• Journal of applied mathematics & informatics
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• v.29 no.3_4
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• pp.879-889
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• 2011

In this paper, we investigate the local asymptotic stability, the invariant intervals, the global attractivity of the equilibrium points, and the asymptotic behavior of the solutions of the difference equation $x_{n+1}=\frac{a+bx_nx_{n-k}}{A+Bx_n+Cx_{n-k}}$, n = 0, 1,${\ldots}$, where the parameters a, b, A, B, C and the initial conditions $x_{-k}$, ${\ldots}$, $x_{-1}$, $x_0$ are positive real numbers.

• Structural Engineering and Mechanics
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• v.5 no.5
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• pp.577-586
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• 1997

In nonlinear finite element stability analysis of structures, the foremost necessary procedure is the computation to precisely locate a singular equilibrium point, at which the instability occurs. The present study describes global and local procedures for the computation of stability points including bifurcation points and limit points. The starting point, at which the procedure will be initiated, may be close to or arbitrarily far away from the target point. It may also be an equilibrium point or non-equilibrium point. Apart from the usual equilibrium path, bypass and homotopy path are proposed as the global path to the stability point. A local iterative method is necessary, when it is inspected that the computed path point is sufficiently close to the stability point.

• Journal of applied mathematics & informatics
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• v.19 no.1_2
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• pp.327-344
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• 2005

The first part of the paper deals with a brief introduction of the plant-herbivore model system along with deterministic analysis of local stability and Hopf-bifurcations. The second part consists of stability analysis of the limit cycle arising from Hopf-bifurcation and uniqueness of limit cycle. The third part deals with the study of global stability of the model system under consideration.

• Bulletin of the Korean Mathematical Society
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• v.50 no.6
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• pp.1827-1840
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• 2013

This paper is concerned with the positive steady states of a diffusive Holling type II predator-prey system, in which two predators and one prey are involved. Under homogeneous Neumann boundary conditions, the local and global asymptotic stability of the spatially homogeneous positive steady state are discussed. Moreover, the large diffusion of predator is considered by proving the nonexistence of non-constant positive steady states, which gives some descriptions of the effect of diffusion on the pattern formation.

• Structural Engineering and Mechanics
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• v.12 no.5
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• pp.507-526
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• 2001

In standard finite element algorithms, the local stability conditions are not accounted for in the formulation of the tangent stiffness matrix. As a result, the loss of the local stability is not adequately related to the onset of the global instability. The phenomenon typically arises with material-type localizations, such as shear bands and plastic hinges. This paper addresses the problem in the context of the planar, finite-strain, rate-independent, materially non-linear beam theory, although the proposed technology is in principle not limited to beam structures. A weak formulation of Reissner's finite-strain beam theory is first presented, where the pseudocurvature of the deformed axis is the only unknown function. We further derive the local stability conditions for the large deformation case, and suggest various possible combinations of the interpolation and numerical integration schemes that trigger the simultaneous loss of the local and global instabilities of a statically determined beam. For practical applications, we advice on a procedure that uses a special numerical integration rule, where interpolation nodes and integration points are equal in number, but not in locations, except for the point of the local instability, where the interpolation node and the integration point coalesce. Provided that the point of instability is an end-point of the beam-a condition often met in engineering practice-the procedure simplifies substantially; one of such algorithms uses the combination of the Lagrangian interpolation and Lobatto's integration. The present paper uses the Galerkin finite element discretization, but a conceptually similar technology could be extended to other discretization methods.

• Communications of the Korean Mathematical Society
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• v.32 no.4
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• pp.851-864
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• 2017

The problems of global and local exponential stability analysis of a class of nonlinear non-autonomous difference equations in Banach spaces are studied in this paper. By a novel comparison technique, new explicit exponential stability conditions are derived. Numerical examples are given to illustrate the effectiveness of the obtained results.

• Journal of applied mathematics & informatics
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• v.19 no.1_2
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• pp.311-326
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• 2005

The paper deals with the problem of selective harvesting in a prey-predator model with predator self limitation. Criteria for local stability and global stability for both the exploited and unexploited system are derived. The effort has been considered as a dynamic variable and taxation as a control instrument to protect the fish populations from over exploitation. Finally, the optimal taxation policy is discussed with the help of control theory.

• Journal of the Korean Institute of Telematics and Electronics C
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• v.34C no.5
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• pp.43-54
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• 1997

The objective of this paper is to present a controller-design method that can guarantee the global stability for nonlinear systems described by takagi-sugeno fuzzy models, and to apply the method to a typical nonlinear control problem. The presented method gives us a compensated fuzzy controller through the following major steps: First, if each local linear model of a given takagi-sugeno fuzzy system does not have the same input matrix, the method expands the system into the one with a method finds a takagi-sugeno fuzzy controller guaranteeing the global stability of the closed loop via solving relevant linear matrix inequalities. Compared to the conventional PDC (paralled distributed compensation) technique, the presented method has an advantage that trial-and-errors to check the global stability are not necessary. An illustrative simulation on the control of inverted pendulum is performed to demonstrate the applicability of the presented method, and its results show that a controller satisfying the global stability and robustness can be obtained by the method.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1998.10a
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• pp.201-207
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• 1998

In this study, a geometric nonlinear analysis formulation for spatial frames is developed using the 3D stability functions. For the formulation, the relationships of local and global coordinate systems in force, deformation, and the initial and current configurations of a frame are derived. The force-deformation relationship in global coordinate system is derived as well. The developed formulation is verified in each derivation by reducing the derived equations into 2D equations. The gradual plastification of connections and critical sections can be implemented effectively to this formulation for the complete second order inelastic advanced analysis of spatial frames.

• Journal of Information Technology Applications and Management
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• v.22 no.1
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• pp.131-152
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• 2015

Environmental differences across countries such as socio-cultural, political, economic, and technological differences require business strategies of multinational corporations to vary business practices across regions. Despite the keen awareness of the necessity for strategic adaptation to local context, IS management and strategy tend to remain similar across countries. One of the reasons is to maintain the stability and compatibility of information technology infrastructure. After a careful observation of retail business practice, this study finds IS strategy should also be highly responsive to the local context. This study shows how information resources including systems architecture, processes, human resources, and national context are interlinked together. Despite global excellence in general systems management, failure in such alignment can be a serious problem in extending competitive advantages across regions. This study aims to reveal issues to be taken care of in order to accomplish global technological alignment. Results of this study provide senior management with guidelines and a framework for aligning IT with regional strategic thrust that can improve local responsiveness of multinational companies.