scholarly journals Bifurcation Analysis of a Rigid Impact Oscillator with Bilinear Damping

2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
Liping Zhang ◽  
Haibo Jiang ◽  
Yang Liu
Keyword(s):  
Mechanical Model ◽  
Period Doubling ◽  
External Excitation ◽  
Coexisting Attractors ◽  
Impact Oscillator ◽  
Grazing Period ◽  
The Stability ◽  
Complex Phenomena ◽  
Impulsive Switched System ◽  
The Impact

This paper studies a rigid impact oscillator with bilinear damping developed as the mechanical model of an impulsive switched system. The stability and the bifurcation of periodic orbits in the impact oscillator are determined by using the mapping methods. One-parameter bifurcation analyses under variation of forcing frequency and amplitude of external excitation are carried out. Coexisting attractors and various types of bifurcations, such as grazing, period-doubling, and saddle-node, are observed, which show the complex phenomena inhered in this impact oscillator.

scholarly journals Analysis of moored ship oscillations in waves

2020 ◽  
Author(s):  
Д.П. Ковалев ◽  
П.Д. Ковалев ◽  
А.С. Борисов
Keyword(s):  
Dynamic System ◽  
Sea Level ◽  
Order Differential Equation ◽  
External Excitation ◽  
Impact Oscillator ◽  
Mooring Lines ◽  
Sea Level Fluctuations ◽  
Port Area ◽  
Sea Level Fluctuation ◽  
The Impact

В работе рассмотрены особенности колебаний пришвартованного судна для основных портов Сахалинской области, поскольку качка судна у причала может представлять опасность и приводить к повреждению судна или швартовых линий. По данным натурных измерений морского волнения в портовых бухтах рассчитаны спектры колебаний уровня и определены периоды существующих в них волн для диапазона периодов от 2 с до 30 минут. Произведен расчет периодов собственных колебаний (качки) двух типов судов, преимущественно швартующихся в портах. С учетом полученных результатов выполнено моделирование движения судов при волнении как динамической с системы внешним возбуждающим воздействием на основе дифференциального уравнения второго порядка. Показано влияние коэффициента вязкого демпфирования и жесткости швартовых на реакцию динамической системы без удара о причал и для режима ударного осциллятора. Установлено, что в случае прихода в район порта Корсаков длинноволновой зыби движения судна могут переходить в хаотические. The paper considers the peculiarities of moored vessel oscillations for the main ports of the Sakhalin region, since the pitching of the vessel at the berth can be dangerous and lead to damages of the vessel or mooring lines. Spectra of sea level fluctuations and periods of waves in port bays were calculated using sea level fluctuation measurements obtained in the range from 2 seconds to 30 minutes. Calculations of resonance periods (pitching) of two types of vessels mainly moored in ports were done. Taking into consideration these results the simulation of the vessel movement in waves as a dynamic system with an external excitation was performed on the base of second-order differential equation. The influence of viscous damping coefficient and mooring stiffness on the response of the dynamic system is shown for two cases: for system without impact and for the impact oscillator mode. It is established that in the event of a long-wave swell coming to the Korsakov port area, the vessels movements may become chaotic.

Antimonotonicity, Chaos and Multiple Attractors in a Novel Autonomous Jerk Circuit

2017 ◽  
Vol 27 (07) ◽  
pp. 1750100 ◽  
Author(s):  
J. Kengne ◽  
A. Nguomkam Negou ◽  
Z. T. Njitacke
Keyword(s):  
Three Dimensional ◽  
Period Doubling ◽  
Basins Of Attraction ◽  
Electrical Circuit ◽  
Semiconductor Diode ◽  
Chaotic Attractors ◽  
Coexisting Attractors ◽  
Multiple Attractors ◽  
Systematic Analysis ◽  
The Stability

We perform a systematic analysis of a system consisting of a novel jerk circuit obtained by replacing the single semiconductor diode of the original jerk circuit described in [Sprott, 2011a] with a pair of semiconductor diodes connected in antiparallel. The model is described by a continuous time three-dimensional autonomous system with hyperbolic sine nonlinearity, and may be viewed as a control system with nonlinear velocity feedback. The stability of the (unique) fixed point, the local bifurcations, and the discrete symmetries of the model equations are discussed. The complex behavior of the system is categorized in terms of its parameters by using bifurcation diagrams, Lyapunov exponents, time series, Poincaré sections, and basins of attraction. Antimonotonicity, period doubling bifurcation, symmetry restoring crises, chaos, and coexisting bifurcations are reported. More interestingly, one of the key contributions of this work is the finding of various regions in the parameters’ space in which the proposed (“elegant”) jerk circuit experiences the unusual phenomenon of multiple competing attractors (i.e. coexistence of four disconnected periodic and chaotic attractors). The basins of attraction of various coexisting attractors display complexity (i.e. fractal basins boundaries), thus suggesting possible jumps between coexisting attractors in experiment. Results of theoretical analyses are perfectly traced by laboratory experimental measurements. To the best of the authors’ knowledge, the jerk circuit/system introduced in this work represents the simplest electrical circuit (only a quadruple op amplifier chip without any analog multiplier chip) reported to date capable of four disconnected periodic and chaotic attractors for the same parameters setting.

Antimonotonicity, Bifurcation and Multistability in the Vallis Model for El Niño

2019 ◽  
Vol 29 (03) ◽  
pp. 1950032 ◽  
Author(s):  
Karthikeyan Rajagopal ◽  
Sajad Jafari ◽  
Viet-Thanh Pham ◽  
Zhouchao Wei ◽  
Durairaj Premraj ◽  
...  
Keyword(s):  
Hopf Bifurcation ◽  
El Niño ◽  
El Nino ◽  
Equilibrium Points ◽  
Period Doubling ◽  
Period Doubling Bifurcation ◽  
Coexisting Attractors ◽  
The Stability ◽  
First Time ◽  
Parameter Condition

In this paper, the well-known Vallis model for El Niño is analyzed for the parameter condition [Formula: see text]. The conditions for the stability of the equilibrium points are derived. The condition for Hopf bifurcation occurring in the system for [Formula: see text] and [Formula: see text] are investigated. The multistability feature of the Vallis model when [Formula: see text] is explained with forward and backward continuation bifurcation plots and with the coexisting attractors. The creation of period doubling followed by their annihilation via inverse period-doubling bifurcation known as antimonotonicity occurrence in the Vallis model for [Formula: see text] is presented for the first time in the literature.

Neimark-Sacker Bifurcations Near Degenerate Grazing Point in a Two Degree-of-Freedom Impact Oscillator

2018 ◽  
Vol 13 (11) ◽  
Author(s):  
Shan Yin ◽  
Jinchen Ji ◽  
Shuning Deng ◽  
Guilin Wen
Keyword(s):  
Periodic Motion ◽  
Small Neighborhood ◽  
Period Doubling ◽  
Degree Of Freedom ◽  
Grazing Impact ◽  
Mapping Technique ◽  
Impact Oscillator ◽  
Parameter Continuation ◽  
The Impact ◽  
Two Degree Of Freedom

Saddle-node or period-doubling bifurcations of the near-grazing impact periodic motions have been extensively studied in the impact oscillators, but the near-grazing Neimark-Sacker bifurcations have not been discussed yet. For the first time, this paper uncovers the novel dynamic behavior of Neimark-Sacker bifurcations, which can appear in a small neighborhood of the degenerate grazing point in a two degree-of-freedom impact oscillator. The higher order discontinuity mapping technique is used to determine the degenerate grazing point. Then, shooting method is applied to obtain the one-parameter continuation of the elementary impact periodic motion near degenerate grazing point and the peculiar phenomena of Neimark-Sacker bifurcations are revealed consequently. A two-parameter continuation is presented to illustrate the relationship between the observed Neimark-Sacker bifurcations and degenerate grazing point. New features that differ from the reported situations in literature can be found. Finally, the observed Neimark-Sacker bifurcation is verified by checking the existence and stability conditions in line with the generic theory of Neimark-Sacker bifurcation. The unstable bifurcating quasi-periodic motion is numerically demonstrated on the Poincaré section.

Bistable and Coexisting Attractors in Current Modulated Edge Emitting Semiconductor Laser: Control and Microcontroller-Based Design

2021 ◽  
Author(s):  
Nasr Saeed ◽  
Serdar Çiçek ◽  
André Cheage Chamgoué ◽  
Sifeu Takougang Kingni ◽  
Zhouchao Wei
Keyword(s):  
Numerical Analysis ◽  
Semiconductor Laser ◽  
Limit Cycle ◽  
Chaotic Behavior ◽  
Equilibrium Points ◽  
Period Doubling ◽  
Chaotic Attractors ◽  
Coexisting Attractors ◽  
Laser Control ◽  
The Stability

Abstract This paper reports on the numerical analysis, control of coexisting attractors and microcontroller-based design of current modulated edge emitting semiconductor laser (CMEESL). The stability of equilibrium points of solitary edge emitting semiconductor laser found is investigated. By varying the amplitude of modulation current density, CMEESL displays periodic behaviors, period-doubling to chaotic behavior, bistability and coexistence between limit cycle and chaotic attractors. The coexistence between chaotic and limit cycle attractors is destroyed and controlled to a desired monostable trajectory by means of the linear augmentation method. In addition, a microcontroller-based circuit is also designed to indicate that CMEESL can be used in real applications. Microcontroller-based circuit outputs and numerical analysis results confirm each other.

The Dynamics of an Impact Print Hammer

1988 ◽  
Vol 110 (2) ◽  
pp. 193-200 ◽  
Author(s):  
P. C. Tung ◽  
S. W. Shaw
Keyword(s):  
Period Doubling ◽  
Cycle Period ◽  
Flexible Beam ◽  
Qualitative Behavior ◽  
Periodic Motions ◽  
Chaotic Motions ◽  
Linear Spring ◽  
The Stability ◽  
Energy Type ◽  
The Impact

A mathematical model is developed to describe the characteristic behavior of an impact print hammer of the stored energy type. The armature of the impact print hammer is represented by a rigid mass held against a backstop by a preloaded linear spring with negative stiffness which characterizes the net effect of a permanent magnet and a prestressed flexible beam acting on the armature. Periodic sine pulses are adopted to represent currents which release the armature to strike the ribbon and paper which is represented by a linear spring and a linear viscous dashpot. A coefficient of restitution is employed to characterize the instantaneous behavior of impact and rebound at the backstop. In this paper, periodic motions with n impacts against the backstop per forcing cycle, period doubling bifurcations, and chaotic motions are found. The stability of the periodic motions is investigated as is the influence of various parameters on the performance of the impact print hammer. With this simple model we can predict much of the qualitative behavior of the actual physical system.

Experimental study of impact oscillator with one-sided elastic constraint

2007 ◽  
Vol 366 (1866) ◽  
pp. 679-705 ◽  
Author(s):  
James Ing ◽  
Ekaterina Pavlovskaia ◽  
Marian Wiercigroch ◽  
Soumitro Banerjee
Keyword(s):  
Excitation Frequency ◽  
Excitation Amplitude ◽  
Experimental Investigations ◽  
Coexisting Attractors ◽  
Impact Oscillator ◽  
Good Correspondence ◽  
Experimental Procedure ◽  
Acceleration Signal ◽  
The Stability ◽  
Elastic Constraint

In this paper, extensive experimental investigations of an impact oscillator with a one-sided elastic constraint are presented. Different bifurcation scenarios under varying the excitation frequency near grazing are shown for a number of values of the excitation amplitude. The mass acceleration signal is used to effectively detect contacts with the secondary spring. The most typical recorded scenario is when a non-impacting periodic orbit bifurcates into an impacting one via grazing mechanism. The resulting orbit can be stable, but in many cases it loses stability through grazing. Following such an event, the evolution of the attractor is governed by a complex interplay between smooth and non-smooth bifurcations. In some cases, the occurrence of coexisting attractors is manifested through discontinuous transition from one orbit to another through boundary crisis. The stability of non-impacting and impacting period-1 orbits is then studied using a newly proposed experimental procedure. The results are compared with the predictions obtained from standard theoretical stability analysis and a good correspondence between them is shown for different stiffness ratios. A mathematical model of a damped impact oscillator with one-sided elastic constraint is used in the theoretical studies.

Dietary Vitamin and Stability of Oral Anticoagulation: Proposal of a Diet with Constant Vitamin K1 Content

1997 ◽  
Vol 77 (03) ◽  
pp. 504-509 ◽  
Author(s):  
Sarah L Booth ◽  
Jacqueline M Charnley ◽  
James A Sadowski ◽  
Edward Saltzman ◽  
Edwin G Bovill ◽  
...  
Keyword(s):  
Dietary Intake ◽  
Vitamin K ◽  
High Performance ◽  
Case Reports ◽  
Food Composition ◽  
Dietary Guidelines ◽  
Dietary Vitamin ◽  
Vitamin K1 ◽  
The Stability ◽  
The Impact

SummaryCase reports cited in Medline or Biological Abstracts (1966-1996) were reviewed to evaluate the impact of vitamin K1 dietary intake on the stability of anticoagulant control in patients using coumarin derivatives. Reported nutrient-drug interactions cannot always be explained by the vitamin K1 content of the food items. However, metabolic data indicate that a consistent dietary intake of vitamin K is important to attain a daily equilibrium in vitamin K status. We report a diet that provides a stable intake of vitamin K1, equivalent to the current U.S. Recommended Dietary Allowance, using food composition data derived from high-performance liquid chromatography. Inconsistencies in the published literature indicate that prospective clinical studies should be undertaken to clarify the putative dietary vitamin K1-coumarin interaction. The dietary guidelines reported here may be used in such studies.

IMPACT OF GOVERNMENT DEBT ON FINANCIAL SECURITY OF UKRAINE

2017 ◽  
Author(s):  
Olena Pikaliuk ◽  
◽  
Dmitry Kovalenko ◽  
Keyword(s):  
Economic Development ◽  
Public Debt ◽  
Positive Impact ◽  
The State ◽  
Financial Security ◽  
State Budget ◽  
The Public ◽  
Debt Security ◽  
The Stability ◽  
The Impact

One of the main criteria for economic development is the size of the public debt and its dynamics. The article considers the impact of public debt on the financial security of Ukraine. The views of scientists on the essence of public debt and financial security of the state are substantiated. An analysis of the dynamics and structure of public debt of Ukraine for 2014-2019. It is proved that one of the main criteria for economic development is the size of public debt and its dynamics. State budget deficit, attracting and using loans to cover it have led to the formation and significant growth of public debt in Ukraine. The volume of public debt indicates an increase in the debt security of the state, which is a component of financial security. Therefore, the issue of the impact of public debt on the financial security of Ukraine is becoming increasingly relevant. The constant growth and large amounts of debt make it necessary to study it, which will have a positive impact on economic processes that will ensure the stability of the financial system and enhance its security.

Influence of internal and external risks on sustainability of financial system of Аltai krai

2018 ◽  
Vol 35 (4) ◽  
pp. 133-136
Author(s):  
R. N. Ibragimov
Keyword(s):  
Sustainable Development ◽  
Financial Stability ◽  
Management Strategy ◽  
Financial System ◽  
Risk Management Strategy ◽  
The Sustainable Development ◽  
The Stability ◽  
The Impact

The article examines the impact of internal and external risks on the stability of the financial system of the Altai Territory. Classification of internal and external risks of decline, affecting the sustainable development of the financial system, is presented. A risk management strategy is proposed that will allow monitoring of risks, thereby these measures will help reduce the loss of financial stability and ensure the long-term development of the economy of the region.

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