Basin of Attraction of Controller Gain for Chaotic Behavior of Universal Motor Drive

We consider the dynamics of the first vibrational mode of a suspension bridge, resulting from the coupling between its roadbed (elastic beam) and the hangers, supposed to be one-sided springs which respond only to stretching. The external forcing is due to time-periodic vortices produced by impinging wind on the bridge structure. We have studied some relevant dynamical phenomena in such a system, like periodic and quasiperiodic responses, chaotic motion, and boundary crises. In the weak dissipative limit the dynamics is mainly multistable, presenting a variety of coexisting attractors, both periodic and chaotic, with a highly involved basin of attraction structure.

Download Full-text

Generation and Evolution of Chaos in Double-Well Duffing Oscillator under Parametrical Excitation

Shock and Vibration ◽

10.1155/2016/6109062 ◽

2016 ◽

Vol 2016 ◽

pp. 1-8

Author(s):

Ying Zhang ◽

Xiaole Yue ◽

Lin Du ◽

Liang Wang ◽

Tong Fang

Keyword(s):

Numerical Simulation ◽

Chaotic Behavior ◽

Duffing Oscillator ◽

Basin Of Attraction ◽

Threshold Value ◽

Smale Horseshoe ◽

Transient Motion ◽

Basin Boundary ◽

Dynamical Behaviors ◽

Insight Into

The generation and evolution of chaotic motion in double-well Duffing oscillator under harmonic parametrical excitation are investigated. Firstly, the complex dynamical behaviors are studied by applying multibifurcation diagram and Poincaré sections. Secondly, by means of Melnikov’s approach, the threshold value of parameterμfor generation of chaotic behavior in Smale horseshoe sense is calculated. By the numerical simulation, it is obvious that asμexceeds this threshold value, the behavior of Duffing oscillator is still steady-state periodic but the transient motion is chaotic; until the top Lyapunov exponent turns to positive, the motion of system turns to permanent chaos. Therefore, in order to gain an insight into the evolution of chaotic behavior afterμpassing the threshold value, the transient motion, basin of attraction, and basin boundary are also investigated.

Download Full-text

Melnikov Chaos in a Modified Rayleigh–Duffing Oscillator with ϕ6 Potential

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127416500851 ◽

2016 ◽

Vol 26 (05) ◽

pp. 1650085 ◽

Cited By ~ 8

Author(s):

C. H. Miwadinou ◽

A. V. Monwanou ◽

L. A. Hinvi ◽

A. A. Koukpemedji ◽

C. Ainamon ◽

...

Keyword(s):

Chaotic Behavior ◽

Duffing Oscillator ◽

Basin Of Attraction ◽

Melnikov Method ◽

Nonlinear Damping ◽

External Excitation ◽

Melnikov Criterion ◽

Single Well ◽

Quadratic Damping ◽

The Basin Of Attraction

The chaotic behavior of the modified Rayleigh–Duffing oscillator with [Formula: see text] potential and external excitation is investigated both analytically and numerically. The so-called oscillator models, for example, ship rolling motions. The single well and triple well potential cases are considered. Melnikov method is applied and the conditions for the existence of homoclinic and heteroclinic chaos are obtained. The effects of nonlinear damping on roll motion of ships are analyzed in detail. As it is known, nonlinear roll damping is a very important parameter in estimating ship responses. It is noted that the pure and unpure quadratic damping parameters affect the Melnikov criterion in the heteroclinic and homoclinic cases respectively while the pure cubic parameter affects the amplitude in both cases. The predictions have been tested with numerical simulations based on the basin of attraction. It is pointed out that certain quadratic damping effects are contrary to cubic damping effect.

Download Full-text

CHAOTIC BEHAVIOR OF A NEURAL NETWORK WITH DYNAMICAL THRESHOLDS

International Journal of Neural Systems ◽

10.1142/s0129065791000364 ◽

1991 ◽

Vol 01 (04) ◽

pp. 327-335 ◽

Cited By ~ 14

Author(s):

O. Hendin ◽

D. Horn ◽

M. Usher

Keyword(s):

Chaotic Motion ◽

Chaotic Behavior ◽

Closed Orbit ◽

Basin Of Attraction ◽

Inhibitory Neurons ◽

General Character ◽

Closed Loops ◽

Feedback Network ◽

Short Time ◽

Qualitative Changes

Models of neural networks which include dynamical thresholds can display motion in pattern space, the space of all memories. We investigate this motion in a particular model which is based on a feedback network of excitatory and inhibitory neurons. We find that small variations in the parameters of the model can lead to big qualitative changes of its behavior. We display results of closed loops and chaotic motion which turn from one to the other through intermittency. We show that the basin of attraction of a closed orbit has a fractal shape, and find that the dimension of the chaotic motion is slightly bigger than 2. The general character of the dynamics of this model is convergence to centers of attraction on short time scales and divergence on long ones.

Download Full-text