WO1999027765A3 - Sustaining chaos by using basin boundary saddles - Google Patents

Sustaining chaos by using basin boundary saddles Download PDF

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Publication number
WO1999027765A3
WO1999027765A3 PCT/US1998/027745 US9827745W WO9927765A3 WO 1999027765 A3 WO1999027765 A3 WO 1999027765A3 US 9827745 W US9827745 W US 9827745W WO 9927765 A3 WO9927765 A3 WO 9927765A3
Authority
WO
WIPO (PCT)
Prior art keywords
chaos
saddles
sustaining
basin boundary
unstable
Prior art date
Application number
PCT/US1998/027745
Other languages
French (fr)
Other versions
WO1999027765A2 (en
Inventor
Ira B Schwartz
Ioana Triandaf
Original Assignee
Us Navy
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Us Navy filed Critical Us Navy
Priority to AU26523/99A priority Critical patent/AU2652399A/en
Publication of WO1999027765A2 publication Critical patent/WO1999027765A2/en
Publication of WO1999027765A3 publication Critical patent/WO1999027765A3/en

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Classifications

    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B21/00—Systems involving sampling of the variable controlled
    • G05B21/02—Systems involving sampling of the variable controlled electric

Abstract

A method and apparatus for sustaining chaos in a system by using the natural dynamics of the system to redirect flow towards a chaotic region along unstable manifolds of basin boundary saddles by utilizing small, infrequent parameter perturbations. The perturbations are determined based on the location of an unstable state, which is used as a control reference. The location of the unstable state, which is unobservable, is estimated by calculating a theoretical branch connecting the current state of the system to the target unstable state.
PCT/US1998/027745 1997-12-04 1998-12-04 Sustaining chaos by using basin boundary saddles WO1999027765A2 (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
AU26523/99A AU2652399A (en) 1997-12-04 1998-12-04 Sustaining chaos by using basin boundary saddles

Applications Claiming Priority (2)

Application Number Priority Date Filing Date Title
US6705097P 1997-12-04 1997-12-04
US60/067,050 1997-12-04

Publications (2)

Publication Number Publication Date
WO1999027765A2 WO1999027765A2 (en) 1999-06-10
WO1999027765A3 true WO1999027765A3 (en) 1999-07-15

Family

ID=22073399

Family Applications (1)

Application Number Title Priority Date Filing Date
PCT/US1998/027745 WO1999027765A2 (en) 1997-12-04 1998-12-04 Sustaining chaos by using basin boundary saddles

Country Status (3)

Country Link
US (1) USH1945H1 (en)
AU (1) AU2652399A (en)
WO (1) WO1999027765A2 (en)

Families Citing this family (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US6763271B2 (en) * 2001-04-12 2004-07-13 The United States Of America As Represented By The Secretary Of The Navy Tracking sustained chaos

Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US5706192A (en) * 1995-11-16 1998-01-06 The United States Of America As Represented By The Secretary Of The Navy Antiphase switching in arrays of globally coupled oscillators
US5815413A (en) * 1997-05-08 1998-09-29 Lockheed Martin Energy Research Corporation Integrated method for chaotic time series analysis

Family Cites Families (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US5402334A (en) 1992-05-11 1995-03-28 The United States Of America As Represented By The Secretary Of The Navy Method and apparatus for pseudoperiodic drive
US5342401A (en) 1992-08-19 1994-08-30 The Regents Of The University Of California Real time cardiac arrhythmia stabilizing system
US5442510A (en) * 1993-06-23 1995-08-15 The United States Of America As Represented By The Secretary Of The Navy Control system for tracking nonlinear systems
US5486280A (en) 1994-10-20 1996-01-23 Martin Marietta Energy Systems, Inc. Process for applying control variables having fractal structures
US5612973A (en) 1995-06-19 1997-03-18 Massachusetts Institute Of Technology System employing dissipative pseudorandom dynamics for communications and measurement

Patent Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US5706192A (en) * 1995-11-16 1998-01-06 The United States Of America As Represented By The Secretary Of The Navy Antiphase switching in arrays of globally coupled oscillators
US5815413A (en) * 1997-05-08 1998-09-29 Lockheed Martin Energy Research Corporation Integrated method for chaotic time series analysis

Non-Patent Citations (1)

* Cited by examiner, † Cited by third party
Title
SCHWARTZ I B, TRIANDAF I: "SUSTAINING CHAOS BY USING BASIN BOUNDARY SADDLES", PHYSICAL REVIEW LETTERS, AMERICAN PHYSICAL SOCIETY., US, vol. 77, no. 23, 2 December 1996 (1996-12-02), US, pages 4740 - 4743, XP002919365, ISSN: 0031-9007, DOI: 10.1103/PhysRevLett.77.4740 *

Also Published As

Publication number Publication date
AU2652399A (en) 1999-06-16
USH1945H1 (en) 2001-03-06
WO1999027765A2 (en) 1999-06-10

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