scholarly journals New Chaotic Oscillator Derived from Class C Single Transistor-Based Amplifier

2020 ◽  
Vol 2020 ◽  
pp. 1-18
Author(s):  
Jiri Petrzela
Keyword(s):  
Dynamical System ◽  
Mathematical Model ◽  
High Frequency ◽  
Piecewise Linear ◽  
Chaotic Oscillator ◽  
Chaotic Dynamical System ◽  
Transient Behaviour ◽  
Local Polynomial ◽  
Good Accordance ◽  
Class C

This paper describes a new autonomous deterministic chaotic dynamical system having a single unstable saddle-spiral fixed point. A mathematical model originates in the fundamental structure of the class C amplifier. Evolution of robust strange attractors is conditioned by a bilateral nature of bipolar transistor with local polynomial or piecewise linear feedforward transconductance and high frequency of operation. Numerical analysis is supported by experimental verification and both results prove that chaos is neither a numerical artifact nor a long transient behaviour. Also, good accordance between theory and measurement has been observed.

NETWORK AS A CHAOTIC DYNAMICAL SYSTEM

2007 ◽  
Vol 17 (10) ◽  
pp. 3529-3533 ◽  
Author(s):  
SYUJI MIYAZAKI ◽  
YASUSHI NAGASHIMA
Keyword(s):  
Dynamical System ◽  
Network Structure ◽  
Transition Matrix ◽  
Chaotic Dynamics ◽  
Large Deviation ◽  
Piecewise Linear ◽  
Directed Network ◽  
Chaotic Dynamical System ◽  
One Dimensional ◽  
Finite Time Lyapunov Exponents

A directed network such as the WWW can be represented by a transition matrix. Comparing this matrix to a Frobenius–Perron matrix of a chaotic piecewise-linear one-dimensional map whose domain can be divided into Markov subintervals, we are able to relate the network structure itself to chaotic dynamics. Just like various large deviation properties of local expansion rates (finite-time Lyapunov exponents) related to chaotic dynamics, we can also discuss those properties of network structure.

On the Potential for Entangled States Between Chaotic Systems

2014 ◽  
Vol 24 (06) ◽  
pp. 1450077 ◽  
Author(s):  
Matthew A. Morena ◽  
Kevin M. Short
Keyword(s):  
Dynamical System ◽  
Periodic Orbits ◽  
Chaotic Systems ◽  
Entangled States ◽  
Future Research ◽  
Unstable Periodic Orbits ◽  
Qualitative Information ◽  
Chaotic Dynamical System ◽  
Naturally Occurring ◽  
External Intervention

We report on the tendency of chaotic systems to be controlled onto their unstable periodic orbits in such a way that these orbits are stabilized. The resulting orbits are known as cupolets and collectively provide a rich source of qualitative information on the associated chaotic dynamical system. We show that pairs of interacting cupolets may be induced into a state of mutually sustained stabilization that requires no external intervention in order to be maintained and is thus considered bound or entangled. A number of properties of this sort of entanglement are discussed. For instance, should the interaction be disturbed, then the chaotic entanglement would be broken. Based on certain properties of chaotic systems and on examples which we present, there is further potential for chaotic entanglement to be naturally occurring. A discussion of this and of the implications of chaotic entanglement in future research investigations is also presented.

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.

A CIRCLE MAP FOR A PHYTOPLANKTONIC LIFE CYCLE

2000 ◽  
Vol 10 (02) ◽  
pp. 325-344 ◽  
Author(s):  
ERIC P. M. GRIST
Keyword(s):  
Dynamical System ◽  
Life Cycle ◽  
Seasonal Change ◽  
West Coast ◽  
Temporal Dynamics ◽  
Piecewise Linear ◽  
Circle Map ◽  
Development Data ◽  
Linear Sections ◽  
Successive Generations

I focus on the temporal dynamics generated by a life cycle consisting of two contiguous stages developing under the influence of a stimulus which pulsates between on and off. I ask: under what general conditions does a population held in exposure to this kind of periodic stimulus achieve life cycle synchrony? The situation is represented by a dynamical system consisting of a nondecreasing circle map whose plot is made up of 45° and horizontal piecewise-linear sections. These features permit the iterative dynamics (itineraries) followed by successive generations to be derived and algebraic conditions for high-ordered synchronization to be derived. Using development data obtained for the phytoplankton Thalassiorira pseudonana and mean daily irradiation intensities recorded over different months at the latitude of Oban (west coast of Scotland), I apply the model to investigate how seasonal change in daily irradiance may directly influence the synchronous dynamics of such populations.

TREATMENT OF THE ERROR DUE TO UNRESOLVED SCALES IN SEQUENTIAL DATA ASSIMILATION

2011 ◽  
Vol 21 (12) ◽  
pp. 3619-3626 ◽  
Author(s):  
ALBERTO CARRASSI ◽  
STÉPHANE VANNITSEM
Keyword(s):  
Dynamical System ◽  
Kalman Filter ◽  
Data Assimilation ◽  
Large Scale ◽  
Model Error ◽  
Environmental Modeling ◽  
Sequential Data ◽  
Chaotic Dynamical System ◽  
Error Covariance ◽  
Sequential Data Assimilation

In this paper, a method to account for model error due to unresolved scales in sequential data assimilation, is proposed. An equation for the model error covariance required in the extended Kalman filter update is derived along with an approximation suitable for application with large scale dynamics typical in environmental modeling. This approach is tested in the context of a low order chaotic dynamical system. The results show that the filter skill is significantly improved by implementing the proposed scheme for the treatment of the unresolved scales.

A New Chaotic Electro-Mechanical Oscillator

2016 ◽  
Vol 26 (10) ◽  
pp. 1650161 ◽  
Author(s):  
Arturo Buscarino ◽  
Carlo Famoso ◽  
Luigi Fortuna ◽  
Mattia Frasca
Keyword(s):  
Mathematical Model ◽  
Chaotic Motion ◽  
Chaotic Oscillator ◽  
Mechanical Oscillator ◽  
Mechanical Structure ◽  
Metal Tip ◽  
Double Well Potential

In this paper, a new electro-mechanical chaotic oscillator is presented. The system is based on the motion of the metal tip of a beam in a double-well potential generated by two magnets, and works thanks to the vibrations generated in the flexible mechanical structure by two rotating coils that produce noise-like signals. As the source of vibration is internal, the system may be considered an autonomous oscillator. Chaotic motion is experimentally observed and verified with a mathematical model of the phenomenon.

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