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Laureano, M., Mendes, D. A. & Ferreira, M. A. M. (2013). Dislocated Negative Feedback Control with Partial Replacemrnt between Chaotic Lorenz Systems. Mathematica Aeterna. 3 (5), 337-348

M. D. Laureano et al.,  "Dislocated Negative Feedback Control with Partial Replacemrnt between Chaotic Lorenz Systems", in Mathematica Aeterna, vol. 3, no. 5, pp. 337-348, 2013

@article{laureano2013_1731867568753,
	author = "Laureano, M. and Mendes, D. A. and Ferreira, M. A. M.",
	title = "Dislocated Negative Feedback Control with Partial Replacemrnt between Chaotic Lorenz Systems",
	journal = "Mathematica Aeterna",
	year = "2013",
	volume = "3",
	number = "5",
	pages = "337-348",
	url = "http://www.e-hilaris.com/MA/2013/MA3_5_2.pdf"
}

TY  - JOUR
TI  - Dislocated Negative Feedback Control with Partial Replacemrnt between Chaotic Lorenz Systems
T2  - Mathematica Aeterna
VL  - 3
IS  - 5
AU  - Laureano, M.
AU  - Mendes, D. A.
AU  - Ferreira, M. A. M.
PY  - 2013
SP  - 337-348
SN  - 1314-3336
UR  - http://www.e-hilaris.com/MA/2013/MA3_5_2.pdf
AB  - In order to obtain asymptotical synchronization, we combine negative feedback control and dislocated negative feedback control with
partial replacement to the nonlinear terms of the response system, a
coupling version that was less explored. All these unidirectional coupling schemes are applied between Lorenz systems where we consider
some values for the control parameters that lead to chaotic behavior.
The sufficient conditions for global stable synchronization are ob-
tained from a different approach of the Lyapunov direct method for the
transversal system. In one of the coupling we apply a result based on
the classification of the symmetric matrix AT +A as negative definite,
where A is characterizing the transversal system. In the other couplings
presented here, the sufficient conditions are based on the derivative in-
crease of an appropriate Lyapunov function. In fact, the effectiveness
of the coupling between systems with equal dimension follows from the
Ros´ario D. Laureano, Diana A. Mendes and Manuel Alberto M. Ferreira
analysis of the synchronization error, e(t), and, if the system variables
can be bounded by positive constants, then the derivative of an appro-
priate Lyapunov function can be increased as required by the Lyapunov
direct method.
Mathematics Subject Classification: 34D06, 34D23
ER  -