Nonlinear behavior around fixed points: bifurcation analysis

1995 ◽  
pp. 94-127
Keyword(s):  
Fixed Points ◽  
Bifurcation Analysis ◽  
Nonlinear Behavior

scholarly journals ANALYSIS AND CONTROL OF BIFURCATION AND CHAOS IN AVERAGE QUEUE LENGTH IN TCP/RED MODEL

2008 ◽  
Vol 18 (08) ◽  
pp. 2449-2459 ◽  
Author(s):  
J. H. C. NGA ◽  
H. H. C. IU ◽  
B. W. K. LING ◽  
H. K. LAM
Keyword(s):  
Bifurcation Analysis ◽  
Queue Length ◽  
Network Performance ◽  
Transmission Control Protocol ◽  
Nonlinear Behavior ◽  
Random Early Detection ◽  
Network Systems ◽  
Bifurcation And Chaos ◽  
Queuing Delay ◽  
And Control

This paper studies the bifurcation and chaos phenomena in average queue length in a developed Transmission Control Protocol (TCP) model with Random Early Detection (RED) mechanism. Bifurcation and chaos phenomena are nonlinear behavior in network systems that lead to degradation of the network performance. The TCP/RED model used is a model validated previously. In our study, only the average queue size [Formula: see text] is considered, and the results are based on analytical model rather than actual measurements. The instabilities in the model are studied numerically using the conventional nonlinear bifurcation analysis. Extending from this bifurcation analysis, a modified RED algorithm is derived to prevent the observed bifurcation and chaos regardless of the selected parameters. Our modification is for the simple scenario of a single RED router carrying only TCP traffic. The algorithm neither compromises the throughput nor the average queuing delay of the system.

Nonlinear behavior of solar gravity modes driven by He-3 in the core. I - Bifurcation analysis

1990 ◽  
Vol 353 ◽  
pp. 678 ◽  
Author(s):  
William J. Merryfield ◽  
Douglas Gough ◽  
Juri Toomre
Keyword(s):  
Bifurcation Analysis ◽  
Nonlinear Behavior ◽  
The Core ◽  
Solar Gravity

scholarly journals Bifurcation Analysis of a Discrete Food Chain Model with Harvesting

2021 ◽  
Vol 2021 ◽  
pp. 1-31
Author(s):  
Abdul Qadeer Khan ◽  
Shahid Mehmood Qureshi
Keyword(s):  
Fixed Points ◽  
Bifurcation Analysis ◽  
Food Chain ◽  
Periodic Points ◽  
Chain Model ◽  
Prime Period ◽  
Food Chain Model ◽  
Theoretical Results

We explore existence of fixed points, topological classifications around fixed points, existence of periodic points and prime period, and bifurcation analysis of a three-species discrete food chain model with harvesting. Finally, theoretical results are numerically verified.

scholarly journals Global Dynamics, Bifurcation Analysis, and Chaos in a Discrete Kolmogorov Model with Piecewise-Constant Argument

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Abdul Qadeer Khan
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Bifurcation Analysis ◽  
Global Attractivity ◽  
Global Dynamics ◽  
Flip Bifurcation ◽  
Piecewise Constant ◽  
Kolmogorov Model ◽  
Piecewise Constant Argument ◽  
Constant Argument

The local behavior with topological classifications, bifurcation analysis, chaos control, boundedness, and global attractivity of the discrete-time Kolmogorov model with piecewise-constant argument are investigated. It is explored that Kolmogorov model has trivial and two semitrival fixed points for all involved parameters, but it has an interior fixed point under definite parametric condition. Then, by linear stability theory, local dynamics with different topological classifications are investigated around trivial, semitrival, and interior fixed points. Further for the discrete Kolmogorov model, existence of periodic points is also investigated. It is also investigated the occurrence of bifurcations at interior fixed point and proved that at interior fixed point, there exists no bifurcation, except flip bifurcation by bifurcation theory. Next, feedback control method is utilized to stabilize chaos existing in discrete Kolmogorov model. Boundedness and global attractivity of the discrete Kolmogorov model are also investigated. Finally, obtained results are numerically verified.

Bifurcation Analysis of a Two-Phase PEMFC Model

2008 ◽  
Vol 5 (2) ◽  
Author(s):  
Markus Grötsch ◽  
Richard Hanke-Rauschenbach ◽  
Michael Mangold
Keyword(s):  
Fuel Cell ◽  
Bifurcation Analysis ◽  
Cell Model ◽  
Control Strategies ◽  
Polymer Electrolyte Membrane ◽  
Nonlinear Behavior ◽  
Pem Fuel Cell ◽  
Continuation Methods ◽  
Two Phase ◽  
Cell Parameters

A major issue of polymer-electrolyte-membrane (PEM) fuel cell operation is the water management of the cells. This article tries to contribute to an improved understanding of flooding/drying out effects by performing a analysis for a rigorous two-phase PEM fuel cell model. The model is examined by means of a bifurcation analysis. This investigation is performed numerically with parameter continuation methods. The nonlinear behavior is qualified and possible instabilities are detected. A steady state multiplicity is found. The multiplicity is physically explained and the influence of selected fuel cell parameters is investigated. The multiplicity is finally verified in a dynamic simulation. The future work aims at a model reduction of the analyzed fuel cell model to gain a low order model suitable for model-based control strategies.

Development of a Jacobian Module for Advanced Pulp and Paper Simulation and Control

TAPPI Journal ◽  
2009 ◽  
Vol 8 (1) ◽  
pp. 4-11
Author(s):  
MOHAMED CHBEL ◽  
LUC LAPERRIÈRE
Keyword(s):  
Control System ◽  
Nonlinear Behavior ◽  
Simulation Software ◽  
Pulp And Paper ◽  
Pid Controllers ◽  
Tuning Parameters ◽  
Pid Tuning ◽  
Fixed Set ◽  
And Control ◽  
Operating Points

Pulp and paper processes frequently present nonlinear behavior, which means that process dynam-ics change with the operating points. These nonlinearities can challenge process control. PID controllers are the most popular controllers because they are simple and robust. However, a fixed set of PID tuning parameters is gen-erally not sufficient to optimize control of the process. Problems related to nonlinearities such as sluggish or oscilla-tory response can arise in different operating regions. Gain scheduling is a potential solution. In processes with mul-tiple control objectives, the control strategy must further evaluate loop interactions to decide on the pairing of manipulated and controlled variables that minimize the effect of such interactions and hence, optimize controller’s performance and stability. Using the CADSIM Plus™ commercial simulation software, we developed a Jacobian sim-ulation module that enables automatic bumps on the manipulated variables to calculate process gains at different operating points. These gains can be used in controller tuning. The module also enables the control system designer to evaluate loop interactions in a multivariable control system by calculating the Relative Gain Array (RGA) matrix, of which the Jacobian is an essential part.

REDUCED MODEL OF PLASMA DISCHARGE CONTROL IN TOKAMAK WITH IRON CORE

2020 ◽  
Vol 7 (3) ◽  
pp. 11-22
Author(s):  
VALERY ANDREEV ◽  
◽  
ALEXANDER POPOV
Keyword(s):  
Optimal Control ◽  
Inverse Problem ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Nonlinear Behavior ◽  
Plasma Discharge ◽  
Reduced Model ◽  
Iron Core ◽  
Power Sources ◽  
Real Power

A reduced model has been developed to describe the time evolution of a discharge in an iron core tokamak, taking into account the nonlinear behavior of the ferromagnetic during the discharge. The calculation of the discharge scenario and program regime in the tokamak is formulated as an inverse problem - the optimal control problem. The methods for solving the problem are compared and the analysis of the correctness and stability of the control problem is carried out. A model of “quasi-optimal” control is proposed, which allows one to take into account real power sources. The discharge scenarios are calculated for the T-15 tokamak with an iron core.

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