Stabilizing Unknown Periodic Orbits of a Chaotic Spiking Oscillator
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 orig...
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| Veröffentlicht in: | IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences Communications and Computer Sciences, 2009/05/01, Vol.E92.A(5), pp.1316-1321 |
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| container_title | IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences |
| container_volume | E92.A |
| creator | TSUBONE, Tadashi WADA, Yasuhiro |
| description | 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. |
| doi_str_mv | 10.1587/transfun.E92.A.1316 |
| format | Article |
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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. 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Fundamentals</addtitle><description>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.</description><subject>Bifurcations</subject><subject>chaos</subject><subject>Chaos theory</subject><subject>Dynamical systems</subject><subject>Dynamics</subject><subject>Nonlinear dynamics</subject><subject>Orbits</subject><subject>Oscillators</subject><subject>Spiking</subject><subject>spiking oscillator</subject><subject>stabilization</subject><subject>unknown steady state</subject><subject>unstable periodic orbit</subject><issn>0916-8508</issn><issn>1745-1337</issn><issn>1745-1337</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2009</creationdate><recordtype>article</recordtype><recordid>eNpdkE1LAzEQhoMoWKu_wMvePO2aSTb7cSyLX1ioUHsO2TRp0243NUkR_fVmqfbgaYbheYaZF6FbwBmwqrwPTvReH_rsoSbZJAMKxRkaQZmzFCgtz9EI11CkFcPVJbryfoMxVATyEWrmQbSmM9-mXyWLftvbzz55U87YpZHJzLUm-MTqRCTNWtgQZ_O92Q7wzEvTdSJYd40utOi8uvmtY7R4fHhvntPp7OmlmUxTyaAIKWG6ZaB0qYikCudas1YpBrrIZQV17OqC0BIDiWRZF1gJUtYt02wpMZaEjtHdce_e2Y-D8oHvjJcqHtEre_C8quocKGEQSXokpbPeO6X53pmdcF8cMB8S43-J8ZgYn_AhsWi9Hq2ND2KlTo5w8e9O_XfYqQ72iZJr4bjq6Q9egnzP</recordid><startdate>2009</startdate><enddate>2009</enddate><creator>TSUBONE, Tadashi</creator><creator>WADA, Yasuhiro</creator><general>The Institute of Electronics, Information and Communication Engineers</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7SP</scope><scope>8FD</scope><scope>JQ2</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>2009</creationdate><title>Stabilizing Unknown Periodic Orbits of a Chaotic Spiking Oscillator</title><author>TSUBONE, Tadashi ; WADA, Yasuhiro</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c516t-25fb51ef7e2c3e04ff5bee51f64c819e519623701225f7960ea279b5f5dc00c23</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2009</creationdate><topic>Bifurcations</topic><topic>chaos</topic><topic>Chaos theory</topic><topic>Dynamical systems</topic><topic>Dynamics</topic><topic>Nonlinear dynamics</topic><topic>Orbits</topic><topic>Oscillators</topic><topic>Spiking</topic><topic>spiking oscillator</topic><topic>stabilization</topic><topic>unknown steady state</topic><topic>unstable periodic orbit</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>TSUBONE, Tadashi</creatorcontrib><creatorcontrib>WADA, Yasuhiro</creatorcontrib><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Electronics & Communications Abstracts</collection><collection>Technology Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>TSUBONE, Tadashi</au><au>WADA, Yasuhiro</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Stabilizing Unknown Periodic Orbits of a Chaotic Spiking Oscillator</atitle><jtitle>IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences</jtitle><addtitle>IEICE Trans. Fundamentals</addtitle><date>2009</date><risdate>2009</risdate><volume>E92.A</volume><issue>5</issue><spage>1316</spage><epage>1321</epage><pages>1316-1321</pages><issn>0916-8508</issn><issn>1745-1337</issn><eissn>1745-1337</eissn><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. 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| ispartof | IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, 2009/05/01, Vol.E92.A(5), pp.1316-1321 |
| issn | 0916-8508 1745-1337 1745-1337 |
| language | eng |
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| source | J-STAGE Free |
| subjects | Bifurcations chaos Chaos theory Dynamical systems Dynamics Nonlinear dynamics Orbits Oscillators Spiking spiking oscillator stabilization unknown steady state unstable periodic orbit |
| title | Stabilizing Unknown Periodic Orbits of a Chaotic Spiking Oscillator |
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