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Volumn 56, Issue 6, 1997, Pages 6410-6417

Control of chaos by oscillating feedback

Author keywords

[No Author keywords available]

Indexed keywords

ASYMPTOTIC STABILITY; CHAOS THEORY; DIFFERENTIAL EQUATIONS; EIGENVALUES AND EIGENFUNCTIONS; FEEDBACK CONTROL; FLUID DYNAMICS; LYAPUNOV METHODS; MATHEMATICAL MODELS; OSCILLATIONS; PROBABILITY;

EID: 0031362993     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.56.6410     Document Type: Article
Times cited : (94)

References (24)
  • 8
    • 85037248925 scopus 로고
    • 81, 3088 (1984).
    • (1984) , vol.81 , pp. 3088
  • 13
    • 85037199828 scopus 로고    scopus 로고
    • More complicated periodic functions (Formula presented) will also stabilize unstable orbits. The one chosen here is the simplest one
    • More complicated periodic functions (Formula presented) will also stabilize unstable orbits. The one chosen here is the simplest one.
  • 14
    • 85037252379 scopus 로고    scopus 로고
    • The (Formula presented)-dimensional map (Formula presented) could be linearized around its fixed point (Formula presented) as (Formula presented), where (Formula presented). By decomposing (Formula presented) into the right eigenvectors (Formula presented) of (Formula presented) as (Formula presented), where (Formula presented) are the eigenvalues of (Formula presented), this becomes (Formula presented), i.e., a system of decoupled one-dimensional maps
    • The (Formula presented)-dimensional map (Formula presented) could be linearized around its fixed point (Formula presented) as (Formula presented), where (Formula presented). By decomposing (Formula presented) into the right eigenvectors (Formula presented) of (Formula presented) as (Formula presented), where (Formula presented) are the eigenvalues of (Formula presented), this becomes (Formula presented), i.e., a system of decoupled one-dimensional maps.
  • 16
  • 17
    • 85037213450 scopus 로고    scopus 로고
    • M. Kerzberg and A. Zippelius, Phys. Scr. 33, p. 190.
    • Amit, D.J.1
  • 21
    • 85037199721 scopus 로고    scopus 로고
    • The equation (Formula presented) has the solution (Formula presented) for (Formula presented) and (Formula presented) for (Formula presented) because we need to know (Formula presented) only from the previous interval (Formula presented). This yields (Formula presented). Since (Formula presented) for (Formula presented), the factor (Formula presented) remains larger than one for all values of (Formula presented), i.e., the fixed point cannot be stabilized
    • The equation (Formula presented) has the solution (Formula presented) for (Formula presented) and (Formula presented) for (Formula presented) because we need to know (Formula presented) only from the previous interval (Formula presented). This yields (Formula presented). Since (Formula presented) for (Formula presented), the factor (Formula presented) remains larger than one for all values of (Formula presented), i.e., the fixed point cannot be stabilized.


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.