Empirical evaluation of influential factors on bifurcation in macroscopic fundamental diagrams

Shim, Jisup,Yeo, Jiho,Lee, Sujin,Hamdar, Samer H.,Jang, Kitae Elsevier 2019 Transportation research. Part C, Emerging technolo Vol.102 No.-

<P><B>Abstract</B></P> <P>Observations from empirical data in the roadway network showed that the relation between averages of network flow versus density often exhibit hysteresis and bifurcation phenomena, which may obscure the reproducibility of a well-defined macroscopic fundamental diagram (MFD). In this paper, we analyzed large-scale trip data from passenger vehicles in an urban network of South Korea and evaluated the shapes of MFDs over many days. It was found that MFDs have two distinctive, reproducible forms: a well-defined, unique relation on weekends and a bifurcation in high-density regime on weekdays.</P> <P>With regard to the bifurcation, we observed higher network flows in the morning and lower network flows in the evening for the same average network density. This implies that the same set of drivers in the network collectively formed two different trip patterns. Hence, we evaluated possible factors that may have effects on the bifurcation phenomenon. In view of this, four factors – heterogeneity, trip completion rate, detouring ratio and commute trips – were analyzed in this study. The findings showed that travelers’ detours could be a key factor for the occurrence of bifurcation because, by detouring travelers improve neither their own travel times nor network-wide travel times, and thereby degrade the network production.</P> <P><B>Highlights</B></P> <P> <UL> <LI> Large-scale trip data from passenger vehicles in an urban network were analyzed. </LI> <LI> Distinctive macroscopic fundamental diagrams were observed on weekends and weekdays. </LI> <LI> Consistent and reproducible bifurcation was observed across weekdays. </LI> <LI> Upper bifurcation branch was formed in weekday mornings. </LI> <LI> Detouring trips were a key factor for the occurrence of bifurcation. </LI> </UL> </P>

Bifurcation-enhanced ultrahigh sensitivity of a buckled cantilever

An, Sangmin,Kim, Bongsu,Kwon, Soyoung,Moon, Geol,Lee, Manhee,Jhe, Wonho National Academy of Sciences 2018 Proceedings of the National Academy of Sciences Vol.115 No.12

<▼1><P><B>Significance</B></P><P>This work brings together the fields of nonlinear dynamics and precision measurement, aiming to develop a highly sensitive nonlinear mechanical force sensor. We use dynamic force spectroscopy of the buckled cantilever tip in an ambient condition, which allows sensitive detection of the noise-induced flipping near the bifurcation point. Key parameters, such as the fluctuation enhancement and the activation barrier of the buckling-to-flipping transition, lead to realization of the bifurcation-enhanced sensor. We contiguously observe the buckling–flipping dynamic transition of the softened tip resulting from the competition between fluctuation and bifurcation, providing the in situ continuous sensing of the mechanical vibrations. This work not only furthers our understanding of nonlinear dynamics at the nanoscale, but also is a stepping stone toward the highly sensitive mechanical sensor.</P></▼1><▼2><P>Buckling, first introduced by Euler in 1744 [Euler L (1744) <I>Opera Omnia I</I> 24:231], a sudden mechanical sideways deflection of a structural member under compressive stress, represents a bifurcation in the solution to the equations of static equilibrium. Although it has been investigated in diverse research areas, such a common nonlinear phenomenon may be useful to devise a unique mechanical sensor that addresses the still-challenging features, such as the enhanced sensitivity and polarization-dependent detection capability. We demonstrate the bifurcation-enhanced sensitive measurement of mechanical vibrations using the nonlinear buckled cantilever tip in ambient conditions. The cantilever, initially buckled with its tip pinned, flips its buckling near the bifurcation point (BP), where the buckled tip becomes softened. The enhanced mechanical sensitivity results from the increasing fluctuations, unlike the typical linear sensors, which facilitate the noise-induced buckling-to-flipping transition of the softened cantilever. This allows the in situ continuous or repeated single-shot detection of the surface acoustic waves of different polarizations without any noticeable wear of the tip. We obtained the sensitivity above 10<SUP>6</SUP> V(m/s)<SUP>−1</SUP>, a 1,000-fold enhancement over the conventional seismometers. Our results lead to development of mechanical sensors of high sensitivity, reproducibility, and durability, which may be applied to detect, e.g., the directional surface waves on the laboratory as well as the geological scale.</P></▼2>

Closed-Loop Bifurcation Analysis for a Novel Moving Mass Flight Vehicle

Zhitao Liu,Changsheng Gao,Jianqing Li,Wuxing Jing 한국항공우주학회 2018 International Journal of Aeronautical and Space Sc Vol.19 No.4

In this paper, nonlinear dynamics properties regarding a novel moving mass flight vehicle with large mass ratio are investigated based on bifurcation theory and continuation methods. Of particular interest is the impact of variation of command angle-of-attack and moving mass parameters on the controlled system. The nonlinear longitudinal dynamics model is established and the controller is designed using Immersion and Invariance method. Bifurcation analysis is conducted both from the prospective of static bifurcation and dynamical bifurcation, results of the closed-loop system are compared with the uncontrolled case. Numerical results obtained from bifurcation diagrams indicate that although the introduction of control system is capable of eliminating unstable regions caused by the variation of moving mass parameters, the change of command angle-of-attack still lead to Hopf bifurcation. Furthermore, analysis of limit cycle branch reveals the consecutive birth of Limit Point of Cycle bifurcation (LPC), then based on which a more detailed nonlinear dynamics process of the closed-loop system is analyzed.

Critical Slowing Down과 Phase Radius Filtering을 이용한 Supercritical Hopf Bifurcation의 예측과 Flutter 모델에의 적용

임주섭,이상욱,김태욱 한국항공우주학회 2015 한국항공우주학회 학술발표회 논문집 Vol.2015 No.4

Critical slowing down은 supercritical/subcritical Hopf bifurcation 등의 비선형 불안정 상태의 전조신호 중의 하나이다. Critical slowing down은 안정상태의 시스템이 외란에 의한 perturbation으로부터 안정상태로 돌아가는 과정에서 관측될 수 있으나, 안정상태로 돌아가는 과정에는 시스템 특성에 따른 다른 신호들이 혼재하는 것이 일반적이다. 본 발표 논문은 다양한 신호들 속에서, bifurcation 예측을 위한 critical slowing down 신호를 효과적으로 관측하기 위해 제안된 phase radius filtering 기법에 대하여 다루고 있다. Phase radius filtering에 대하여 간단한 수학 모델을 통해 소개하고, 이를 활용하여 비선형 비틀림 특성을 갖는 2차원 익형 모델에 대한 limit cycle flutter에 대한 예측을 시뮬레이션을 통해 소개하였다. Critical slowing down is one of the precursory signals for nonlinear instability such as supercritical/subcritical Hopf bifurcation. While critical slowing down can be observed when the stable system get stabilized from external perturbation, there are generally mixed signals from difference sources of the system characteristics during recovery of the stability. Herein, phase radius filtering is introduced as an approach to effectively monitor critical slowing down for bifurcation forecasting. After fundamental discussion about phase radius filtering for a simple mathematical model is presented, numerical example of bifurcation forecasting for limit cycle flutter of the 2D airfoil model with pitch nonlinearity.

Hopf bifurcation analysis and optimal control of Treatment in a delayed oncolytic virus dynamics

Kim, Kwang Su,Kim, Sangil,Jung, Il Hyo Elsevier 2018 Mathematics and computers in simulation Vol.149 No.-

<P><B>Abstract</B></P> <P>During cancer viral therapy, there is a time delay from the initial virus infection of the tumor cells up to the time those infected cells reach the stage of being able to infect other cells. Because the duration of this “time delay” varies with each virus, it is important to understand how the delay affects the cancer viral therapy. Herein, we have introduced a mathematical model to explain this time delay. The existence of equilibrium (i.e., whether the treatment was unsuccessful or partially successful) was determined in this model by using a basic reproduction ratio of viral infection ( <SUB> R 0 </SUB> ) to immune response ( <SUB> R 1 </SUB> ). By using the bifurcation parameter as a delay τ , we proved a sufficient condition for the local asymptotic stability of two equilibrium points and the existence of Hopf bifurcation. In addition, we observed that the time delay caused the partial success equilibrium to be unstable and worked together with Hopf bifurcation to create a stable periodic oscillation. Therefore, we investigated the effects of viral cytotoxicity or infection rate, which are characteristics of viruses, on the Hopf bifurcation point. In order to support the analytical findings and to further analyze the effects of delay during cancer viral therapy, we reconstructed the model to include two controls: cancer viral therapy and immunotherapy. In addition, using numerical simulation, we suggested an optimal control problem to examine the effects of delay on oncolytic immunotherapy.</P> <P><B>Highlights</B></P> <P> <UL> <LI> This study performed a stability and bifurcation analysis of the suggested model, which includes a time delay. </LI> <LI> Existence of Hopf bifurcation was proved to explain it as a time delay change. </LI> <LI> We identified the conditions that allow a Hopf bifurcation point to exist. </LI> <LI> Optimal oncolytic immunotherapy treatment method was investigated according to the time delay. </LI> </UL> </P>

3차원 생태계모델의 진동현상

최설매,정진수,한승기 한국물리학회 2011 새물리 Vol.61 No.6

In the three-dimensional population dynamics model of a two-species plant-herbivore system constructed based on the agent model by using the NetLogo simulation software, we observed the presence of a steady state and an oscillatory state. The steady state is characterized by the concentrations of the plant and the herbivore converging asymptotically to fixed values while the oscillatory state is characterized by concentrations that oscillate with time. According to a bifurcation analysis, the oscillatory state emerges from the steady state via a subcritical Hopf bifurcation with increasing birth rate of the herbivore and disappears through a supercritical Hopf bifurcation. We also observed that the two states, the steady state and the oscillatory state, coexist near the subcritical Hopf bifurcation point. Finally, we constructed a phase diagram of the dynamic model in the two-dimensional parameter space of the birth rate and the death rate and the compared it with the agent-based simulation result. NetLogo 시뮬레이션에 기반하여 구축한 식물-초식자(plant-herbivore)시스템의 3차원 모델에서 식물-초식자 개체군(population) 밀도의상호변화에는 정상상태(steady state)와 진동상태(oscillation state)가존재한다. 정상상태에서 식물-초식자의 밀도는 시간이 경과함에 따라각자의 평형밀도로 수렴하고 진동상태에서 식물-초식자의 밀도는 시간에따라 주기적으로 진동하게 된다. 3차원 모델에 대한분기분석(bifurcation analysis)에서 초식자의 출산율이 증가함에 따라정상상태에서 버금임계 호프 분기(subcritical Hopf bifurcation)를 통해진동상태로 되고 또 진동상태에서 초임계 호프 분기(supercritical Hopf bifurcation)를 통해 정상상태로 된다는 결과를 얻었다. 또한 버금임계호프 분기가 일어나는 영역에서는 정상상태와 진동상태가 공존하는현상도 보여주었다. 시뮬레이션에서도 정상상태와 진동상태가 존재하는데초식자의 출산율과 사망률에 따른 상그림(phase diagram)을 통해 3차원모델과 시뮬레이션 모델의 결과를 비교하였다.

전압안정도 향상을 위한 FACTS의 적용과 Bifurcation이론 해석

주기성,김진오 전력전자학회 2000 전력전자학회 논문지 Vol.5 No.4

본 논문온 전압안정도에 Brfurcation 이론을 적용하여 해석하고, FACTS기가인 SVC와 UPFC를 전력계통에 연계하였을 때 전압안정도가 향상되는 효과를 보여주고 있다. 전압안정도는 일반적으로 시스템 파라미터(유효전력 또는 무효전력}를 포행하는 고도의 비선형 동적시스템의 식들에 의해 표현된다. 때때로 전력계통에서의 파라미터 변이는 시스템 불안정을 일으키는 복잡한 동작을 일으킬 수도 있다. 전력계통에서의 FACTS의 연계는 이러한 전압안정도의 범위를 증가시킨다. FACTS를 이용하여 불안정한 HopF Bifurcation과 Saddle Node Bihlfcation을 지연시킴에 의해서 전압안정도기 향상됨을 사례연구를 통하여 입증하였다. This paper proposes a bifurcation theory method applied for voltage stability analysis and shows the improvement of voltage stability by attaching the FACTS devices in the power system. A power system is generally expressed by a set of equations of highly nonlinear dynamical system which includes system parameters(real or reactive power). Sometimes variation of parameters in the system may result in complication behaviors which give rise to system instability. The addition of FACTS increases the range of voltage stability in the power system. The effect of FACTS which improves voltage stability are illustrated in the case studies by delaying of Unstable Hopf Bifurcation and Saddle Node Bifurcation.

Discretization of laser model with bifurcation analysis and chaos control

Qamar Din,Waqas Ishaque,Iqra Maqsood,Abdelouahed Tounsi Techno-Press 2023 Advances in nano research Vol.15 No.1

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.

Global Periodic Solutions in a Delayed Predator-Prey System with Holling II Functional Response

Jiang, Zhichao,Wang, Hongtao,Wang, Hongmei Department of Mathematics 2010 Kyungpook mathematical journal Vol.50 No.2

We consider a delayed predator-prey system with Holling II functional response. Firstly, the paper considers the stability and local Hopf bifurcation for a delayed prey-predator model using the basic theorem on zeros of general transcendental function, which was established by Cook etc.. Secondly, special attention is paid to the global existence of periodic solutions bifurcating from Hopf bifurcations. By using a global Hopf bifurcation result due to Wu, we show that the local Hopf bifurcation implies the global Hopf bifurcation after the second critical value of delay. Finally, several numerical simulations supporting the theoretical analysis are given.

비틀림 비선형성을 갖는 2차원 익형의 Limit Cycle Flutter 해석과 Critical Slowing Down

임주섭(Joosup Lim),김태욱(Tae-uk Kim),황인희(In-hee Hwang) 대한기계학회 2013 대한기계학회 춘추학술대회 Vol.2013 No.12

In this paper, limit cycle flutter induced by Hopf bifurcation is studied with nonlinear system analysis approach and observed for the critical slowing down phenomenon. Considering an attractor of the dynamics of a system, when a small perturbation is applied to the system, the dynamics converge toward the attractor at some rate. The critical slowing down means that this recovery rate approaches zero as a parameter of the system varies and the size of the basin of attraction shrinks to nil. Consequently, in the pre-bifurcation regime, the recovery rates decrease as the system approaches the bifurcation. This phenomenon is one of the features used to forecast bifurcation before they actually occur. Therefore, studying the critical slowing down for limit cycle flutter behavior would have potential applicability for forecasting those types of flutter. Herein, modeling and nonlinear system analysis of the 2D airfoil with torsional nonlinearity have been discussed, followed by observation of the critical slowing down phenomenon.