ScholarBank@NUShttps://scholarbank.nus.edu.sgThe DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.Thu, 03 Dec 2020 13:29:58 GMT2020-12-03T13:29:58Z50151- Disorder versus order: Global multifractal relationship between topological entropies and universal convergence rateshttps://scholarbank.nus.edu.sg/handle/10635/103145Title: Disorder versus order: Global multifractal relationship between topological entropies and universal convergence rates
Authors: Zhang, X.-S.; Liu, X.-D.; Kwek, K.-H.; Peng, S.-L.
Abstract: A multifractal relation between the topological entropies which describe disorder and the universal convergence rates which describe order is found for the first time in one-dimensional chaotic dynamics. There are infinitely many scales in the interval of primitive words and self-similarity in the interval of non-primitive words. After dealing with the singularity of the universal convergence rates at all points of coarse and fine chaos, we obtain the fractal dimension of the curve h-δ(W)-1/∥W∥ to be 1.65 by the fractal interpolation method based on Barnsley's iterated function systems (IFS). The global metric regularity of the disorder versus the order is characterized by the self-similarity of the intervals and its fractal dimension.
Mon, 12 Feb 1996 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1031451996-02-12T00:00:00Z
- Chaotic dynamics and subharmonic bifurcations in a non-linear systemhttps://scholarbank.nus.edu.sg/handle/10635/102972Title: Chaotic dynamics and subharmonic bifurcations in a non-linear system
Authors: Kwek, K.-H.; Li, J.
Abstract: Examples of deterministic chaos abound. A periodically forced system of phase-locked loops or a pendulum is considered. This system has shown to have various types of chaotic motion, in particular pendulum-type, Duffing-type and their combination-type under certain parameter conditions. There exist some parameter regions such that the combination-type of chaos motions and all possible types of subharmonic solutions occur simultaneously. In this case the system has enormous complexity of chaotic regimes which have been well understood theoretically. Copyright © 1996 Elsevier Science Ltd.
Wed, 01 May 1996 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1029721996-05-01T00:00:00Z
- On a problem related to vortex nucleation of superconductivityhttps://scholarbank.nus.edu.sg/handle/10635/112990Title: On a problem related to vortex nucleation of superconductivity
Authors: Pan, X.-B.; Kwek, K.H.
Abstract: In this paper we study a singularly perturbed nonlinear partial differential system which arises in the mathematical theory of superheating field of superconductivity. We prove that the maximum points of the magnitude of solutions are located near the minimum point of curvature of domain boundary. This verifies rigorously a result of Chapman obtained by formal analysis regarding the location of the vortex nucleation. We also show that the solutions exhibit boundary layers. © 2002 Elsevier Science (USA).
Mon, 10 Jun 2002 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1129902002-06-10T00:00:00Z
- Stability criteria and bounds for limit cycles of relay feedback systemshttps://scholarbank.nus.edu.sg/handle/10635/51047Title: Stability criteria and bounds for limit cycles of relay feedback systems
Authors: Lin, C.; Wang, Q.-G.; Lee, T.H.; Loh, A.P.; Kwek, K.H.
Abstract: This paper considers the problems of determining the stability and computing the bounds for maintaining the stability of limit cycles of linear systems under relay feedback. It derives a stability criterion and presents a region such that every trajectory starting from this region will converge to the limit cycle. The deduction is based on the estimation on the Poincare map which appears as a non-linear function.
Tue, 01 Jun 2004 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/510472004-06-01T00:00:00Z
- Exponential dichotomies and Fredholm operator for parabolic equationshttps://scholarbank.nus.edu.sg/handle/10635/112989Title: Exponential dichotomies and Fredholm operator for parabolic equations
Authors: Kwek, K.-H.; Zhang, W.
Abstract: It proved true for infinite-dimensional systems that the operator F:= d/dt - A(t) is Fredholm when A(t), roughly speaking, admits exponential dichotomies on both R+ and R-. It is also interesting to study its converse problem. Although in [1,2] results were given to the question when the Fredholm alternative for bounded solutions of parabolic equations implies exponential dichotomies, but neither of them gave a direct answer to the operator F. In this paper, we try to obtain a direct answer for parabolic equations defined on a Banach space and to give an approach in the space of functions of compact support. © 2002 Elsevier Science Ltd. All rights reserved.
Thu, 16 May 2002 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1129892002-05-16T00:00:00Z
- Periodic solutions and dynamics of a multimolecular reaction systemhttps://scholarbank.nus.edu.sg/handle/10635/112991Title: Periodic solutions and dynamics of a multimolecular reaction system
Authors: Kwek, K.H.; Zhang, W.
Abstract: In this paper, we consider a general multimolecular reaction system, which appears in biochemistry as a theoretical problem of concentration kinetics and in mathematics as a special polynomial vector field of high degree. We shall investigate its global dynamics and discuss existence and nonexistence of periodic solutions. Although the case of trimolecular reactions and some other special cases were studied extensively, it remains difficult to discuss the general case, that there is involved a lot complicated computation for polynomials of any given degree. In this paper, special techniques are used in computation of Lyapunov numbers for Hopf bifurcation, construction of Dulac auxiliary functions for nonexistence of periodic solution, and determination of qualitative properties of degenerate equilibria. © 2002 Elsevier Science Ltd. All rights reserved.
Fri, 02 Aug 2002 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1129912002-08-02T00:00:00Z
- Global existence for the generalised 2D Ginzburg-Landau equationhttps://scholarbank.nus.edu.sg/handle/10635/115747Title: Global existence for the generalised 2D Ginzburg-Landau equation
Authors: Gao, H.; Kwek, K.-H.
Abstract: Ginzburg-Landau type complex partial differential equations are simplified mathematical models for various pattern formation systems in mechanics, physics and chemistry. Most work so far has concentrated on Ginzburg-Landau type equations with one spatial variable (ID). In this paper, the authors study a complex generalised Ginzburg-Landau equation with two spatial variables (2D) and fifth-order and cubic terms containing derivatives. Based on detail analysis, sufficient conditions for the existence and uniqueness of global solutions are obtained. © Australian Mathematical Society 2003.
Wed, 01 Jan 2003 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1157472003-01-01T00:00:00Z
- Solitary waves and chaotic behavior for a class of coupled field equationshttps://scholarbank.nus.edu.sg/handle/10635/112993Title: Solitary waves and chaotic behavior for a class of coupled field equations
Authors: Kwek, K.-H.; Li, J.
Abstract: The existence of solitary wave solutions, distinct periodic solutions and chaotic behavior was established for a class of coupled field equations. The theory of Hamiltonian systems and dynamical systems to a class of coupled field equations were used to establish the existence. Sufficient conditions to guarantee the existence of the given solutions were provided.
Sat, 01 Mar 2003 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1129932003-03-01T00:00:00Z
- Extended generalised predictive control incorporating feedforwardhttps://scholarbank.nus.edu.sg/handle/10635/72628Title: Extended generalised predictive control incorporating feedforward
Authors: Lee, T.H.; Lai, W.C.; Kwek, K.H.
Abstract: An extension of the generalized predictve control which incorporates feedforward action is presented. This extended controller, referred to as GPCF (extended generalized predictive control incorporating feedforward), is applicable to situations in which there are measurable disturbances affecting the process output. Simulation studies together with an application involving real-time control of a heat-exchanger pilot plant demonstrate that the GPCF offers improved regulation in situations where there are measurable disturbances.
Mon, 01 Jan 1990 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/726281990-01-01T00:00:00Z
- Two algorithms for finding a minimal ratio Hamiltonian cycle in a networkhttps://scholarbank.nus.edu.sg/handle/10635/104404Title: Two algorithms for finding a minimal ratio Hamiltonian cycle in a network
Authors: Tung, C.T.; Kwek, K.H.
Abstract: Two parametric algorithms with the support of subroutine NHORSH for finding a Hamiltonian cycle in a network, which minimizes the time-to-profit ratio, are presented in this paper. The difficulty of solving this problem is concerned with the problem of finding a shortest Hamiltonian cycle in a network which may have negative cycles. An subroutine Algorithm NHORSH has been established to cope with this problem. Validation of the algorithms and two illustrative examples are given. Computational experience is also reported.
Wed, 01 Jan 1997 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1044041997-01-01T00:00:00Z
- An initial boundary value problem of Camassa-Holm equationhttps://scholarbank.nus.edu.sg/handle/10635/102843Title: An initial boundary value problem of Camassa-Holm equation
Authors: Kwek, K.-H.; Gao, H.; Zhang, W.; Qu, C.
Abstract: In this paper, the local existence and blow-up for an initial boundary value problem of the Camassa-Holm equation are obtained. © 2000 American Institute of Physics.
Fri, 01 Dec 2000 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1028432000-12-01T00:00:00Z
- On the Cauchy problem of the Camassa-Holm equationhttps://scholarbank.nus.edu.sg/handle/10635/115841Title: On the Cauchy problem of the Camassa-Holm equation
Authors: Dai, H.-H.; Kwek, K.-H.; Gao, H.-J.; Qu, C.-C.
Abstract: The purpose of this paper is to investigate the Cauchy problem of the Camassa-Holm equation. By using the abstract method proposed and studied by T. Kato and priori estimates, the existence and uniqueness of the global solution to the Cauchy problem of the Camassa-Holm equation in L p frame under certain conditions are obtained. In addition, the continuous dependence of the solution of this equation on the linear dispersive coefficient contained in the equation is obtained. © Higher Education Press and Springer-Verlag 2006.
Sun, 01 Jan 2006 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1158412006-01-01T00:00:00Z
- Partial integrability for general nonlinear systemshttps://scholarbank.nus.edu.sg/handle/10635/115223Title: Partial integrability for general nonlinear systems
Authors: Kwek, K.H.; Li, Y.; Shi, S.
Abstract: The purpose of this paper is to find a criterion of partial integrability for general nonlinear systems. Here partial integrability means the existence of a certain numbers of first integrals less than the number required for the complete integration. We also give an algebraic criterion of partial integrability for general semi-quasihomogeneous systems.
Wed, 01 Jan 2003 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1152232003-01-01T00:00:00Z
- A cubic system with eight small-amplitude limit cycleshttps://scholarbank.nus.edu.sg/handle/10635/102630Title: A cubic system with eight small-amplitude limit cycles
Authors: Ning, S.; Ma, S.; Kwek, K.H.; Zheng, Z.
Abstract: In E.M. James and N.G. Lloyd's paper A Cubic System with Eight Small-Amplitude Limit Cycles [1], a set of conditions is given that ensures the origin to be a fine focus of order eight and eight limit cycles to bifurcate from the origin by perturbing parameters. We find that one of the conditions, a9 = σ*a7, where 666/97 < σ* < 103/15, can be weakened as a9 = σ*a7 or a9 = σ1a7, where 283/125 < σ1 < 284/125. In [1], deriving above conditions is reduced to finding the real solutions of a system of some algebraic equations and inequalities. When verifying these conditions by solving this system in a different ordering, we find another real solution to the system, which is leading to above improvement of the conditions. © 1994.
Fri, 01 Jul 1994 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1026301994-07-01T00:00:00Z
- The global asymptotic stability for F-M equationhttps://scholarbank.nus.edu.sg/handle/10635/104305Title: The global asymptotic stability for F-M equation
Authors: Qu, C.; Kwek, K.-H.; Chen, F.
Abstract: In this paper, we consider a class of equations for the flow and magnetic field within the earth with initial-boundary value problem. We prove the existence of the stationary solution and show that it is global asymptotic stability. © 2000 Elsevier Science Ltd. All rights reserved.
Tue, 01 Feb 2000 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1043052000-02-01T00:00:00Z