scholarly journals Lyapunov Indices and the Poincare Mapping in a Study of the Stability of the Krebs Cycle

2015 ◽  
Vol 60 (6) ◽  
pp. 561-574 ◽  
Author(s):  
V.I. Grytsay ◽  
Keyword(s):  
Krebs Cycle ◽  
Poincaré Mapping ◽  
Poincare Mapping ◽  
The Stability

Stability analysis of an electrically actuated microbeam using the Melnikov theorem and Poincaré mapping

2010 ◽  
Vol 225 (2) ◽  
pp. 488-497 ◽  
Author(s):  
M Zamanian ◽  
S E Khadem
Keyword(s):  
Phase Plane ◽  
Chaotic Behaviour ◽  
Damping Factor ◽  
Poincaré Mapping ◽  
System A ◽  
Poincare Mapping ◽  
Electrically Actuated ◽  
Electric Actuation ◽  
The Stability ◽  
Parameter Values

In this article, the stability of a microbeam under an electric actuation is studied. The electric actuation is induced by applying a voltage between the microbeam and an electrode plate that lies at the opposite side of the microbeam. In microswitches, the electric actuation is applied as a DC voltage, and in microresonators it is applied as a combination of AC—DC voltages. It is assumed that the midplane of the microbeam is stretched when it is deflected. It is also shown that by the altering DC electric actuation as a control parameter in a microswitch system, a stable and an unstable branches of equilibrium solution is observed, which meet each other at a saddle-node bifurcation point. The stability of a microresonator is studied using the phase plane diagram and Poincaré mapping. It is shown that depending on the value of damping factor, AC and DC electric voltages, and other parameters of the microresonator, a periodic solution, a quasi periodic, or a pull-in instability may be realized. The prediction of possible chaotic behaviour for microresonator is studied using the Melnikov theorem. It is shown that although for selected domain of system parameters the Melnikov function is satisfied for occurrence of chaotic behaviour, for theses parameter values the pull-in instability occurs before going into the chaotic behaviour. Briefly, the system does not realize any chaotic behaviour.

Global Chaos in a Periodically Forced, Linear System With a Dead-Zone Restoring Force

2003 ◽  
Author(s):  
Albert C. J. Luo ◽  
Santhosh Menon
Keyword(s):  
Linear System ◽  
Periodic Motion ◽  
Dead Zone ◽  
Poincaré Mapping ◽  
Periodic Motions ◽  
Restoring Force ◽  
Chaotic Motions ◽  
Mapping Structures ◽  
Poincare Mapping ◽  
The Stability

The Poincare mapping and the corresponding mapping sections for global motions in a linear system possessing a dead-zone restoring force are developed through the switching planes pertaining to the two constraints. The global periodic motions based on the Poincare mapping are determined, and the analysis for the stability and bifurcation of periodic motion is carried out. From the global periodic motions, the global chaos in such a system is investigated numerically. The bifurcation scenario with varying parameters was presented. The mapping structures of periodic and chaotic motions are discussed. The Poincare mapping sections for global chaos are given for illustration. The grazing phenomenon embedded in chaotic motion is observed.

scholarly journals An Improved Method for Estimating the Domain of Attraction of Passive Biped Walker

2019 ◽  
Vol 2019 ◽  
pp. 1-11 ◽  
Author(s):  
Yu Wang ◽  
Heng Cao ◽  
JinLin Jiang
Keyword(s):  
Domain Of Attraction ◽  
Mapping Method ◽  
Simple Cell ◽  
Iteration Algorithm ◽  
Poincaré Mapping ◽  
Cell Mapping ◽  
Improved Method ◽  
Stable Domain ◽  
Simple Cell Mapping ◽  
Poincare Mapping

An indicator of a passive biped walker’s global stability is its domain of attraction, which is usually estimated by the simple cell mapping method. It needs to calculate a large number of cells’ Poincare mapping result in the estimating process. However, the Poincare mapping is usually computationally expensive and time-consuming due to the complex dynamical equation of the passive biped walker. How to estimate the domain of attraction efficiently and reliably is a problem to be solved. Based on the simple cell mapping method, an improved method is proposed to solve it. The proposed method uses the multiple iteration algorithm to calculate a stable domain of attraction and effectively decreases the total number of Poincare mappings. Through the simulation of the simplest passive biped walker, the improved method can obtain the same domain of attraction as that calculated using the simple cell mapping method and reduce calculation time significantly. Furthermore, this improved method not only proposes a way of rapid estimating the domain of attraction, but also provides a feasible tool for selecting the domain of interest and its discretization level.

scholarly journals Study on Clearance-Rubbing Dynamic Behavior of 2-DOF Supporting System of Magnetic-Liquid Double Suspension Bearing

Processes ◽  
2020 ◽  
Vol 8 (8) ◽  
pp. 973
Author(s):  
Jianhua Zhao ◽  
Weidong Yan ◽  
Ziqi Wang ◽  
Dianrong Gao ◽  
Guojun Du
Keyword(s):  
Stable Operation ◽  
Poincaré Mapping ◽  
Eccentricity Ratio ◽  
Magnetic Liquid ◽  
Rotating Speed ◽  
Single Period ◽  
Operating Stability ◽  
Poincare Mapping ◽  
Assembly Error ◽  
Mapping Point

As a new type of suspension bearing, Magnetic-Liquid Double Suspension Bearing (MLDSB) is mainly supported by electromagnetic suspension and supplemented by hydrostatic supporting. Its bearing capacity and stiffness can be greatly improved. Because of the small liquid film thickness (it is smaller 10 times than air gap), the eccentricity, crack, bending of the rotor, and the assembly error, it is easy to cause a clearance-rubbing fault between the rotor and stator. The coating can be worn and peeled, the operating stability can be reduced, and then it is one of the key problems of restricting the development and application of MLDSB. Therefore, the clearance-rubbing dynamic equation of 2-DOF system of MLDSB is established and converted into Taylor Series form and the nonlinear components are retained. Dimensionless treatment is carried out by dimensional normalization method. Finally, the rotor displacement response under different rotor eccentricity ratio and rotating speeds is numerically simulated. The studies show that the trajectory of the rotor is periodic elliptic without clearance-rubbing phenomenon when the eccentricity ratio is less than 0.2, while the rotor is greatly affected by the rotation speed and a variety of motions, such as single-period, quasi-period, double-period and chaos, are presented when greater than 0.3. Within the largest range of rotating speed and eccentricity ratio, the rotor presents the single-period trajectory, and then the number of Poincare mapping point is 1, without a clearance-rubbing fault. When the rotational speed is in the scope of (9, 13) krpm and the eccentricity ratio is in the scope of (0.27, 0.4), the number of Poincare mapping point is more than one, the maximum dimensionless rubbing force is −5.7, and then clearance-rubbing fault occurs. The research can provide a theoretical basis for the safe and stable operation of MLDSB.

Optical properties and Poincaré mapping in spherical multilayered systems: periodic, quasiperiodic, and disordered

2014 ◽  
Vol 38 (10) ◽  
pp. 2027-2034
Author(s):  
A. Díaz-de-Anda ◽  
M. Nájera-Villeda ◽  
Gennadiy Burlak ◽  
A. Zamudio-Lara
Keyword(s):  
Optical Properties ◽  
Poincaré Mapping ◽  
Poincare Mapping ◽  
Multilayered Systems

POINCARÉ MAPPING OF CONTINUOUS RECURRENT NEURAL NETWORKS EXCITED BY TEMPORAL EXTERNAL INPUT

2000 ◽  
Vol 10 (07) ◽  
pp. 1677-1695 ◽  
Author(s):  
SHOZO SATO ◽  
KAZUTOSHI GOHARA
Keyword(s):  
Neural Networks ◽  
Bifurcation Diagram ◽  
Recurrent Neural Networks ◽  
Continuous Time ◽  
Product Space ◽  
External Input ◽  
Poincaré Mapping ◽  
Network Behavior ◽  
Input Space ◽  
Poincare Mapping

This paper presents qualitative analyses of the dynamics of continuous-time recurrent neural networks (RNNs) with continuous temporal external input. We show how to analyze continuous-time RNNs using Poincaré mapping. We introduce an input space in which the external input is parametrized, and define the product space which consists of the input space and the phase space. We numerically examine the bifurcation caused by changing the external input in the product space. It is shown that the network dynamics can be considered as rapid transitions in the bifurcation diagram. From the bifurcation viewpoint, the learning process of the RNN can be considered as a process to adjust the bifurcation diagram in order to satisfy a given input–output relation. We also numerically investigate the network behavior against the noise of the external input, and show the qualitative conditions for robustness.

scholarly journals Bearing failure prediction using Wigner-Ville distribution, modified Poincare mapping and fast Fourier transform

2018 ◽  
Vol 20 (1) ◽  
pp. 127-137 ◽  
Author(s):  
Pravin Singru ◽  
Vishnuvardhan Krishnakumar ◽  
Dwarkesh Natarajan ◽  
Ayush Raizada
Keyword(s):  
Fourier Transform ◽  
Fast Fourier Transform ◽  
Failure Prediction ◽  
Bearing Failure ◽  
Poincaré Mapping ◽  
Poincare Mapping

Mappings for the First Order Asteroidal Resonance

1992 ◽  
Vol 152 ◽  
pp. 391-394
Author(s):  
T. J. Stuchi ◽  
W. Sessin
Keyword(s):  
Exact Solution ◽  
Periodic Function ◽  
Perturbation Technique ◽  
Simplified Model ◽  
Poincaré Mapping ◽  
Order Resonance ◽  
First Order ◽  
Poincare Mapping

We construct a two step algebraic mapping from Sessin's simplified model for the first order resonance. The orbits obtained with this mapping are compared to the ones calculated with the exact solution. We also derive a reduced Hamiltonian. A plane Poincaré mapping, using delta periodic function, is constructed and compared to the reduced Hamiltonian contour curves showing the splitting of the separatrix due to delta perturbation technique.

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