Browsing by Author "Chen, Hung-Ju"

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Chaos for implicit difference equations with snap-back repellers
(2018-01-01)
Chen, Hung-Ju
;
Li, Ming-Chia
;
Lin, Shi-Xuan
;
應用數學系
;
Department of Applied Mathematics
This paper is a study of chaos for generalized dynamical systems derived from implicit difference equations. We define a snap-back repeller for an implicit difference equation and show that its existence implies chaotic dynamics for all small C-1-perturbed systems. By chaotic dynamics, we mean that the solution set of an implicit difference equation contains a compact subset on which the Bernoulli shift map is invariant and has positive topological entropy.
Chaotic dynamics in a monetary economy with habit persistence
(2008-02-01)
Chen, Hung-Ju
;
Li, Ming-Chia
;
應用數學系
;
Department of Applied Mathematics
This paper develops a cash-in-advance model for persistent habits of consumption. With a binding cash-in-advance constraint, the economic transition can be represented by a one-dimensional or two-dimensional dynamical system, depending on persistent habits of only cash-goods consumption or both cash-goods and credit-goods consumption, respectively. We verify the existence of entropic chaos and ergodic chaos for the former case and identify the presence of entropic chaos for the latter. (C) 2006 Elsevier B.V. All rights reserved.
Chaotic dynamics in an overlapping generations model with myopic and adaptive expectations
(2008-07-01)
Chen, Hung-Ju
;
Li, Ming-Chia
;
Lin, Yung-Ju
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應用數學系
;
Department of Applied Mathematics
In this paper, we study dynamic behavior of an overlapping generations model under three different expectations: perfect foresight, myopic expectations and adaptive expectations. We show that economic transition under myopic or adaptive expectations is very different from that under perfect foresight. When agents are perfectly foresighted, dynamics is simple, with a unique steady state that is globally attracting. However, cycles and chaotic motion can appear under myopic and adaptive expectations. We study the possibility of Li-Yorke chaos under myopic expectations and entropic chaos under adaptive expectations. (C) 2007 Elsevier B.V. All rights reserved.
Child allowances, fertility, and chaotic dynamics
(2013-06-01)
Chen, Hung-Ju
;
Li, Ming-Chia
;
應用數學系
;
Department of Applied Mathematics
This paper analyzes the dynamics in an overlapping generations model with the provision of child allowances. Fertility is an increasing function of child allowances and there exists a threshold effect of the marginal effect of child allowances on fertility. We show that if the effectiveness of child allowances is sufficiently high, an intermediate-sized tax rate will be enough to generate chaotic dynamics. Besides, a decrease in the inter-temporal elasticity of substitution will prevent the occurrence of irregular cycles. (C) 2013 AIP Publishing LLC
Environmental tax policy, habit formation and nonlinear dynamics
(2011-02-01)
Chen, Hung-Ju
;
Li, Ming-Chia
;
應用數學系
;
Department of Applied Mathematics
In this paper, we study the impact of environmental tax policy on the dynamic property in an environment-growth model (John and Pecchenino 1994)[3]. We assume that the government levies consumption tax and uses the tax revenue to improve environmental quality. We show that the economic dynamics can be represented by a first-order difference equation in environmental quality when there is no habit formation of environmental quality. If agents have habit formation of environmental quality, the economic dynamics will be represented by a second-order difference equation in environmental quality. In both cases, chaotic and cyclical fluctuations may exist if agents' preference towards environmental quality, the maintenance efficiency relative to degradation and the tax rate are sufficiently low. However, the economy undergoes transformation from complex dynamics to simple dynamics as the tax rate increases. Furthermore, in the presence of habit formation of environmental quality, an increase in the degree of habit formation lowers the possibility of complex dynamics. (C) 2010 Elsevier Ltd. All rights reserved.
Habit formation and chaotic dynamics in an n-dimensional cash-in-advance economy
(2009-10-01)
Chen, Hung-Ju
;
Li, Ming-Chia
;
應用數學系
;
Department of Applied Mathematics
This paper investigates the global dynamics of an n-dimensional cash-in-advance model where external habits persist for n periods. We find that habit formation is an important determinant to the dynamic property of the economy and identifies conditions generating entropic chaos. Our results indicate that the possibility of chaotic motion increases with the depreciation rate of habits.
Human capital externality and chaotic equilibrium dynamics
(2008-12-01)
Chen, Hung-Ju
;
Li, Ming-Chia
;
應用數學系
;
Department of Applied Mathematics
This study develops a two-period overlapping generations model in which adults undertake educational investment decisions oil behalf of young agents. In addition to educational investment, we argue that the accumulation of human capital is also dependent upon the externality from average human capital within the economy. In a departure from the previous literature in this area, we assume that there is a reduction in the overall productivity of human capital accumulation brought about by human capital externality, and show that complicated dynamics will emerge under this circumstance. In addition to displaying the chaotic dynamics in the sense of Li and Yorke, we also verify the existence of Devaney's chaos and Smale's chaos.
Productive public expenditures, expectation formations and nonlinear dynamics
(2008-07-01)
Chen, Hung-Ju
;
Li, Ming-Chia
;
應用數學系
;
Department of Applied Mathematics
In this paper, we investigate the dynamic properties of an overlapping generations' model with capital accumulation and publicly funded inventions under three different expectations: perfect foresight, myopic expectations and adaptive expectations. We show that considering productive public expenditures in the model will increase the dimension of the dynamical system. To study the dynamic behavior of a high-dimensional dynamical system, we focus on the case when the elasticity of publicly funded invention to output is small and approximate the system by using a one-dimensional dynamical system. This approximation method provides an efficient way to rigorously prove the existence of chaos in high-dimensional dynamical systems. We show that when agents are perfectly foresighted, there exists a unique, nontrivial steady state which is a global attractor. Cycles or even chaos may occur under myopic and adaptive expectations when the inter-temporal elasticity of substitution of consumption is large enough. Furthermore, we find that the impact of fiscal policy is sensible to the expectation formation. (C) 2008 Elsevier B.V. All rights reserved.
Stability of symbolic embeddings for difference equations and their multidimensional perturbations
(2015-02-01)
Chen, Hung-Ju
;
Li, Ming-Chia
;
應用數學系
;
Department of Applied Mathematics
In this paper, we study complexity of solutions of a high-dimensional difference equation of the form Phi(x(i-m), . . . , x(i-1), x(i), x(i+1), . . . , x(i+n)) = 0, i is an element of Z, where Phi is a C-1 function from (R-l)(m+n+1) to R-l. Our main result provides a sufficient condition for any sufficiently small C-1 perturbation of Phi to have symbolic embedding, that is, to possess a closed set of solutions Lambda that is invariant under the shift map, such that the restriction of the shift map to Lambda is topologically conjugate to a subshift of finite type. The sufficient condition can be easily verified when Phi depends on few variables, including the logistic and Henon families. To prove the result, we establish a global version of the implicit function theorem for perturbed equations. The proof of the main result is based on the Brouwer fixed point theorem, and the proof of the global implicit function theorem is based on the contraction mapping principle and other ingredients. Our novel approach extends results in [2,3,8,15,21]. (C) 2014 Elsevier Inc. All rights reserved.