Period doubling bifurcation problems in the softening Duffing oscillator with nonstationary excitation

1994 ◽  
Vol 5 (4) ◽  
pp. 401-420 ◽  
Author(s):  
C. H. Lu ◽  
R. M. Evan-Iwanowski
Keyword(s):  
Duffing Oscillator ◽  
Period Doubling ◽  
Period Doubling Bifurcation ◽  
Bifurcation Problems

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 Complex dynamics and coexistence of period-doubling and period-halving bifurcations in an integrated pest management model with nonlinear impulsive control

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Changtong Li ◽  
Sanyi Tang ◽  
Robert A. Cheke
Keyword(s):  
Periodic Solution ◽  
Integrated Pest Management ◽  
Pest Management ◽  
Pest Control ◽  
Impulsive Control ◽  
Period Doubling ◽  
Dynamical Behaviour ◽  
Period Doubling Bifurcation ◽  
Predator Prey ◽  
Predator Prey Model

Abstract An expectation for optimal integrated pest management is that the instantaneous numbers of natural enemies released should depend on the densities of both pest and natural enemy in the field. For this, a generalised predator–prey model with nonlinear impulsive control tactics is proposed and its dynamics is investigated. The threshold conditions for the global stability of the pest-free periodic solution are obtained based on the Floquet theorem and analytic methods. Also, the sufficient conditions for permanence are given. Additionally, the problem of finding a nontrivial periodic solution is confirmed by showing the existence of a nontrivial fixed point of the model’s stroboscopic map determined by a time snapshot equal to the common impulsive period. In order to address the effects of nonlinear pulse control on the dynamics and success of pest control, a predator–prey model incorporating the Holling type II functional response function as an example is investigated. Finally, numerical simulations show that the proposed model has very complex dynamical behaviour, including period-doubling bifurcation, chaotic solutions, chaos crisis, period-halving bifurcations and periodic windows. Moreover, there exists an interesting phenomenon whereby period-doubling bifurcation and period-halving bifurcation always coexist when nonlinear impulsive controls are adopted, which makes the dynamical behaviour of the model more complicated, resulting in difficulties when designing successful pest control strategies.

Period-doubling bifurcation in an electronic circuit with a fast-recovery diode and square-wave input

1988 ◽  
Vol 38 (3) ◽  
pp. 1645-1648 ◽  
Author(s):  
Chil-Min Kim ◽  
Chang-Ho Cho ◽  
Chul-Se Lee ◽  
Jae-Hag Yim ◽  
Jintai Kim ◽  
...  
Keyword(s):  
Electronic Circuit ◽  
Period Doubling ◽  
Period Doubling Bifurcation ◽  
Fast Recovery ◽  
Square Wave

scholarly journals Control of period-doubling bifurcation and chaos in a discrete nonlinear system by the feedback of states and parameter adjustment

2003 ◽  
Vol 52 (4) ◽  
pp. 790
Author(s):  
Luo Xiao-Shu ◽  
Chen Guan-Rong ◽  
Wang Bing-Hong ◽  
Fang Jin-Qing ◽  
Zou Yan-Li ◽  
...  
Keyword(s):  
Nonlinear System ◽  
Period Doubling ◽  
Period Doubling Bifurcation ◽  
Bifurcation And Chaos ◽  
Parameter Adjustment

scholarly journals Mechanism of period-doubling bifurcation in DCM DC-DC converter

2008 ◽  
Vol 57 (5) ◽  
pp. 2728
Author(s):  
Wang Xue-Mei ◽  
Zhang Bo ◽  
Qiu Dong-Yuan
Keyword(s):  
Period Doubling ◽  
Period Doubling Bifurcation

CHAOTIC DYNAMICS OF A SIMPLE PARAMETRICALLY DRIVEN DISSIPATIVE CIRCUIT

2011 ◽  
Vol 21 (07) ◽  
pp. 1927-1933 ◽  
Author(s):  
P. PHILOMINATHAN ◽  
M. SANTHIAH ◽  
I. RAJA MOHAMED ◽  
K. MURALI ◽  
S. RAJASEKAR
Keyword(s):  
Numerical Simulation ◽  
Lyapunov Exponents ◽  
Chaotic Dynamics ◽  
Period Doubling ◽  
Classic Period ◽  
Control Signal ◽  
Period Doubling Bifurcation ◽  
Chaotic Circuit ◽  
Route To Chaos ◽  
Parameter Values

We introduce a simple parametrically driven dissipative second-order chaotic circuit. In this circuit, one of the circuit parameters is varied by an external periodic control signal. Thus by tuning the parameter values of this circuit, classic period-doubling bifurcation route to chaos is found to occur. The experimentally observed phenomena is further validated through corresponding numerical simulation of the circuit equations. The periodic and chaotic dynamics of this model is further characterized by computing Lyapunov exponents.

scholarly journals Period-Doubling Bifurcation to Alternans in Paced Cardiac Tissue: Crossover from Smooth to Border-Collision Characteristics

2007 ◽  
Vol 99 (5) ◽  
Author(s):  
Carolyn M. Berger ◽  
Xiaopeng Zhao ◽  
David G. Schaeffer ◽  
Hana M. Dobrovolny ◽  
Wanda Krassowska ◽  
...  
Keyword(s):  
Cardiac Tissue ◽  
Period Doubling ◽  
Period Doubling Bifurcation

THE EFFECT OF NONLINEAR DAMPING ON THE UNIVERSAL ESCAPE OSCILLATOR

1999 ◽  
Vol 09 (04) ◽  
pp. 735-744 ◽  
Author(s):  
MIGUEL A. F. SANJUÁN
Keyword(s):  
Energy Dissipation ◽  
Period Doubling ◽  
Nonlinear Damping ◽  
Basins Of Attraction ◽  
Period Doubling Bifurcation ◽  
Damping Coefficient ◽  
Nonlinear Dissipation ◽  
Fractal Basin Boundaries ◽  
Basin Boundaries

This paper analyzes the role of nonlinear dissipation on the universal escape oscillator. Nonlinear damping terms proportional to the power of the velocity are assumed and an investigation on its effects on the dynamics of the oscillator, such as the threshold of period-doubling bifurcation, fractal basin boundaries and how the basins of attraction are destroyed, is carried out. The results suggest that increasing the power of the nonlinear damping, has similar effects as of decreasing the damping coefficient for a linearly damped case, showing the very importance of the level or amount of energy dissipation.

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