Browsing by Author "Juang, Jong"

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AVOIDING COLLISIONS IN CUCKER SMALE FLOCKING MODELS UNDER GROUP-HIERARCHICAL MULTILEADERSHIP
(2018-01-01)
Juang, Jong
;
Liang, Yu-Hao
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應用數學系
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Department of Applied Mathematics
The Cucker Smale (C-S) flocking model can be applied to design several mobile autonomous agent systems such as unmanned aerial vehicles and robot systems. In these applications, the problem of collision is usually a nonnegligible issue that should be addressed. In the literature, extra bonding/repulsive forces are added to solve the problem of collision. However, all the known results are limited to the symmetric coupling topology. In this paper, we address this problem under a group-hierarchical multileadership consisting of symmetric coupling topologies and the hierarchical leadership. We obtain the following three main results. First, we show that the augmented C-S model achieves asymptotic flocking provided, roughly, that the ratio between the rate of bounding force and communication rate is sufficiently large. Second, we prove that, for a given augmented C-S model, there exists a set of initial states, which can be explicitly described, such that their corresponding solutions maintain some minimum distance between them. Finally, we show that, for a given set of initial states, we can control the system so that its corresponding solution is collision free by suitably choosing bounding forces, which are independent of given initial states. This in turn suggests that the corresponding system can be collision free by having tolerance for error in their initial states.
On a piecewise-smooth map arising in ecology
(2014-10-15)
Huang, Chun-Ming
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Juang, Jong
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應用數學系
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數學建模與科學計算所(含中心)
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Department of Applied Mathematics
In this paper, we study a two-dimensional piecewise smooth map arising in ecology. Such map, containing two parameters d and beta, is derived from a model describing how masting of a mature forest happens and synchronizes. Here d is the energy depletion quantity and beta is the coupling strength. Our main results are the following. First, we obtain a "weak" Sharkovskii ordering for the map on its nondiagonal invariant region for a certain set of parameters. In particular, we show that its Sharkovskii ordering is the natural number (resp., the positive even number) for beta > 1 (resp., 0 < beta < 1). Second, we obtain a region of parameter space for which its corresponding global dynamics can be completely characterized. (C) 2014 Elsevier Inc. All rights reserved.
Solution of a nonsymmetric algebraic Riccati equation from a one-dimensional multistate transport model
(2011-10-01)
Li, Tiexiang
;
Chu, Eric King-Wah
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Juang, Jong
;
Lin, Wen-Wei
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應用數學系
For the steady-state solution of a differential equation from a one-dimensional multistate model in transport theory, we shall derive and study a nonsymmetric algebraic Riccati equation B(-) -XF(-) -F(+) X + XB(+)X = 0, where F(+/-) = (I -F) D(+/-) and B(+/-) = BD(+/-) with positive diagonal matrices D(+/-) and possibly low-ranked matrices F and B. We prove the existence of the minimal positive solution X* under a set of physically reasonable assumptions and study its numerical computation by fixed-point iteration, Newton's method and the doubling algorithm. We shall also study several special cases. For example when B and F are low ranked then X* = Gamma circle(Sigma(r)(i=1)U(i)V(i)(T)) with low-ranked U(i) and V(i) that can be computed using more efficient iterative processes. Numerical examples will be given to illustrate our theoretical results.
Solution of a nonsymmetric algebraic Riccati equation from a two-dimensional transport model
(2011-01-01)
Li, Tie-Xiang
;
Chu, Eric King-wah
;
Juang, Jong
;
Lin, Wen-Wei
;
電子物理學系
For the steady-state solution of an integral-differential equation from a two-dimensional model in transport theory, we shall derive and study a nonsymmetric algebraic Riccati equation B(-) - XF(-) - F(+)X + XB(+)X = 0, where F(+/-) equivalent to I - (s) over cap PD(+/-), B(-) equivalent to (b) over capl + (s) over capP)D(-))D(-) and B(+) equivalent to (b) over capl + (s) over capP)D(+))D(+) with a nonnegative matrix P, positive diagonal matrices D, and nonnegative parameters f, (b) over cap equivalent to(1 - f) and (s) over cap equivalent to (1 - f). We prove the existence of the minimal nonnegative solution X* under the physically reasonable assumption f + b + s parallel to P(D(+) + D-)parallel to(infinity) < 1, and study its numerical computation by fixed-point iteration, Newton's method and doubling. We shall also study several special cases; e.g. when = 0 and P is low-ranked, then X* = <(s)over cap>/2 UV is low-ranked and can be computed using more efficient iterative processes in U and V. Numerical examples will be given to illustrate our theoretical results. (C) 2010 Elsevier Inc. All rights reserved.
The wavelet transform method applied to a coupled chaotic system with asymmetric coupling schemes
(2013-10-01)
Juang, Jong
;
Li, Chin-Lung
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應用數學系
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Department of Applied Mathematics
The wavelet transform method originated by Wei et al. (2002) [19] is an effective tool for enhancing the transverse stability of the synchronous manifold of a coupled chaotic system. Much of the theoretical study on this matter is centered on networks that are symmetrically coupled. However, in real applications, the coupling topology of a network is often asymmetric; see Belykh et al. (2006) [23,24], Chavez et al. (2005) [25], Hwang et al. (2005) [26], Juang et al. (2007) [17], and Wu (2003) [13]. In this work, a certain type of asymmetric sparse connection topology for networks of coupled chaotic systems is presented. Moreover, our work here represents the first step in understanding how to actually control the stability of global synchronization from dynamical chaos for asymmetrically connected networks of coupled chaotic systems via the wavelet transform method. In particular, we obtain the following results. First, it is shown that the lower bound for achieving synchrony of the coupled chaotic system with the wavelet transform method is independent of the number of nodes. Second, we demonstrate that the wavelet transform method as applied to networks of coupled chaotic systems is even more effective and controllable for asymmetric coupling schemes as compared to the symmetric cases. (C) 2013 Elsevier Ltd. All rights reserved.