scholarly journals Effects of additive noise on a nonlinear oscillator exhibiting period doubling and chaotic behavior

1983 ◽  
Vol 6 (3) ◽  
pp. 413-414
Keyword(s):  
Nonlinear Oscillator ◽  
Additive Noise ◽  
Chaotic Behavior ◽  
Period Doubling

Robust Estimation-Based Control of Chaotic Behavior in an Oscillator with Inertial and Elastic Symmetric Nonlinearities

2003 ◽  
Vol 9 (6) ◽  
pp. 665-684 ◽  
Author(s):  
A. A. Al-Qaisia ◽  
A. M. Harb ◽  
A. A. Zaher ◽  
M. A. Zohdy
Keyword(s):  
Robust Estimation ◽  
Nonlinear Oscillator ◽  
Chaotic Behavior ◽  
Period Doubling ◽  
Physical Parameters ◽  
Bifurcation And Chaos ◽  
Transition To Chaos ◽  
Simulation Results ◽  
Forced Nonlinear Oscillator ◽  
Period Doubling Bifurcations

In this paper, we study the dynamics of a forced nonlinear oscillator with inertial and elastic symmetric nonlinearities using modern nonlinear, bifurcation and chaos theories. The results for the response have shown that, for a certain combination of physical parameters, this oscillator exhibits a chaotic behavior or a transition to chaos through a sequence of period doubling bifurcations. The main objective of this paper is to control the chaotic behavior for this type of oscillator. A nonlinear estimation-based controller is proposed and the transient performance is investigated. The design of the parameter update mechanism is analyzed while discussing ways to extend its performance to further account for other types of uncertainties. We examine robustness problems as well as ways to tune the controller parameters. Simulation results are presented for the uncontrolled and controlled cases, verifying the effectiveness and the capability of the proposed controller. Finally, a discussion and conclusions are given with possible future extensions.

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 Period-doubling bifurcation analysis and chaos control for load torque using FLC

2021 ◽  
Author(s):  
Eman Moustafa ◽  
Abdel-Azem Sobaih ◽  
Belal Abozalam ◽  
Amged Sayed A. Mahmoud
Keyword(s):  
Floquet Theory ◽  
Chaos Control ◽  
Fuzzy Logic Controller ◽  
Chaotic Behavior ◽  
Period Doubling ◽  
Parameter Variation ◽  
Period Doubling Bifurcation ◽  
Load Torque ◽  
Nonlinear Behaviors ◽  
Scientific Fields

AbstractChaotic phenomena are observed in several practical and scientific fields; however, the chaos is harmful to systems as they can lead them to be unstable. Consequently, the purpose of this study is to analyze the bifurcation of permanent magnet direct current (PMDC) motor and develop a controller that can suppress chaotic behavior resulted from parameter variation such as the loading effect. The nonlinear behaviors of PMDC motors were investigated by time-domain waveform, phase portrait, and Floquet theory. By varying the load torque, a period-doubling bifurcation appeared which in turn led to chaotic behavior in the system. So, a fuzzy logic controller and developing the Floquet theory techniques are applied to eliminate the bifurcation and the chaos effects. The controller is used to enhance the performance of the system by getting a faster response without overshoot or oscillation, moreover, tends to reduce the steady-state error while maintaining its stability. The simulation results emphasize that fuzzy control provides better performance than that obtained from the other controller.

scholarly journals Nonlinear absorption of ultra short laser pulses by clusters

2006 ◽  
Vol 24 (1) ◽  
pp. 9-14 ◽  
Author(s):  
M. KANAPATHIPILLAI
Keyword(s):  
Initial Phase ◽  
Nonlinear Oscillator ◽  
Chaotic Behavior ◽  
Nonlinear Resonance ◽  
Laser Pulses ◽  
Cluster Interaction ◽  
Lyapunov Spectra ◽  
Short Laser Pulses ◽  
Established Fact ◽  
Eigen Frequencies

Very good absorption of ultra short laser pulses by clusters is a well established fact. Efficient collisional absorption occurs only in the initial phase of the pulse. However, experiments and numerical simulations show that even after collisional absorption becomes inefficient subsequent to heating of the electrons, strong absorption continues. There have been a few attempts to model this phenomenon in terms of driven “linear” oscillator models with time dependent eigen-frequencies. Here we propose a nonlinear oscillator model and show that nonlinear resonance is the leading mechanism responsible for the collisionless absorption. Further it is demonstrated, on the basis of Lyapunov spectra, that laser-cluster interaction, under certain conditions, exhibits chaotic behavior.

EFFECTS OF CONTRARIAN INVESTOR TYPE IN ASSET PRICE DYNAMICS

2009 ◽  
Vol 19 (08) ◽  
pp. 2463-2472 ◽  
Author(s):  
NATASHA KIRBY ◽  
ANDREW FOSTER
Keyword(s):  
Asset Pricing ◽  
Chaotic Behavior ◽  
Price Change ◽  
Asset Price ◽  
Period Doubling ◽  
Global Bifurcations ◽  
Pricing Model ◽  
Significant Group ◽  
Asset Pricing Model ◽  
Planar Maps

We develop an asset pricing model based on the interaction of heterogeneous trading groups. In addition to the two main trader groups, fundamentalists and trend-chasing chartists, we include a third significant group known as contrarian chartists. We model the case of opportunistic contrarian behavior, where the contrarian group disagrees with the trend-chasing chartists only when the return differential is high. We also consider absolute contrarian behavior, in which the contrarians consistently disagree with trend-chasers. The models are nonlinear planar maps, exhibiting period doubling, Neimark–Sacker and global bifurcations leading to local chaotic behavior. Absolute contrarian behavior is found to have a moderating effect on price change, while opportunistic contrarian behavior is found to further complicate the price cycles present in other models.

scholarly journals Discrete-Time Predator-Prey Interaction with Selective Harvesting and Predator Self-Limitation

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Zhihua Chen ◽  
Qamar Din ◽  
Muhammad Rafaqat ◽  
Umer Saeed ◽  
Muhammad Bilal Ajaz
Keyword(s):  
Discrete Time ◽  
Chaotic Behavior ◽  
Period Doubling ◽  
State Feedback Control ◽  
Time Model ◽  
Predator Prey ◽  
Selective Harvesting ◽  
Predator Prey Model ◽  
Prey System ◽  
Prey Interaction

Selective harvesting plays an important role on the dynamics of predator-prey interaction. On the other hand, the effect of predator self-limitation contributes remarkably to the stabilization of exploitative interactions. Keeping in view the selective harvesting and predator self-limitation, a discrete-time predator-prey model is discussed. Existence of fixed points and their local dynamics is explored for the proposed discrete-time model. Explicit principles of Neimark–Sacker bifurcation and period-doubling bifurcation are used for discussion related to bifurcation analysis in the discrete-time predator-prey system. The control of chaotic behavior is discussed with the help of methods related to state feedback control and parameter perturbation. At the end, some numerical examples are presented for verification and illustration of theoretical findings.

CHAOTIC BEHAVIOR INDUCED BY THERMAL MODULATION IN A MODEL OF THE CONVECTIVE FLOW OF A FLUID MIXTURE IN A POROUS MEDIUM

1999 ◽  
Vol 09 (02) ◽  
pp. 383-396 ◽  
Author(s):  
J.-M. MALASOMA ◽  
P. WERNY ◽  
C.-H. LAMARQUE
Keyword(s):  
Porous Medium ◽  
Convective Flow ◽  
Chaotic Behavior ◽  
Period Doubling ◽  
Chaotic Attractors ◽  
Global Behavior ◽  
Type I ◽  
Fluid Mixture ◽  
Numerical Investigations ◽  
Period Doubling Bifurcations

Numerical investigations of the global behavior of a model of the convective flow of a binary mixture in a porous medium are reported. We find a complex behavior characterized by the presence of coexisting periodic, quasiperiodic and chaotic attractors. Bifurcations of periodic solutions and routes to chaos via type-I intermittency and period-doubling bifurcations are described. Boundary crises and band merging crises have also been observed.

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