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 DESIGN OF TIME DELAYED CHAOTIC CIRCUIT WITH THRESHOLD CONTROLLER

2011 ◽  
Vol 21 (03) ◽  
pp. 725-735 ◽  
Author(s):  
K. SRINIVASAN ◽  
I. RAJA MOHAMED ◽  
K. MURALI ◽  
M. LAKSHMANAN ◽  
SUDESHNA SINHA
Keyword(s):  
Numerical Simulations ◽  
Linear Function ◽  
Piecewise Linear ◽  
Piecewise Linear Function ◽  
Operational Amplifiers ◽  
Phase Portraits ◽  
Chaotic Attractors ◽  
Chaotic Oscillator ◽  
Threshold Values ◽  
Chaotic Circuit

A novel time delayed chaotic oscillator exhibiting mono- and double scroll complex chaotic attractors is designed. This circuit consists of only a few operational amplifiers and diodes and employs a threshold controller for flexibility. It efficiently implements a piecewise linear function. The control of piecewise linear function facilitates controlling the shape of the attractors. This is demonstrated by constructing the phase portraits of the attractors through numerical simulations and hardware experiments. Based on these studies, we find that this circuit can produce multi-scroll chaotic attractors by just introducing more number of threshold values.

BIFURCATION ANALYSIS OF A PWL CHAOTIC CIRCUIT BASED ON HYSTERESIS THROUGH A ONE-DIMENSIONAL MAP

2001 ◽  
Vol 11 (07) ◽  
pp. 1911-1927 ◽  
Author(s):  
FEDERICO BIZZARRI ◽  
MARCO STORACE ◽  
LAURA GARDINI ◽  
RENZO LUPINI
Keyword(s):  
Bifurcation Analysis ◽  
Piecewise Linear ◽  
Three Dimensional ◽  
Chaotic Circuit ◽  
One Dimensional ◽  
Local And Global Bifurcations ◽  
The One ◽  
Planar Flows ◽  
Analytical Expressions ◽  
Linear Nature

Bifurcations in the dynamics of a chaotic circuit based on hysteresis are evaluated. Owing to the piecewise-linear nature of the nonlinear elements of the circuit, such bifurcations are discussed by resorting to a suitable one-dimensional map. As the ordinary differential equations governing the circuit are piecewise linear, the analytical expressions of their solutions can be derived in each linear region. Consequently, the proposed results have been obtained not by resorting to numerical integration, but by properly connecting pieces of planar flows. The bifurcation analysis is carried out by varying one of the three dimensionless parameters that the system of normalized circuit equations depends on. Local and global bifurcations, regular and chaotic asymptotic behaviors are pointed out by analyzing both the one-dimensional map and the three-dimensional flow induced by the circuit dynamics.

Effects of Non-smooth Phenomena on the Dynamics of DC-DC Converters

2011 ◽  
Vol 29 (1) ◽  
pp. 119-122
Author(s):  
Dmitry Pikulin
Keyword(s):  
Dynamical Systems ◽  
Nonlinear Systems ◽  
Bifurcation Analysis ◽  
Power Converters ◽  
Piecewise Linear ◽  
Nonlinear Phenomena ◽  
Switching Converters ◽  
Bifurcation Diagrams ◽  
Linear Dynamical Systems ◽  
Switch Mode

Effects of Non-smooth Phenomena on the Dynamics of DC-DC ConvertersThis paper provides the analysis of nonlinear phenomena in switch-mode power converters. In distinction to majority of known researches this paper presents novelty approach, allowing the complete bifurcation analysis, considering stable and various types of unstable behavior of nonlinear systems. Main results are illustrated on one of the most widely used switching converters - current controlled boost converter, for which the complete one-parametric bifurcation diagrams are constructed. The results include the detection of various types of rare attractors, smooth bifurcations and non-smooth phenomena, specific to piecewise linear dynamical systems.

Coexisting Multi-Dynamics of a Physical SBT Memristor-Based Chaotic Circuit

2020 ◽  
Vol 30 (11) ◽  
pp. 2030043
Author(s):  
Gang Dou ◽  
Hai Yang ◽  
Zhenhao Gao ◽  
Peng Li ◽  
Minglong Dou ◽  
...  
Keyword(s):  
Equilibrium Point ◽  
Lyapunov Exponents ◽  
Phase Portraits ◽  
Circuit Parameter ◽  
Bifurcation Diagrams ◽  
Chaotic Circuit ◽  
Initial State ◽  
Stable Point ◽  
The Stability ◽  
Physical Formula

This paper presents a new physical [Formula: see text] (SBT) memristor-based chaotic circuit. The equilibrium point and the stability of the chaotic circuit are analyzed theoretically. This circuit system exhibits multiple dynamics such as stable point, periodic cycle and chaos by means of Lyapunov exponents spectra, bifurcation diagrams, Poincaré maps and phase portraits, when the initial state or the circuit parameter changes. Specially, the circuit system exhibits coexisting multi-dynamics. This study provides insightful guidance for the design and analysis of physical memristor-based circuits.

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.

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.

A STUDY OF TWO‐DIMENSIONAL HEAD WAVES IN FLUID AND SOLID SYSTEMS

Geophysics ◽  
1963 ◽  
Vol 28 (4) ◽  
pp. 563-581 ◽  
Author(s):  
John W. Dunkin
Keyword(s):  
Half Space ◽  
Vertical Displacement ◽  
Point Of View ◽  
Head Wave ◽  
Apparent Velocity ◽  
Two Dimensional ◽  
Multiple Reflections ◽  
Transient Wave ◽  
Line Load ◽  
Head Waves

The problem of transient wave propagation in a three‐layered, fluid or solid half‐plane is investigated with the point of view of determining the effect of refracting bed thickness on the character of the two‐dimensional head wave. The “ray‐theory” technique is used to obtain exact expressions for the vertical displacement at the surface caused by an impulsive line load. The impulsive solutions are convolved with a time function having the shape of one cycle of a sinusoid. The multiple reflections in the refracting bed are found to affect the head wave significantly. For thin refracting beds in the fluid half‐space the character of the head wave can be completely altered by the strong multiple reflections. In the solid half‐space the weaker multiple reflections affect both the rate of decay of the amplitude of the head wave with distance and the apparent velocity of the head wave by changing its shape. A comparison is made of the results for the solid half‐space with previously published results of model experiments.

Poly[[μ2-1,3-bis(pyridin-4-yl)propane](μ3-1,4-phenylenediacetato)cadmium]

2012 ◽  
Vol 68 (2) ◽  
pp. m34-m36 ◽  
Author(s):  
Dong Liu
Keyword(s):  
Title Complex ◽  
Point Of View ◽  
Solvothermal Reaction ◽  
Dimensional Chain ◽  
Two Dimensional ◽  
One Dimensional ◽  
Connected Network ◽  
Dimensional Network

Solvothermal reaction between Cd(NO3)2, 1,4-phenylenediacetate (1,4-PDA) and 1,3-bis(pyridin-4-yl)propane (bpp) afforded the title complex, [Cd(C10H8O4)(C13H14N2)]n. Adjacent carboxylate-bridged CdIIions are related by an inversion centre. The 1,4-PDA ligands adopt acisconformation and connect the CdIIions to form a one-dimensional chain extending along thecaxis. These chains are in turn linked into a two-dimensional network through bpp bridges. The bpp ligands adopt ananti–gaucheconformation. From a topological point of view, each bpp ligand and each pair of 1,4-PDA ligands can be considered as linkers, while the dinuclear CdIIunit can be regarded as a 6-connecting node. Thus, the structure can be simplified to a two-dimensional 6-connected network.

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