• Coupled systems mechanics
• /
• 제2권2호
• /
• pp.159-174
• /
• 2013

The present work aims at investigating the nonlinear dynamics, bifurcations, and stability of an axially accelerating beam with an intermediate spring-support. The problem of a parametrically excited system is addressed for the gyroscopic system. A geometric nonlinearity due to mid-plane stretching is considered and Hamilton's principle is employed to derive the nonlinear equation of motion. The equation is then reduced into a set of nonlinear ordinary differential equations with coupled terms via Galerkin's method. For the system in the sub-critical speed regime, the pseudo-arclength continuation technique is employed to plot the frequency-response curves. The results are presented for the system with and without a three-to-one internal resonance between the first two transverse modes. Also, the global dynamics of the system is investigated using direct time integration of the discretized equations. The mean axial speed and the amplitude of speed variations are varied as the bifurcation parameters and the bifurcation diagrams of Poincare maps are constructed.

• 대한수학회지
• /
• 제48권6호
• /
• pp.1225-1248
• /
• 2011

The present paper is concerned with a two-competitor/oneprey population system with Holling type-II functional response and two discrete delays. By linearizing the system at the positive equilibrium and analyzing the associated characteristic equation, the asymptotic stability of the positive equilibrium and existence of local Hopf bifurcations are investigated. Particularly, by applying the normal form theory and the center manifold reduction for functional differential equations (FDEs) explicit formulae determining the direction of bifurcations and the stability of bifurcating periodic solutions are derived. Finally, to verify our theoretical predictions, some numerical simulations are also included at the end of this paper.

• 대한수학회지
• /
• 제48권6호
• /
• pp.1101-1123
• /
• 2011

Numerical schemes are routinely used to predict the behavior of continuous dynamical systems. All such schemes transform flows into maps, which can possess dynamical behavior deviating from their continuous counterparts. Here the common bifurcations of scalar dynamical systems are transformed under a class of algorithms known as linearized one-point collocation methods. Through the use of normal forms, we prove that each such bifurcation in an originating flow gives rise to an exactly corresponding one in its discretization. The conditions for spurious period doubling behavior under this class of algorithm are derived. We discuss the global behavioral consequences of a singular set induced by the discretizing methods, including loss of monotonicity of solutions, intermittency, and distortion of attractor basins.

• 한국전산유체공학회지
• /
• 제11권2호
• /
• pp.49-55
• /
• 2006

This study investigates the oscillatory thermal convection of a fluid with Pr=0.02 in a wide-gap horizontal annulus with constant heat flux inner wall. When Pr=0.02, dual steady-state flows are not found. After the first Hopf bifurcation from a steady to a time-periodic flow, five successive period-doubling bifurcations are recorded before chaos. The power spectrum shows the $period-2^4\;and\;2^5$ flows clearly, and a window of period $3{\times}2^3$ flow is found in the chaotic regime. The approximate value of the Feigenbaum number for the last three period-doubling bifurcations is 4.76. The transition route to chaos of the present simulations is consistent with the period-doubling route of Feigenbaum.

• 대한수학회지
• /
• 제50권4호
• /
• pp.695-713
• /
• 2013

We formulate and study a predator-prey model with non-monotonic functional response type and weak Allee effects on the prey, which extends the system studied by Ruan and Xiao in [Global analysis in a predator-prey system with nonmonotonic functional response, SIAM J. Appl. Math. 61 (2001), no. 4, 1445-1472] but containing an extra term describing weak Allee effects on the prey. We obtain the global dynamics of the model by combining the global qualitative and bifurcation analysis. Our bifurcation analysis of the model indicates that it exhibits numerous kinds of bifurcation phenomena, including the saddle-node bifurcation, the supercritical and the subcritical Hopf bifurcations, and the homoclinic bifurcation, as the values of parameters vary. In the generic case, the model has the bifurcation of cusp type of codimension 2 (i.e., Bogdanov-Takens bifurcation).

• Kyungpook Mathematical Journal
• /
• 제49권4호
• /
• pp.605-618
• /
• 2009

A stage-structured predator-prey system with time delay and Beddington-DeAngelis functional response is considered. By analyzing the corresponding characteristic equation, the local stability of a positive equilibrium is investigated. The existence of Hopf bifurcations is established. Formulae are derived to determine the direction of bifurcations and the stability of bifurcating periodic solutions by using the normal form theory and center manifold theorem. Numerical simulations are carried out to illustrate the theoretical results.

• International Journal of Contents
• /
• 제2권3호
• /
• pp.27-32
• /
• 2006

We present an effective algorithm for automatic tracing of retinal vessel structure and vascular landmark extraction of bifurcations and ending points. In this paper we deal with vascular patterns from RGB images for personal identification. Vessel tracing algorithms are of interest in a variety of biometric and medical application such as personal identification, biometrics, and ophthalmic disorders like vessel change detection. However eye surface vasculature tracing in RGB images has many problems which are subject to improper illumination, glare, fade-out, shadow and artifacts arising from reflection, refraction, and dispersion. The proposed algorithm on vascular tracing employs multi-stage processing of ten-layers as followings: Image Acquisition, Image Enhancement by gray scale retinal image enhancement, reducing background artifact and illuminations and removing interlacing minute characteristics of vessels, Vascular Structure Extraction by connecting broken vessels, extracting vascular structure using eight directional information, and extracting retinal vascular structure, and Vascular Landmark Extraction by extracting bifurcations and ending points. The results of automatic retinal vessel extraction using jive different thresholds applied 34 eye images are presented. The results of vasculature tracing algorithm shows that the suggested algorithm can obtain not only robust and accurate vessel tracing but also vascular landmarks according to thresholds.

• Advances in nano research
• /
• 제15권1호
• /
• pp.25-34
• /
• 2023

This paper investigates the dynamics and stability of steady states in a continuous and discrete-time single-mode laser system. By using an explicit criteria we explored the Neimark-Sacker bifurcation of the single mode continuous and discrete-time laser model at its positive equilibrium points. Moreover, we discussed the parametric conditions for the existence of period-doubling bifurcations at their positive steady states for the discrete time system. Both types of bifurcations are verified by the Lyapunov exponents, while the maximum Lyapunov ensures chaotic and complex behaviour. Furthermore, in a three-dimensional discrete-time laser model, we used a hybrid control method to control period-doubling and Neimark-Sacker bifurcation. To validate our theoretical discussion, we provide some numerical simulations.

• Steel and Composite Structures
• /
• 제6권5호
• /
• pp.401-415
• /
• 2006

Based on a non-linear model taking into account flexural-torsional couplings, analytical solutions are derived for lateral buckling of simply supported I beams under some representative load cases. A closed form is established for lateral buckling moments. It accounts for bending distribution, load height application and pre-buckling deflections. Coefficients $C_1$ and $C_2$ affected to these parameters are then derived. Regard to well known linear stability solutions, these coefficients are not constant but depend on another coefficient $k_1$ that represents the pre-buckling deflection effects. In numerical simulations, shell elements are used in mesh process. The buckling loads are achieved from solutions of eigenvalue problem and by bifurcations observed on non linear equilibrium paths. It is proved that both the buckling loads derived from linear stability and eigenvalue problem lead to poor results, especially for I sections with large flanges for which the behaviour is predominated by pre-buckling deflection and the coefficient $k_1$ is large. The proposed solutions are in good agreement with numerical bifurcations observed on non linear equilibrium paths.

• 대한전기학회:학술대회논문집
• /
• 대한전기학회 1999년도 하계학술대회 논문집 C
• /
• pp.1308-1310
• /
• 1999

The addition of SVC increases the range of dynamic stability in the power system. The inclusion of SVC is explained in detail and a numerical example is presented. The entire construction of the system A matrix is analyzed, and then the effect of SVC on Hopf bifurcations and the PV curves are illustrated in the cabs study.