BIFURCATION ANALYSIS IN A PWM CURRENT-CONTROLLED H-BRIDGE INVERTER

2011 ◽  
Vol 21 (03) ◽  
pp. 985-996 ◽  
Author(s):  
HIROYUKI ASAHARA ◽  
TAKUJI KOUSAKA
Keyword(s):  
Dynamical System ◽  
Parameter Space ◽  
Bifurcation Analysis ◽  
Specific Property ◽  
Two Dimensional ◽  
Bifurcation Diagrams ◽  
Rigorous Analysis ◽  
Bifurcation Phenomena ◽  
The One ◽  
Switched Dynamical System

This paper introduces the complete bifurcation analysis in a PWM current-controlled H-Bridge inverter in a wide parameter space. First, we briefly explain the behavior of the waveform in the circuit in terms of the switched dynamical system. Then, the consecutive waveform during the duration of the clock interval is exactly discretized, and the return map is defined for the rigorous analysis. Using the map, we derive the one- and two-dimensional bifurcation diagrams, and discuss the specific property of each bifurcation phenomena in the circuit.

scholarly journals No Chaos in Dixon’s System

2021 ◽  
Vol 31 (03) ◽  
pp. 2150044
Author(s):  
Werner M. Seiler ◽  
Matthias Seiß
Keyword(s):  
Dynamical System ◽  
Parameter Space ◽  
Bifurcation Analysis ◽  
Chaotic Behavior ◽  
Homoclinic Orbits ◽  
Rigorous Proof ◽  
Two Dimensional ◽  
Continuous Dynamical System ◽  
Two Parameters

The so-called Dixon system is often cited as an example of a two-dimensional (continuous) dynamical system that exhibits chaotic behavior, if its two parameters take their values in a certain domain. We provide first a rigorous proof that there is no chaos in Dixon’s system. Then we perform a complete bifurcation analysis of the system showing that the parameter space can be decomposed into 16 different regions in each of which the system exhibits qualitatively the same behavior. In particular, we prove that in some regions two elliptic sectors with infinitely many homoclinic orbits exist.

Effects of DC electric fields on neuronal excitability: A bifurcation analysis

2014 ◽  
Vol 28 (18) ◽  
pp. 1450114 ◽  
Author(s):  
Yanqiu Che ◽  
Huiyan Li ◽  
Chunxiao Han ◽  
Xile Wei ◽  
Bin Deng ◽  
...  
Keyword(s):  
Electric Field ◽  
Electric Fields ◽  
Parameter Space ◽  
Bifurcation Analysis ◽  
Neural Control ◽  
Neuronal Excitability ◽  
Modulation Method ◽  
Two Dimensional ◽  
Dimensional Parameter ◽  
Dc Electric Fields

In this paper, the effects of external DC electric fields on the neuro-computational properties are investigated in the context of Morris–Lecar (ML) model with bifurcation analysis. We obtain the detailed bifurcation diagram in two-dimensional parameter space of externally applied DC current and trans-membrane potential induced by external DC electric field. The bifurcation sets partition the two-dimensional parameter space in terms of the qualitatively different behaviors of the ML model. Thus the neuron's information encodes the stimulus information, and vice versa, which is significant in neural control. Furthermore, we identify the electric field as a key parameter to control the transitions among four different excitability and spiking properties, which facilitates the design of electric fields based neuronal modulation method.

An Extended Continuation Problem for Bifurcation Analysis in the Presence of Constraints

2010 ◽  
Vol 6 (3) ◽  
Author(s):  
Harry Dankowicz ◽  
Frank Schilder
Keyword(s):  
Dynamical System ◽  
Periodic Orbits ◽  
Bifurcation Analysis ◽  
The Other ◽  
Extended Formulation ◽  
Hybrid Dynamical System ◽  
Families Of Periodic Orbits ◽  
Continuation Problem ◽  
The One ◽  
Additional Constraints

This paper presents an extended formulation of the basic continuation problem for implicitly defined, embedded manifolds in Rn. The formulation is chosen so as to allow for the arbitrary imposition of additional constraints during continuation and the restriction to selective parametrizations of the corresponding higher-codimension solution manifolds. In particular, the formalism is demonstrated to clearly separate between the essential functionality required of core routines in application-oriented continuation packages, on the one hand, and the functionality provided by auxiliary toolboxes that encode classes of continuation problems and user definitions that narrowly focus on a particular problem implementation, on the other hand. Several examples are chosen to illustrate the formalism and its implementation in the recently developed continuation core package COCO and auxiliary toolboxes, including the continuation of families of periodic orbits in a hybrid dynamical system with impacts and friction as well as the detection and constrained continuation of selected degeneracies characteristic of such systems, such as grazing and switching-sliding bifurcations.

CONNECTIONS BETWEEN SADDLES FOR THE FITZHUGH–NAGUMO SYSTEM

2001 ◽  
Vol 11 (02) ◽  
pp. 533-540 ◽  
Author(s):  
CARMEN ROCŞOREANU ◽  
NICOLAIE GIURGIŢEANU ◽  
ADELINA GEORGESCU
Keyword(s):  
Dynamical System ◽  
Homoclinic Bifurcation ◽  
Parameter Plane ◽  
Saddle Connection ◽  
Local Bifurcation ◽  
Two Dimensional ◽  
Bifurcation Diagrams ◽  
Numerical Investigations ◽  
Codimension One ◽  
Saddle Node

By studying the two-dimensional FitzHugh–Nagumo (F–N) dynamical system, points of Bogdanov–Takens bifurcation were detected (Sec. 1). Two of the curves of homoclinic bifurcation emerging from these points intersect each other at a point of double breaking saddle connection bifurcation (Sec. 2). Numerical investigations of the bifurcation curves emerging from this point, in the parameter plane, allowed us to find other types of codimension-one and -two bifurcations concerning the connections between saddles and saddle-nodes, referred to as saddle-node–saddle connection bifurcation and saddle-node–saddle with separatrix connection bifurcation, respectively. The local bifurcation diagrams corresponding to these bifurcations are presented in Sec. 3. An analogy between the bifurcation corresponding to the point of double homoclinic bifurcation and the point of double breaking saddle connection bifurcation is also presented in Sec. 3.

scholarly journals A Diagrammatic Representation of Phase Portraits and Bifurcation Diagrams of Two-Dimensional Dynamical Systems

2017 ◽  
Vol 27 (13) ◽  
pp. 1730045
Author(s):  
Javier Roulet ◽  
Gabriel B. Mindlin
Keyword(s):  
Dynamical Systems ◽  
Parameter Space ◽  
Partial Information ◽  
Quantitative Information ◽  
Phase Portraits ◽  
Two Dimensional ◽  
Bifurcation Diagrams ◽  
Diagrammatic Representation ◽  
Topological Features

We treat the problem of characterizing in a systematic way the qualitative features of two-dimensional dynamical systems. To that end, we construct a representation of the topological features of phase portraits by means of diagrams that discard their quantitative information. All codimension 1 bifurcations are naturally embodied in the possible ways of transitioning smoothly between diagrams. We introduce a representation of bifurcation curves in parameter space that guides the proposition of bifurcation diagrams compatible with partial information about the system.

Stochastic Averaging Near a Homoclinic Orbit with Multiplicative Noise

2003 ◽  
Vol 03 (03) ◽  
pp. 299-391 ◽  
Author(s):  
Richard B. Sowers
Keyword(s):  
Dynamical System ◽  
Homoclinic Orbit ◽  
Multiplicative Noise ◽  
Stochastic Averaging ◽  
Two Dimensional ◽  
Test Function ◽  
Limiting Behavior ◽  
Position Variable ◽  
Dirichlet Operators ◽  
The One

We consider a randomly perturbed two-dimensional Hamiltonian dynamical system containing a homoclinic orbit. The noise is multiplicative in the position variable. We prove a result similar to the one of Freidlin and Weber; this result states that as the noise becomes smaller, a graph-valued Markov process characterizes the limiting behavior. Our analysis of the glueing conditions hinges upon a coordinate transformation introduced by Khasminskii and a perturbed test function methodology. We find that the glueing conditions exactly correspond to the solvability of a linear equation involving coupled Neumann-to-Dirichlet operators.

scholarly journals On the notion of the dimension with respect to a dynamical system

1984 ◽  
Vol 4 (3) ◽  
pp. 405-420 ◽  
Author(s):  
Ya. B. Pesin
Keyword(s):  
Dynamical System ◽  
Hausdorff Dimension ◽  
Invariant Sets ◽  
Dimensional Case ◽  
Two Dimensional ◽  
One Dimensional ◽  
Common Features ◽  
Dynamical Properties ◽  
The One ◽  
Hyperbolic Sets

AbstractFor the invariant sets of dynamical systems a new notion of dimension-the so-called dimension with respect to a dynamical system-is introduced. It has some common features with the general topological notion of the dimension, but it also reflects the dynamical properties of the system. In the one-dimensional case it coincides with the Hausdorff dimension. For multi-dimensional hyperbolic sets formulae for the calculation of our dimension are obtained. These results are generalizations of Manning's results obtained by him for the Hausdorff dimension in the two-dimensional case.

TWO-DIMENSIONAL BIFURCATION DIAGRAMS OF A CHAOTIC CIRCUIT BASED ON HYSTERESIS

2002 ◽  
Vol 12 (01) ◽  
pp. 43-69 ◽  
Author(s):  
FEDERICO BIZZARRI ◽  
MARCO STORACE
Keyword(s):  
Bifurcation Analysis ◽  
Piecewise Linear ◽  
Point Of View ◽  
Chaotic Oscillator ◽  
Circuit Parameter ◽  
Two Dimensional ◽  
Bifurcation Diagrams ◽  
Chaotic Circuit ◽  
Analysis Point

This paper deals with the bifurcation analysis of a chaotic oscillator based on hysteresis. The analysis is carried out using two different models of the nonlinear resistive elements of the oscillator. The first model (more convenient from an analysis point of view) is piecewise linear (PWL), whereas the second (more realistic from a synthesis point of view) is smooth. For both models, the main results presented in this paper are two-dimensional bifurcation diagrams obtained for several values of a third circuit parameter.

scholarly journals Uniqueness of Traveling Waves for a Two-Dimensional Bistable Periodic Lattice Dynamical System

2012 ◽  
Vol 2012 ◽  
pp. 1-10
Author(s):  
Chin-Chin Wu
Keyword(s):  
Dynamical System ◽  
Traveling Waves ◽  
Periodic Lattice ◽  
Two Dimensional ◽  
Periodic Media ◽  
Dimensional Lattice ◽  
One Dimensional ◽  
Sliding Method ◽  
Lattice Dynamical System ◽  
The One

We study traveling waves for a two-dimensional lattice dynamical system with bistable nonlinearity in periodic media. The existence and the monotonicity in time of traveling waves can be derived in the same way as the one-dimensional lattice case. In this paper, we derive the uniqueness of nonzero speed traveling waves by using the comparison principle and the sliding method.

Transitions of flow past a row of square bars

2000 ◽  
Vol 405 ◽  
pp. 305-323 ◽  
Author(s):  
J. MIZUSHIMA ◽  
Y. KAWAGUCHI
Keyword(s):  
Numerical Simulations ◽  
Flow Pattern ◽  
Bifurcation Analysis ◽  
Pitchfork Bifurcation ◽  
Side Length ◽  
Length Ratio ◽  
Two Dimensional ◽  
Bifurcation Diagrams ◽  
Flow Past ◽  
Flow Visualizations

Transitions of flow past a row of square bars placed across a uniform flow are investigated by numerical simulations and the bifurcation analysis of the numerical results. The flow is assumed two-dimensional and incompressible. It is already known that jets coming through gaps between square bars are independent of each other when the pitch-to-side-length ratio of the row is large, whereas the confluence of two or three jets occurs due to a first pitchfork bifurcation from the flow with independent jets when the pitch-to-side-length ratio is small. It is found that confluence of four jets occurs in consequence of the second pitchfork bifurcation from the flow with pairs of jets joined to each other. Bifurcation diagrams of the flow are obtained, which include confluences of double, triple and quadruple jets. Lengths of the twin vortices are evaluated for each flow pattern. The confluences of two, three and four jets are qualitatively confirmed experimentally by flow visualizations.

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