IEICE TRANSACTIONS on Fundamentals
Stabilizing Unknown Periodic Orbits of a Chaotic Spiking Oscillator
Summary :
In this paper, we propose a simple nonlinear system which consists of a chaotic spiking oscillator and a controlling circuit to stabilize unknown periodic orbits. Our proposed system generates various stabilized unknown Unstable Periodic Orbits which are embedded on the chaotic attractor of the original chaotic spiking oscillator. The proposed system is simple and exhibits various bifurcation phenomena. The dynamics of the system is governed by 1-D piecewise linear return map. Therefore, the rigorous analysis can be performed. We provide conditions for stability and almost complete analysis for bifurcation and co-existence phenomena by using the 1-D return map. An implementation example of the controlled chaotic spiking oscillator is provided to confirm some theoretical results.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E92-A No.5 pp.1316-1321
- Publication Date
- 2009/05/01
- Publicized
- Online ISSN
- 1745-1337
- DOI
- 10.1587/transfun.E92.A.1316
- Type of Manuscript
- PAPER
- Category
- Nonlinear Problems
Authors
Keyword
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Tadashi TSUBONE, Yasuhiro WADA, "Stabilizing Unknown Periodic Orbits of a Chaotic Spiking Oscillator" in IEICE TRANSACTIONS on Fundamentals,
vol. E92-A, no. 5, pp. 1316-1321, May 2009, doi: 10.1587/transfun.E92.A.1316.
Abstract: In this paper, we propose a simple nonlinear system which consists of a chaotic spiking oscillator and a controlling circuit to stabilize unknown periodic orbits. Our proposed system generates various stabilized unknown Unstable Periodic Orbits which are embedded on the chaotic attractor of the original chaotic spiking oscillator. The proposed system is simple and exhibits various bifurcation phenomena. The dynamics of the system is governed by 1-D piecewise linear return map. Therefore, the rigorous analysis can be performed. We provide conditions for stability and almost complete analysis for bifurcation and co-existence phenomena by using the 1-D return map. An implementation example of the controlled chaotic spiking oscillator is provided to confirm some theoretical results.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E92.A.1316/_p
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@ARTICLE{e92-a_5_1316,
author={Tadashi TSUBONE, Yasuhiro WADA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Stabilizing Unknown Periodic Orbits of a Chaotic Spiking Oscillator},
year={2009},
volume={E92-A},
number={5},
pages={1316-1321},
abstract={In this paper, we propose a simple nonlinear system which consists of a chaotic spiking oscillator and a controlling circuit to stabilize unknown periodic orbits. Our proposed system generates various stabilized unknown Unstable Periodic Orbits which are embedded on the chaotic attractor of the original chaotic spiking oscillator. The proposed system is simple and exhibits various bifurcation phenomena. The dynamics of the system is governed by 1-D piecewise linear return map. Therefore, the rigorous analysis can be performed. We provide conditions for stability and almost complete analysis for bifurcation and co-existence phenomena by using the 1-D return map. An implementation example of the controlled chaotic spiking oscillator is provided to confirm some theoretical results.},
keywords={},
doi={10.1587/transfun.E92.A.1316},
ISSN={1745-1337},
month={May},}
Copy
TY - JOUR
TI - Stabilizing Unknown Periodic Orbits of a Chaotic Spiking Oscillator
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1316
EP - 1321
AU - Tadashi TSUBONE
AU - Yasuhiro WADA
PY - 2009
DO - 10.1587/transfun.E92.A.1316
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E92-A
IS - 5
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - May 2009
AB - In this paper, we propose a simple nonlinear system which consists of a chaotic spiking oscillator and a controlling circuit to stabilize unknown periodic orbits. Our proposed system generates various stabilized unknown Unstable Periodic Orbits which are embedded on the chaotic attractor of the original chaotic spiking oscillator. The proposed system is simple and exhibits various bifurcation phenomena. The dynamics of the system is governed by 1-D piecewise linear return map. Therefore, the rigorous analysis can be performed. We provide conditions for stability and almost complete analysis for bifurcation and co-existence phenomena by using the 1-D return map. An implementation example of the controlled chaotic spiking oscillator is provided to confirm some theoretical results.
ER -
English
