Browsing by Author "Peng, Chen-Chang"

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Chaotic orbits for differentiable maps near anti-integrable limits
(2016-03-01)
Chen, Te-Hsuan
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Lin, Wen-Wei
;
Peng, Chen-Chang
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應用數學系
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Department of Applied Mathematics
In this work, we study the dynamical system which can be transformed into a difference equation of the form epsilon g(x(t-n2),...,x(t),..,x(t+n1) ;epsilon) + go (x(t)) = 0 where epsilon is an element of R is a parameter, g : Rn1+n2+1 -> R and go : R -> R. are both C-1 functions and n(1), n(2) are both nonnegative integers. Suppose that the function go has k simple zeros where k >= 2. We give criteria of existence of some kinds of chaotic orbits, and construct infinite ones explicitly. As applications of these results, we establish snap-back repellers and heteroclinical repellers for the modified Mira maps and transversal homoclinic orbits or transversal heteroclinic orbits for the Henon maps, the Arneodo-Coullet-Tresser maps and the quadratic volume preserving maps. (C) 2015 Elsevier Inc. All rights reserved.
Chaotic synchronization in lattices of two-variable maps coupled with one variable
(2009-12-01)
Lin, Wen-Wei
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Peng, Chen-Chang
;
Wang, Yi-Qian
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應用數學系
;
Department of Applied Mathematics
In this paper, we study chaotic synchronization in 1D lattices of two-variable maps coupled with one variable. We give a rigourous proof for the occurrence of chaotic synchronization of spatially homogeneous solutions in such coupled map lattices (CMLs) of lattice size n = 4 with suitable coupling coefficients. For the case of lattice size n > 4, we demonstrate numerical results of synchronized chaotic behaviour of the CMLs. Moreover, we show numerically that the difference between two variables manifests chaotic behaviour. This behaviour combined with the special coupling method in the CMLs guarantees high security in applications using our new model.
Effects of soil parameter variation and grid deformation on the numerical simulation of aquitard consolidation
(2018-08-01)
Tsai, Tung-Lin
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Peng, Chen-Chang
;
Wang, Xi-Jun
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土木工程學系
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Department of Civil Engineering
Changes in soil parameters such as saturated unit weight (body force), hydraulic conductivity, and elastic modulus must be considered for simulating aquitard consolidation. In addition to changes in soil parameters, grid intervals change the subsequent soil deformation in such simulations. This study incorporated and examined the effects of both the grid deformation and soil parameter variation on the numerical simulation of aquitard consolidation caused by hydraulic head decline in a multilayered aquifer system. According to the nondimensional analysis, the deformation number can be regarded as a dimensionless parameter for assessing whether the grid deformation and soil parameter variation affect this simulation. The results revealed that when the deformation number exceeds 0.01 (i.e., when the aquitard is thick or soft), both the grid deformation and soil parameter variation must be simultaneously considered to increase accuracy. Aquitard consolidation was always overestimated when only the soil parameter variation was considered. However, when only the grid deformation was considered, the aquitard consolidation was either overestimated or underestimated depending on whether the influence of the change in the body force was more substantial than that of the elastic modulus.