Faculty of Science - Mahidol University

Mahidol University Annual Research Abstracts, Vol. 33 299
CONTROLLABILITY AND STABILITY OF THE
PERTURBED CHEN CHAOTIC DYNAMICAL
SYSTEM (NO. 784)
Plienpanich T. 1 , Niamsup P. 1 , Lenbury Y. 2
1 Department of Mathematics, Chiang Mai University, Huaykaw
Rd., Muang Chiangmai 50200, Thailand. E-mail :
scipnmsp@chiangmai.ac.th; 2 Department of Mathematics,
Faculty of Science, Mahidol University, Bangkok 10400,
Thailand. E-mail : scylb@mahidol.ac.th
Key words : Perturbed Chen chaotic dynamical system; Controlling
chaos; Synchronization
In this paper, we study perturbed Chen chaotic dynamical
system. Firstly, we study the sufficient conditions of parameters
which guarantee that the equilibrium points of perturbed Chen
chaotic dynamical system are asymptotically stable. Secondly, we
study methods for controlling chaos such as feedback control and
bounded feedback control that suppress the chaotic behavior to
unstable equilibrium points. Finally, we present chaos
synchronization of perturbed Chen chaotic dynamical system by
using active control and adaptive control.
(Applied Mathematics and Computatons. Inpress)
KINETIC MODELING OF LIPOPROTEIN
PEROXIDATION INITIATED BY COPPER
AND AZO COMPOUNDS (NO. 785)
Yanarojana S. 1 , Chantharaksria U. 1 , Wilairat P. 2 ,Lenbury Y. 3
1 Department of Pharmacology, Mahidol University, Bangkok
10400, Thailand. E-mail scuct@mahidol.ac.th; 2 Department of
Chemistry, Mahidol University, Bangkok 10400, Thailand. Email
scpwr@mahidol.ac.th; 3 Department of Mathematics,
Mahidol University, Bangkok 10400, Thailand. E-mail:
scylb@mahidol.ac.th
Key words : Lipid Perixidation, Tocopherol, Atherosclerosis,
Kinetic Modeling, Simulation
Oxidation of low density lipoprotein (LDL) has been
postulated as the main cause of atherogenesis resulting in formation
of foam cells and triggering of various pathways leading to the
development of the disease. Therefore, antioxidants would naturally
be expected to attenuate the progress of atherosclerosis α-Tocopherol
(α-TocH) is the most abundant form of vitamin E in nature and the
major antioxidant of biological membranes , α-TocH is also present
at a much higher concentration than other antioxidants in plasma
lipoproteins. The large amount of α-TocH present in LDL leads to
the expectation that lipid peroxidation would be strongly inhibited
by α-TocH. However, advanced atherosclerotic plaques are not
deficient in antioxidant vitamin C and E, despite the occurrence of
massive lipid oxidation. Thus conventional mechanism associated
with the antioxidant properties of α-TocH can not explain why lipid
peroxidation occurs in atherosclerotic lesions in the presence of
compounds that are usually considered to be antioxidants. A kinetic
model was developed and applied to explore the mechanism of lipid
peroxidation process under various conditions and to examine the
possible occurrence of lipid peroxidation in the presence of α-
tocopherol. The model incorporated many factors, which we believe
to play important roles in the different outcome of the process, that
were not included in previous models. As a result, the numerical
simulation was capable of illustrating that lipid peroxidation in the
lipoprotein particle can occur in the presence of vitamin E ( α-TocH)
and C under certain conditions, which include high initiation rate,
high initial α-TocH level, low ratio of [vitamin C]/[α-TocH], and
small lipoprotein particles. The kinetic scheme developed in this
study defined the type of relationship that α-TocH in an environment
exhibits either pro- or anti-oxidative property. Thus, antioxidant
and pro-oxidant effects of tocopherol merely depend on the condition
in which its properties are exhibited.
(ScienceAsia. Inpress)
STUDY OF PATTERN SELECTION ON ION-
SPUTTERED SURFACES BY WEAKLY
NONLINEAR STABILITY ANALYSIS (NO. 786)
Lenbury Y. 1 , Pansuwan A. 1 , Rattanakul C. 1 , Wollkind D.J. 2 ,
Harrison L 2 , Rajapakse I. 2
1 Department of Mathematics, Faculty of Science, Mahidol
University, Bangkok 10400, Thailand. E-mail :
scylb@mahidol.ac.th. pansuwan@alpha.tu.ac.th.
sccrt@mahido.ac.th; 2 Department of Mathematics, Washington
State University, Pullman WA 99164-3113, USA. E-mail :
dwolkind@wsu.edu.
One of the methods found suitable for predicting pattern
selection in nonlinear phenomena is a weakly nonlinear stability
analysis that, although incorporating the nonlinearities of the relevant
model system, basically pivots a pertubation procedure about the
critical point of linear stability theory [reviewed by Wollkind et.al.
(1994)]. The advantage of such an approach over strictly numerical
procedures is that it allows one to deduce quantitative relationships
between system parameters and stable patterns which are valuable
for experimental design and difficult to accomplish using simulation
alone. The development of spontaneous stationary equilibrium
patterns on metallic or semiconductor solid surfaces during ionsputtered
erosion at normal incidence can be investigated by means
of various weakly nonlinear stability analyses applied to the
appropriate governing equation for this phenomena.
(Asian Mathematicl Conference 2005. National University of
Singapore Singapore, 20-23 July 2005.)
NONLINEAR DELAY DIFFERENTIAL EQUATIONS
FOR POPULATION MODELS : ASYMPTOTIC
STABILITY AND NONTRIVIAL PERIODICITY
Giang D.V. 1 , Lenbury Y. 2 , Seidman T.I. 3
(NO. 787)
1 Hanoi Institute of Mathematics, 18 Hoang Quoc Viet 10307
Hanoi, Vietnam. E-mail : dvginag@math .ac.vn.; 2 Department
of Mathematics, Mahidol University, Bangkok 10400, Thailand.
E-mail : scylb@mahidol.ac.th.; 3 Department of Mathematics and
Statistics, University of Maryland, Baltimore Country,
Maryland, USA. E-mail : seidman@math.umbc.edu
We investigate the effect of delay on the asymptotic behavior
of the model x + μx = f(x(‘ – τ))
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