Introduction to anti-control of discrete chaos: Theory and applications. (English) Zbl 1152.93394

Chen, Guanrong; Shi, Yuming

Philos. Trans. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 364, No. 1846, 2433-2447 (2006).

Summary: In this paper, the notion of anti-control of chaos (or chaotification) is introduced, which means to make an originally non-chaotic dynamical system chaotic or enhance the existing chaos of a chaotic system. The main interest in this paper is to employ the classical feedback control techniques. Only the discrete case is discussed in detail, including both finite-dimensional and infinite-dimensional settings.

MSC:

93C10	Nonlinear systems in control theory
37D45	Strange attractors, chaotic dynamics of systems with hyperbolic behavior
37N35	Dynamical systems in control

Keywords:

chaos; chaotification; finite- and infinite-dimensional discrete chaos

References:

[1]	AMER MATH MONTHLY 99 pp 332– (1992)
[2]	IEEE CIRCUITS SYST SOC NEWSLETT 9 pp 1– (1998)
[3]	J SYST SCI COMPLEX 14 pp 32– (2001)
[4]	6 pp 1341– (1996)
[5]	8 pp 1585– (1998)
[6]	J MATH PHYS 39 pp 6459– (1998)
[7]	25 pp 637– (2005)
[8]	10 pp 593– (2000)
[9]	TOPOLOGY APPL 117 pp 259– (2002)
[10]	IEEE TRANS CIRC SYSTI 48 pp 163– (2001)
[11]	IEEE TRANS CIRC SYSTI 48 pp 1385– (2001)
[12]	J SYST SCI COMPLEX 16 pp 159– (2003)
[13]	18 pp 69– (2003)
[14]	AMER MATH MONTHLY 82 pp 481– (1975)
[15]	12 pp 1129– (2002)
[16]	3 pp 199– (1978)
[17]	Schiff, Nature; Physical Science (London) 370 (6491) pp 615– (1994)
[18]	22 pp 555– (2004)
[19]	SCIENCE CHINA SER A MATH 34 pp 595– (2004)
[20]	15 pp 547– (2005)
[21]	EGOD TH DYNAM SYST 23 pp 621– (2003)
[22]	AMER MATH MONTHLY 104 pp 411– (1997)
[23]	9 pp 1435– (1999)
[24]	10 pp 549– (2000)
[25]	INT J CIRC THEORY APPL 28 pp 305– (2000)
[26]	14 pp 3317– (2004)
[27]	14 pp 279– (2004)
[28]	13 pp 3443– (2004)
[29]	SCI BULL CHINA 32 pp 248– (1987)