FORECASTING OF BIFURCATION PHENOMENA IN DYNAMICS OF PULSE ENERGY CONVERTERS WITH PARAMETER UNCERTAINTIES

2009 ◽  
Vol 19 (02) ◽  
pp. 591-604 ◽  
Author(s):  
YURY V. KOLOKOLOV ◽  
ANNA V. MONOVSKAYA
Keyword(s):  
Nonlinear Dynamics ◽  
Pulse Energy ◽  
Time Estimation ◽  
Problem Solution ◽  
Parameter Uncertainties ◽  
Geometrical Structures ◽  
Bifurcation Phenomenon ◽  
Bifurcation Phenomena ◽  
Problem Setting ◽  
Energy Converters

The results of bifurcation analysis seem to be used somehow or other as the basis of any method in nonlinear dynamics forecasting. The peculiarity of the problem setting in the paper is related to the fact that dynamics forecasting supposes the recognition of a bifurcation phenomenon before its beginning. In particular, this problem setting is important from the viewpoint of practical application of pulse energy converters (PEC). So, the necessity of real-time estimation of the direction of transient convergence appears. The complexity of such estimation is stipulated by the information on transients that is not mapped in bifurcation diagrams, and also time series do not contain preliminary information on a nonlinear dynamics picture. Moreover, PEC operation under parameter uncertainties leads to information on a bifurcation boundary location becomes fuzzy. The symbolic description of dynamical processes over time is offered with the purpose of the problem solution. This description is provided by the use of fractal regularities in the geometrical structures of phase trajectories, which are stipulated by the physical essence of both PWM process and transient convergence towards a limit cycle.

On Generalized Hopf Bifurcations

1984 ◽  
Vol 106 (4) ◽  
pp. 327-334 ◽  
Author(s):  
K. Huseyin ◽  
A. S. Atadan
Keyword(s):  
Hopf Bifurcation ◽  
Additional Condition ◽  
System Parameter ◽  
Transversality Condition ◽  
Existence Condition ◽  
The Other ◽  
Hopf Bifurcations ◽  
Bifurcation Phenomenon ◽  
Bifurcation Phenomena ◽  
Lumped Parameter

Two distinct degenerate Hopf bifurcation phenomena associated with autonomous lumped-parameter systems are explored in great detail via the intrinsic harmonic balancing method. It is assumed that the Hopf’s transversality condition is violated and certain other conditions prevail. In one of the cases, the system exhibits a cusp shape bifurcation path which exists for either positive or negative values of the system parameter. On the other hand, the second case is concerned with a tangential bifurcation phenomenon which may not be exhibited unless an additional condition is satisfied. This existence condition is obtained in the course of analysis. The distinctive feature of the paper is that the results concerning the bifurcating paths and limit cycles are given in general, explicit forms which are expected to be very useful in a variety of applications.

scholarly journals INFLUENCE OF DIDACTIC CONDITIONS ON EFFECTIVENESS OF FORMATION AT YOUNGER SCHOOL STUDENTS OF INFORMATIVE UNIVERSAL EDUCATIONAL ACTIONS OF STATEMENT AND A SOLUTION

2020 ◽  
Vol 3 ◽  
pp. 19
Author(s):  
Tatiana Alekseeva
Keyword(s):  
Problem Solving ◽  
Primary School ◽  
Educational Activity ◽  
Problem Solution ◽  
School Students ◽  
Problem Situations ◽  
Control Stage ◽  
Procedural Components ◽  
Education Of Students ◽  
Problem Setting

The article presents methodological, diagnostic and technological (procedural) components of the formation in younger schoolchildren of cognitive universal educational actions (PAP) of the setting and solution of the problem. The methodology of forming the components of «problem setting» and «problem solving» is disclosed in the article from the perspective of the system approach. The diagnostic component presents the diagnostic tactics (criteria, indicators, model of formation levels) of the PDS «problem setting» and «problem solving» in younger schoolchildren; There is provided didactic-methodical instrumentation for determining possible levels of UDM formation, problem setting and problem solution at the control stage of the experiment (qualitative and quantitative analysis of the execution of complex diagnostic tasks by junior students). The procedural component shows that compliance in the educational activity of the primary school with the principles of technology of intellectual and developing education, provision of visualization of problem situations, implementation of speech control of the process of setting and solving the problem through the development of speech logic in children increases the efficiency of the process of formation of education of students of the primary school in the younger schoolchildren in the ability to formulate and solve problems.The study carried out and the analysis of its results make it possible to draw a conclusion on the expediency of implementing in the educational activity of the primary school a designated didactic strategy, which helps the teacher to master the universal didactic tools of teaching younger schoolchildren to solve the educational problem and solve it. 

Analysis of the interaction among weed, inorganic fertilizer and herbivore in paddy ecosystem in fallow season

2017 ◽  
Vol 10 (08) ◽  
pp. 1750120 ◽  
Author(s):  
Meihong Xiang ◽  
Zhaohua Wu ◽  
Tiejun Zhou
Keyword(s):  
Hopf Bifurcation ◽  
Equilibrium Point ◽  
Equation Model ◽  
Inorganic Fertilizer ◽  
Stable Region ◽  
Positive Equilibrium ◽  
Bifurcation Phenomenon ◽  
Bifurcation Phenomena ◽  
Paddy Ecosystem ◽  
Positive Equilibrium Point

Paddy growth is influenced by the amount of inorganic fertilizer in paddy ecosystem in fallow season. To discover the interaction among weed, inorganic fertilizer and herbivore in the system, we put forward a differential equation model and investigate its properties. Results show that the system has a weed and herbivore extinct equilibrium and a herbivore extinct equilibrium. The two equilibria are proven to be unstable using the center manifold method. Under certain conditions, the system also has a positive equilibrium point. We give the stable region and the unstable region of the positive equilibrium point, which are determined by some parameters. We find that the system has the Hopf bifurcation phenomenon, and give the critical value of Hopf bifurcation by taking a system parameter as the bifurcation parameter. By comparing the equilibrium states between a paddy ecosystem with herbivore and one without herbivore, we find that the content of inorganic fertilizer can be improved by putting herbivore into a paddy field. An example is given to illustrate the feasibility of the results. Numerical simulation shows that Hopf bifurcation phenomena exist in the system.

BIFURCATION ANALYSIS OF SYNCHRONIZED REGIONS IN COMPLEX DYNAMICAL NETWORKS

2012 ◽  
Vol 22 (11) ◽  
pp. 1250282 ◽  
Author(s):  
LONGKUN TANG ◽  
JUN-AN LU ◽  
JINHU LÜ ◽  
XINGHUO YU
Keyword(s):  
Equilibrium Points ◽  
Complex Dynamical Networks ◽  
Mode Iii ◽  
Dynamical Networks ◽  
Network Nodes ◽  
Synchronous State ◽  
Bifurcation Phenomenon ◽  
Unified Chaotic System ◽  
Bifurcation Phenomena ◽  
The Stability

This paper aims to investigate the bifurcation phenomena of synchronized regions in complex dynamical networks with varying node parameters and fixed inner-linking matrices. In particular, by using the unified chaotic system as network nodes, this paper further explores the bifurcation patterns of synchronized regions with synchronous states of both equilibrium points and attractors in complex dynamical networks based on two types of inner-linking matrices, respectively. Our results indicate that there does not exist any bifurcation phenomenon in the above synchronized regions for some specific inner-linking matrices. It means that the stability of network synchronous state will not change for some specific inner-linking matrices as the parameter of node dynamics changes. However, the above synchronized regions generate various bifurcation patterns for some inner-linking matrices and varying node parameters as follows: (i) The unbounded–empty set bifurcation mode; (ii) The bounded–empty set bifurcation mode; (iii) The single bounded–multiple bounded–single bounded–empty set bifurcation mode; (iv) The unbounded–multiple disconnected–empty set bifurcation mode. All these results tell us that the inner-linking matrices play a key role for determining the bifurcation patterns of synchronized regions.

A Practice-Oriented Bifurcation Analysis for Pulse Energy Converters: A Stability Margin

2017 ◽  
Vol 27 (09) ◽  
pp. 1750134 ◽  
Author(s):  
Yury Kolokolov ◽  
Anna Monovskaya
Keyword(s):  
Nonlinear Dynamics ◽  
Energy Conversion ◽  
Bifurcation Analysis ◽  
Pulse Energy ◽  
Stability Margin ◽  
Variable Structure ◽  
Operating Regime ◽  
Buck Converter ◽  
Practical Applications ◽  
Operating Process

The popularity of systems of pulse energy conversion (PEC-systems) for practical applications is due to the heightened efficiency of energy conversion processes with comparatively simple realizations. Nevertheless, a PEC-system represents a nonlinear object with a variable structure, and the bifurcation analysis remains the basic tool to describe PEC dynamics evolution. The paper is devoted to the discussion on whether the scientific viewpoint on the natural nonlinear dynamics evolution can be involved in practical applications. We focus on the problems connected with stability boundaries of an operating regime. The results of both small-signal analysis and computational bifurcation analysis are considered in the parametrical space in comparison with the results of the experimental identification of the zonal heterogeneity of the operating process. This allows to propose an adapted stability margin as a sufficiently safe distance before the point after which the operating process begins to lose the stability. Such stability margin can extend the permissible operating domain in the parametrical space at the expense of using cause-and-effect relations in the context of natural regularities of nonlinear dynamics. Reasoning and discussion are based on the experimental and computational results for a synchronous buck converter with a pulse-width modulation. The presented results can be useful, first of all, for PEC-systems with significant variation of equivalent inductance and/or capacity. We believe that the discussion supports a viewpoint by which the contemporary methods of the computational and experimental bifurcation analyses possess both analytical abilities and experimental techniques for promising solutions which could be practice-oriented for PEC-systems.

scholarly journals New Traveling Wave Solutions and Interesting Bifurcation Phenomena of Generalized KdV-mKdV-Like Equation

2021 ◽  
Vol 2021 ◽  
pp. 1-6
Author(s):  
Yiren Chen ◽  
Shaoyong Li
Keyword(s):  
Dynamical Systems ◽  
Solitary Waves ◽  
Nonlinear Waves ◽  
Traveling Wave ◽  
Blow Up ◽  
Traveling Wave Solutions ◽  
Bifurcation Method ◽  
Bifurcation Phenomenon ◽  
Wave Solutions ◽  
Bifurcation Phenomena

Using the bifurcation method of dynamical systems, we investigate the nonlinear waves and their limit properties for the generalized KdV-mKdV-like equation. We obtain the following results: (i) three types of new explicit expressions of nonlinear waves are obtained. (ii) Under different parameter conditions, we point out these expressions represent different waves, such as the solitary waves, the 1-blow-up waves, and the 2-blow-up waves. (iii) We revealed a kind of new interesting bifurcation phenomenon. The phenomenon is that the 1-blow-up waves can be bifurcated from 2-blow-up waves. Also, we gain other interesting bifurcation phenomena. We also show that our expressions include existing results.

A Practice-Oriented Bifurcation Analysis for Pulse Energy Converters. Part 2: An Operating Regime

2018 ◽  
Vol 28 (02) ◽  
pp. 1850023 ◽  
Author(s):  
Yury Kolokolov ◽  
Anna Monovskaya
Keyword(s):  
Nonlinear Dynamics ◽  
Energy Conversion ◽  
Bifurcation Analysis ◽  
Pulse Energy ◽  
Output Signal ◽  
Operating Characteristic ◽  
Operating Regime ◽  
Operating Characteristics ◽  
Operating Process ◽  
And Performance

The paper continues the discussion on bifurcation analysis for applications in practice-oriented solutions for pulse energy conversion systems (PEC-systems). Since a PEC-system represents a nonlinear object with a variable structure, then the description of its dynamics evolution involves bifurcation analysis conceptions. This means the necessity to resolve the conflict-of-units between the notions used to describe natural evolution (i.e. evolution of the operating process towards nonoperating processes and vice versa) and the notions used to describe a desirable artificial regime (i.e. an operating regime). We consider cause-effect relations in the following sequence: nonlinear dynamics-output signal-operating characteristics, where these characteristics include stability and performance. Then regularities of nonlinear dynamics should be translated into regularities of the output signal dynamics, and, after, into an evolutional picture of each operating characteristic. In order to make the translation without losses, we first take into account heterogeneous properties within the structures of the operating process in the parametrical (P-) and phase (X-) spaces, and analyze regularities of the operating stability and performance on the common basis by use of the modified bifurcation diagrams built in joint PX-space. Then, the correspondence between causes (degradation of the operating process stability) and effects (changes of the operating characteristics) is decomposed into three groups of abnormalities: conditionally unavoidable abnormalities (CU-abnormalities); conditionally probable abnormalities (CP-abnormalities); conditionally regular abnormalities (CR-abnormalities). Within each of these groups the evolutional homogeneity is retained. After, the resultant evolution of each operating characteristic is naturally aggregated through the superposition of cause-effect relations in accordance with each of the abnormalities. We demonstrate that the practice-oriented bifurcation analysis has fundamentally specific purposes and tools, like for the computer-based bifurcation analysis and the experimental bifurcation analysis. That is why, from our viewpoint, it seems to be a rather novel direction in the general context of bifurcation analysis conceptions. We believe that the discussion could be interesting to pioneer research intended for the design of promising systems of pulse energy conversion.

scholarly journals A Practice-Oriented Bifurcation Analysis for Pulse Energy Converters. Part 5: A View Towards the Future

2021 ◽  
Vol 31 (07) ◽  
pp. 2150106
Author(s):  
Yury Kolokolov ◽  
Anna Monovskaya
Keyword(s):  
Pulse Energy ◽  
Signal Design ◽  
The Novel ◽  
Bifurcation Diagrams ◽  
Local Climate ◽  
Evolutionary Changes ◽  
Computer Based ◽  
Desirable Behavior ◽  
Qualitative And Quantitative Characteristics ◽  
Energy Converters

The paper concludes the series of the research works on the interdisciplinary analytical approach (the so-called bifurcation-fractal analytics) to forecast the dynamics of pulse systems on the basis of modified bifurcation diagrams. These diagrams are intended to integrate incompatible-in-traditional-spaces images (mainly transients from the phase space and evolution pictures from the parametric space) in order to analyze whether the running transient converges towards the domain of a desirable behavior taking into account its qualitative and quantitative characteristics. The interdisciplinary context of the analytics appears because the novel mathematical images need physical meaning and further this research should be continued for proposing the expedient engineering decision. Here, the advantages to forecast the evolutionary tendencies in different scales of the modified bifurcation diagrams are illustrated by computer-based simulations. Translations of the mathematical images into their physical implementations follow the principle of the bifurcation poker and the principle of the spatial nonuniformity. The experimental results to verify these principles are presented. Variants of engineering proposals are commented in comparison with traditional abilities of the small-signal design. The results systematized in the paper confirm that fundamental obstacles to forecast abnormal evolutionary changes in the dynamics of pulse energy converters are absent. Prospects of the outcome from the experience accumulated in engineering to similar problem statements independently of a pulse system nature are finally discussed. And the regulatory hypothesis on local climate dynamics is considered in this connection. This discussion is quite suitable here because a local climate system can be described as a converter of the solar energy under a specific pulse control realized by the astronomic forcing and there are circumstances, in which electrotechnical simulations can remain a unique way to accelerate the research on prerequisites and sequels of the forthcoming climate changes. Then the bifurcation-fractal analytics provides an initial theoretical foundation to this research.

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