scholarly journals Complex Dynamical Behavior of a Two-Stage Colpitts Oscillator with Magnetically Coupled Inductors

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
V. Kamdoum Tamba ◽  
H. B. Fotsin ◽  
J. Kengne ◽  
F. Kapche Tagne ◽  
P. K. Talla
Keyword(s):  
Complex Dynamics ◽  
Piecewise Linear ◽  
Dynamical Behavior ◽  
Period Doubling ◽  
Colpitts Oscillator ◽  
Two Stage ◽  
Frequency Spectra ◽  
Variable Resistor ◽  
Exponential Nonlinearity ◽  
Coupled Inductors

A five-dimensional (5D) controlled two-stage Colpitts oscillator is introduced and analyzed. This new electronic oscillator is constructed by considering the well-known two-stage Colpitts oscillator with two further elements (coupled inductors and variable resistor). In contrast to current approaches based on piecewise linear (PWL) model, we propose a smooth mathematical model (with exponential nonlinearity) to investigate the dynamics of the oscillator. Several issues, such as the basic dynamical behaviour, bifurcation diagrams, Lyapunov exponents, and frequency spectra of the oscillator, are investigated theoretically and numerically by varying a single control resistor. It is found that the oscillator moves from the state of fixed point motion to chaos via the usual paths of period-doubling and interior crisis routes as the single control resistor is monitored. Furthermore, an experimental study of controlled Colpitts oscillator is carried out. An appropriate electronic circuit is proposed for the investigations of the complex dynamics behaviour of the system. A very good qualitative agreement is obtained between the theoretical/numerical and experimental results.

COUPLED INDUCTORS-BASED CHAOTIC COLPITTS OSCILLATOR

2011 ◽  
Vol 21 (02) ◽  
pp. 569-574 ◽  
Author(s):  
ARTURO BUSCARINO ◽  
LUIGI FORTUNA ◽  
MATTIA FRASCA ◽  
GREGORIO SCIUTO
Keyword(s):  
Bifurcation Diagram ◽  
Oscillation Frequency ◽  
Control Parameter ◽  
External Control ◽  
Chaotic Circuit ◽  
Colpitts Oscillator ◽  
Variable Resistor ◽  
Coupled Inductors

In this paper, a new chaotic circuit is introduced, conceived by considering a Colpitts oscillator with the inclusion of two further elements: a coupled inductor and a variable resistor. The proposed circuit exhibits a rich dynamics that has been experimentally characterized through the bifurcation diagram with respect to the resistor value. The main result that can be derived from the analysis of the new circuit leads to a simple way to control chaos in the chaotic Colpitts oscillator by varying a single external control parameter. The same technique has then been applied to the classical periodic Colpitts oscillator, demonstrating how in this way the oscillation frequency can be controlled.

Complex Dynamics in a Harmonically Excited Lennard-Jones Oscillator: Microcantilever-Sample Interaction in Scanning Probe Microscopes1

1998 ◽  
Vol 122 (1) ◽  
pp. 240-245 ◽  
Author(s):  
M. Basso ◽  
L. Giarre´ ◽  
M. Dahleh ◽  
I. Mezic´
Keyword(s):  
Parameter Space ◽  
Complex Dynamics ◽  
Chaotic Behavior ◽  
Dynamical Behavior ◽  
Period Doubling ◽  
Operating Conditions ◽  
Invariant Sets ◽  
Jones Potential ◽  
Lennard Jones ◽  
Atomic Force

In this paper we model the microcantilever-sample interaction in an atomic force microscope (AFM) via a Lennard-Jones potential and consider the dynamical behavior of a harmonically forced system. Using nonlinear analysis techniques on attracting limit sets, we numerically verify the presence of chaotic invariant sets. The chaotic behavior appears to be generated via a cascade of period doubling, whose occurrence has been studied as a function of the system parameters. As expected, the chaotic attractors are obtained for values of parameters predicted by Melnikov theory. Moreover, the numerical analysis can be fruitfully employed to analyze the region of the parameter space where no theoretical information on the presence of a chaotic invariant set is available. In addition to explaining the experimentally observed chaotic behavior, this analysis can be useful in finding a controller that stabilizes the system on a nonchaotic trajectory. The analysis can also be used to change the AFM operating conditions to a region of the parameter space where regular motion is ensured. [S0022-0434(00)01401-5]

A New Time-Delay Model for Chaotic Glucose-Insulin Regulatory System

2020 ◽  
Vol 30 (12) ◽  
pp. 2050178
Author(s):  
Abdul-Basset A. AL-Hussein ◽  
Fadhil Rahma ◽  
Luigi Fortuna ◽  
Maide Bucolo ◽  
Mattia Frasca ◽  
...  
Keyword(s):  
Time Delay ◽  
Complex Dynamics ◽  
Dynamical Behavior ◽  
Period Doubling ◽  
Regulatory System ◽  
Periodic Oscillation ◽  
Insulin Level ◽  
Insulin Degradation ◽  
Delay Model ◽  
New Time

Mathematical modeling is very helpful for noninvasive investigation of glucose-insulin interaction. In this paper, a new time-delay mathematical model is proposed for glucose-insulin endocrine metabolic regulatory feedback system incorporating the [Formula: see text]-cell dynamic and function for regulating and maintaining bloodstream insulin level. The model includes the insulin degradation due to glucose interaction. The dynamical behavior of the model is analyzed and two-dimensional bifurcation diagrams with respect to two essential parameters of the model are obtained. The results show that the time-delay in insulin secretion in response to blood glucose level, and the delay in glucose drop due to increased insulin concentration, can give rise to complex dynamics, such as periodic oscillation. These dynamics are consistent with the biological findings and period doubling cascade and chaotic state which represent metabolic disorder that may lead to diabetes mellitus.

scholarly journals Asymmetric Double Strange Attractors in a Simple Autonomous Jerk Circuit

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-16 ◽  
Author(s):  
G. H. Kom ◽  
J. Kengne ◽  
J. R. Mboupda Pone ◽  
G. Kenne ◽  
A. B. Tiedeu
Keyword(s):  
Autonomous System ◽  
Period Doubling ◽  
Bifurcation Diagrams ◽  
Colpitts Oscillator ◽  
Exponential Nonlinearity ◽  
Unusual Phenomenon ◽  
Initial States ◽  
Type Of Behavior ◽  
Period Doubling Bifurcations ◽  
Lower Dimensional

The dynamics of a simple autonomous jerk circuit previously introduced by Sprott in 2011 are investigated. In this paper, the model is described by a three-time continuous dimensional autonomous system with an exponential nonlinearity. Using standard nonlinear techniques such as time series, bifurcation diagrams, Lyapunov exponent plots, and Poincaré sections, the dynamics of the system are characterized with respect to its parameters. Period-doubling bifurcations, periodic windows, and coexisting bifurcations are reported. As a major result of this work, it is found that the system experiences the unusual phenomenon of asymmetric bistability marked by the presence of two different attractors (e.g., screw-like Shilnikov attractor with a spiralling-like Feigenbaum attractor) for the same parameters setting, depending solely on the choice of initial states. Among few cases of lower dimensional systems capable of such type of behavior reported to date (e.g., Colpitts oscillator, Newton–Leipnik system, and hyperchaotic oscillator with gyrators), the jerk circuit/system considered in this work represents the simplest prototype. Results of theoretical analysis are perfectly reproduced by laboratory experimental measurements.

CHAOTIC BEHAVIOR OF A PERIODICALLY FORCED PREDATOR–PREY SYSTEM WITH BEDDINGTON–DEANGELIS FUNCTIONAL RESPONSE AND IMPULSIVE PERTURBATIONS

2006 ◽  
Vol 09 (03) ◽  
pp. 209-222 ◽  
Author(s):  
SHUWEN ZHANG ◽  
DEJUN TAN ◽  
LANSUN CHEN
Keyword(s):  
Functional Response ◽  
Complex Dynamics ◽  
Chaotic Behavior ◽  
Dynamical Behavior ◽  
Period Doubling ◽  
Periodic Variation ◽  
Periodic Forcing ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Impulsive Perturbations

The effects of periodic forcing and impulsive perturbations on the predator–prey model with Beddington–DeAngelis functional response are investigated. We assume periodic variation in the intrinsic growth rate of the prey as well as periodic constant impulsive immigration of the predator. The dynamical behavior of the system is simulated and bifurcation diagrams are obtained for different parameters. The results show that periodic forcing and impulsive perturbation can very easily give rise to complex dynamics, including quasi-periodic oscillating, a period-doubling cascade, chaos, a period-halving cascade, non-unique dynamics, and period windows.

Bifurcation and Chaos in a Discrete Fractional Order Prey-Predator System Involving Infection in Prey

2020 ◽  
pp. 95-119
Author(s):  
A. George Maria Selvam ◽  
R. Dhineshbabu
Keyword(s):  
Fractional Order ◽  
Control Method ◽  
Complex Dynamics ◽  
Chaotic Behavior ◽  
Dynamical Behavior ◽  
Period Doubling ◽  
Order System ◽  
Qualitative Behavior ◽  
Uniqueness Of Solutions ◽  
Predator System

This chapter considers the dynamical behavior of a new form of fractional order three-dimensional continuous time prey-predator system and its discretized counterpart. Existence and uniqueness of solutions is obtained. The dynamic nature of the model is discussed through local stability analysis of the steady states. Qualitative behavior of the model reveals rich and complex dynamics as exhibited by the discrete-time fractional order model. Moreover, the bifurcation theory is applied to investigate the presence of Neimark-Sacker and period-doubling bifurcations at the coexistence steady state taking h as a bifurcation parameter for the discrete fractional order system. Also, the trajectories, phase diagrams, limit cycles, bifurcation diagrams, and chaotic attractors are obtained for biologically meaningful sets of parameter values for the discretized system. Finally, the analytical results are strengthened with appropriate numerical examples and they demonstrate the chaotic behavior over a range of parameters. Chaos control is achieved by the hybrid control method.

scholarly journals Bifurcation Analysis of a Van der Pol-Duffing Circuit with Parallel Resistor

2009 ◽  
Vol 2009 ◽  
pp. 1-26 ◽  
Author(s):  
Denis de Carvalho Braga ◽  
Luis Fernando Mello ◽  
Marcelo Messias
Keyword(s):  
Analytical Study ◽  
Complex Dynamics ◽  
Equilibrium Points ◽  
Dynamical Behavior ◽  
Period Doubling ◽  
Van Der Pol ◽  
Codimension One ◽  
Local Bifurcations ◽  
Parameter Values ◽  
Small Periodic

We study the local codimension one, two, and three bifurcations which occur in a recently proposed Van der Pol-Duffing circuit (ADVP) with parallel resistor, which is an extension of the classical Chua's circuit with cubic nonlinearity. The ADVP system presents a very rich dynamical behavior, ranging from stable equilibrium points to periodic and even chaotic oscillations. Aiming to contribute to the understand of the complex dynamics of this new system we present an analytical study of its local bifurcations and give the corresponding bifurcation diagrams. A complete description of the regions in the parameter space for which multiple small periodic solutions arise through the Hopf bifurcations at the equilibria is given. Then, by studying the continuation of such periodic orbits, we numerically find a sequence of period doubling and symmetric homoclinic bifurcations which leads to the creation of strange attractors, for a given set of the parameter values.

Dynamics, Synchronization and Electronic Implementations of a New Lorenz-like Chaotic System with Nonhyperbolic Equilibria

2019 ◽  
Vol 29 (14) ◽  
pp. 1950197 ◽  
Author(s):  
P. D. Kamdem Kuate ◽  
Qiang Lai ◽  
Hilaire Fotsin
Keyword(s):  
Chaotic System ◽  
Chaotic Systems ◽  
Lorenz System ◽  
Chaotic Behavior ◽  
Piecewise Linear ◽  
Period Doubling ◽  
Adaptive Synchronization ◽  
The Novel ◽  
Algebraic Equations ◽  
The Lorenz System

The Lorenz system has attracted increasing attention on the issue of its simplification in order to produce the simplest three-dimensional chaotic systems suitable for secure information processing. Meanwhile, Sprott’s work on elegant chaos has revealed a set of 19 chaotic systems all described by simple algebraic equations. This paper presents a new piecewise-linear chaotic system emerging from the simplification of the Lorenz system combined with the elegance of Sprott systems. Unlike the majority, the new system is a non-Shilnikov chaotic system with two nonhyperbolic equilibria. It is multiplier-free, variable-boostable and exclusively based on absolute value and signum nonlinearities. The use of familiar tools such as Lyapunov exponents spectra, bifurcation diagrams, frequency power spectra as well as Poincaré map help to demonstrate its chaotic behavior. The novel system exhibits inverse period doubling bifurcations and multistability. It has only five terms, one bifurcation parameter and a total amplitude controller. These features allow a simple and low cost electronic implementation. The adaptive synchronization of the novel system is investigated and the corresponding electronic circuit is presented to confirm its feasibility.

scholarly journals Dynamical visualization of anisotropic electromagnetic re-emissions from a single metal micro-helix at THz frequencies

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
T. Notake ◽  
T. Iyoda ◽  
T. Arikawa ◽  
K. Tanaka ◽  
C. Otani ◽  
...  
Keyword(s):  
Real Time ◽  
Electromagnetic Waves ◽  
Electromagnetic Compatibility ◽  
Smart Antenna ◽  
Dynamical Behavior ◽  
Measurement Techniques ◽  
Spatial Evolution ◽  
Frequency Spectra ◽  
3D Objects ◽  
Current Oscillations

AbstractThe capability for actual measurements—not just simulations—of the dynamical behavior of THz electromagnetic waves, including interactions with prevalent 3D objects, has become increasingly important not only for developments of various THz devices, but also for reliable evaluation of electromagnetic compatibility. We have obtained real-time visualizations of the spatial evolution of THz electromagnetic waves interacting with a single metal micro-helix. After the micro-helix is stimulated by a broadband pico-second pulse of THz electromagnetic waves, two types of anisotropic re-emissions can occur following overall inductive current oscillations in the micro-helix. They propagate in orthogonally crossed directions with different THz frequency spectra. This unique radiative feature can be very useful for the development of a smart antenna with broadband multiplexing/demultiplexing ability and directional adaptivity. In this way, we have demonstrated that our advanced measurement techniques can lead to the development of novel functional THz devices.

Behavior of a Self-Sustained Electromechanical Transducer and Routes to Chaos

2005 ◽  
Vol 128 (3) ◽  
pp. 282-293 ◽  
Author(s):  
J. C. Chedjou ◽  
K. Kyamakya ◽  
I. Moussa ◽  
H.-P. Kuchenbecker ◽  
W. Mathis
Keyword(s):  
Electronic Circuit ◽  
Initial Conditions ◽  
Dynamical Behavior ◽  
Period Doubling ◽  
Electromechanical System ◽  
Phase Portraits ◽  
Coupling Coefficients ◽  
Oscillatory Solutions ◽  
Electromechanical Transducer ◽  
Design Engineers

This paper studies the dynamics of a self-sustained electromechanical transducer. The stability of fixed points in the linear response is examined. Their local bifurcations are investigated and different types of bifurcation likely to occur are found. Conditions for the occurrence of Hopf bifurcations are derived. Harmonic oscillatory solutions are obtained in both nonresonant and resonant cases. Their stability is analyzed in the resonant case. Various bifurcation diagrams associated to the largest one-dimensional (1-D) numerical Lyapunov exponent are obtained, and it is found that chaos can appear suddenly, through period doubling, period adding, or torus breakdown. The extreme sensitivity of the electromechanical system to both initial conditions and tiny variations of the coupling coefficients is also outlined. The experimental study of̱the electromechanical system is carried out. An appropriate electronic circuit (analog simulator) is proposed for the investigation of the dynamical behavior of the electromechanical system. Correspondences are established between the coefficients of the electromechanical system model and the components of the electronic circuit. Harmonic oscillatory solutions and phase portraits are obtained experimentally. One of the most important contributions of this work is to provide a set of reliable analytical expressions (formulas) describing the electromechanical system behavior. These formulas are of great importance for design engineers as they can be used to predict the states of the electromechanical systems and respectively to avoid their destruction. The reliability of the analytical formulas is demonstrated by the very good agreement with the results obtained by both the numeric and the experimental analysis.

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