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MAKING A DISCRETE DYNAMICAL SYSTEM CHAOTIC: THEORETICAL RESULTS AND NUMERICAL SIMULATIONS

DEJIAN LAI

Program in Biometry, School of Public Health, University of Texas, Health Science Center at Houston, TX 77030, USA

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and

GUANRONG CHEN

Department of Electronic Engineering, City University of Hong Kong, Kowloon, Hong Kong, P.R. China

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https://doi.org/10.1142/S0218127403008648Cited by:10 (Source: Crossref)

Abstract

In this paper, we study state-feedback controller design for controlling the Lyapunov exponents of an n-dimensional dynamical system. We examine some theoretical results and perform numerical simulations for systems with and without noise influence. The controlled Lyapunov exponents are asymptotically normally distributed if the system has noisy inputs. Computer simulations on finite samples are all consistent with the theoretical results.

Keywords:

References

P. Billingsley , Probability and Measure , 2nd edn. ( John Wiley , NY , 1986 ) . Google Scholar
G. Chen and J. L. Moiola, J. Franklin Instit. B 331, 819 (1994), DOI: 10.1016/0016-0032(94)90090-6. Crossref, Web of Science, Google Scholar
G. Chen and D. Lai, Int. J. Bifurcation and Chaos 6, 1341 (1996). Link, Web of Science, Google Scholar
G. Chen and D. Lai, IEEE Trans. Circuits Syst.-I 44, 250 (1997). Crossref, Web of Science, Google Scholar
G. Chen and D. Dong , From Chaos to Order: Methodologies, Perspectives and Applications ( World Scientific , Singapore , 1998 ) . Link, Google Scholar
G. Chen and D. Lai, Int. J. Bifurcation and Chaos 8, 1585 (1998), DOI: 10.1142/S0218127498001236. Link, Web of Science, Google Scholar
D. S. Dendrinos and M. Sonis , Chaos and Socio-Spatial Dynamics ( Springer-Verlag , NY , 1990 ) . Crossref, Google Scholar
G. Hu, Z. Qu and K. He, Int. J. Bifurcation and Chaos 5, 901 (1995). Link, Web of Science, Google Scholar
V. Inet al., Phys. Rev. Lett. 74, 4420 (1995). Crossref, Web of Science, Google Scholar
D. Lai and G. Chen, Int. J. Bifurcation and Chaos 5, 1721 (1995). Link, Web of Science, Google Scholar
D. Lai and G. Chen, Mathl. Comput. Model. 27, 1 (1998). Crossref, Web of Science, Google Scholar
D. Lai and G. Chen, Comput. Stat. Data Anal. 33, 69 (2000). Crossref, Web of Science, Google Scholar
M. J. Ogorzalek, IEEE Trans. Circuits Syst.-I 40, 700 (1993). Crossref, Web of Science, Google Scholar
S. J. Schiffet al., Nature 370, 615 (1994). Crossref, Web of Science, Google Scholar
T. Shinbrotet al., Nature 363, 411 (1993). Crossref, Web of Science, Google Scholar
H. Tong , Non-linear Time Series: A Dynamical System Approach ( Oxford University Press , NY , 1990 ) . Crossref, Google Scholar
I. Triandaf and I. B. Schwartz, Phys. Rev. E 62, 3529 (2000), DOI: 10.1103/PhysRevE.62.3529. Crossref, Web of Science, Google Scholar
X. Wang and G. Chen, Int. J. Bifurcation and Chaos 10, 549 (2000), DOI: 10.1142/S0218127400000372. Link, Web of Science, Google Scholar
W. Yanget al., Phys. Rev. E 51, 102 (1995). Crossref, Web of Science, Google Scholar