain hyperbolic homoclinic classes. Discrete & Continuous Dynamical Systems - A, 2016, 36 (7) : 3911-3925. doi: 10.3934/dcds.2016.36.3911 [14] Nicola Soave, Susanna Terracini. Symbolic dynamics for the $N$-centre problem at negative energies. Discrete & Continuous Dynamical Systems - A, 2012, 32 (9) : 3245-3301. doi: 10.3934/dcds.2012.32.3245 [15] Dieter Mayer, Fredrik Strömberg. Symbolic dynamics for the geodesic flow on Hecke surfaces. Journal of Modern Dynamics, 2008, 2 (4) : 581-627. doi: 10.3934/jmd.2008.2.581 [16] Frédéric Naud. Birkhoff cones, symbolic dynamics and spectrum of transfer operators. Discrete & Continuous Dynamical Systems - A, 2004, 11 (2&3) : 581-598. doi: 10.3934/dcds.2004.11.581 [17] David Ralston. Heaviness in symbolic dynamics: Substitution and Sturmian systems. Discrete & Continuous Dynamical Systems - S, 2009, 2 (2) : 287-300. doi: 10.3934/dcdss.2009.2.287 [18] Graeme W. Milton, Pierre Seppecher. Electromagnetic circuits. Networks & Heterogeneous Media, 2010, 5 (2) : 335-360. doi: 10.3934/nhm.2010.5.335 [19] Martin Wechselberger, Warren Weckesser. Homoclinic clusters and chaos associated with a folded node in a stellate cell model. Discrete & Continuous Dynamical Systems - S, 2009, 2 (4) : 829-850. doi: 10.3934/dcdss.2009.2.829 [20] David Burguet. Examples of $\mathcal{C}^r$ interval map with large symbolic extension entropy. Discrete & Continuous Dynamical Systems - A, 2010, 26 (3) : 873-899. doi: 10.3934/dcds.2010.26.873

2018 Impact Factor: 1.143