scholarly journals Chaos and Control in Coronary Artery System

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Yanxiang Shi
Keyword(s):  
Coronary Artery ◽  
Feedback Control ◽  
Numerical Simulations ◽  
Melnikov Method ◽  
Phase Portraits ◽  
Bifurcation Diagrams ◽  
Nonlinear Dynamical ◽  
The Road ◽  
Two Systems ◽  
And Control

Two types of coronary artery system N-type and S-type, are investigated. The threshold conditions for the occurrence of Smale horseshoe chaos are obtained by using Melnikov method. Numerical simulations including phase portraits, potential diagram, homoclinic bifurcation curve diagrams, bifurcation diagrams, and Poincaré maps not only prove the correctness of theoretical analysis but also show the interesting bifurcation diagrams and the more new complex dynamical behaviors. Numerical simulations are used to investigate the nonlinear dynamical characteristics and complexity of the two systems, revealing bifurcation forms and the road leading to chaotic motion. Finally the chaotic states of the two systems are effectively controlled by two control methods: variable feedback control and coupled feedback control.

ON ADAPTIVE SYNCHRONIZATION AND CONTROL OF NONLINEAR DYNAMICAL SYSTEMS

1996 ◽  
Vol 06 (03) ◽  
pp. 455-471 ◽  
Author(s):  
CHAI WAH WU ◽  
TAO YANG ◽  
LEON O. CHUA
Keyword(s):  
Spread Spectrum ◽  
Communication Systems ◽  
Chaotic Systems ◽  
Nonlinear Dynamical Systems ◽  
Adaptive Synchronization ◽  
Adaptive Controllers ◽  
Nonlinear Dynamical ◽  
Two Systems ◽  
And Control

In this paper, we study the synchronization of two coupled nonlinear, in particular chaotic, systems which are not identical. We show how adaptive controllers can be used to adjust the parameters of the systems such that the two systems will synchronize. We use a Lyapunov function approach to prove a global result which shows that our choice of controllers will synchronize the two systems. We show how it is related to Huberman-Lumer adaptive control and the LMS adaptive algorithm. We illustrate the applicability of this method using Chua's oscillators as the chaotic systems. We choose parameters for the two systems which are orders of magnitude apart to illustrate the effectiveness of the adaptive controllers. Finally, we discuss the role of adaptive synchronization in the context of secure and spread spectrum communication systems. In particular, we show how several signals can be encoded onto a single scalar chaotic carrier signal.

Subharmonic Bifurcations and Transition to Chaos in a Pipe Conveying Fluid under Harmonic Excitation

2013 ◽  
Vol 444-445 ◽  
pp. 791-795
Author(s):  
Yi Xiang Geng ◽  
Han Ze Liu
Keyword(s):  
Chaotic Behavior ◽  
Melnikov Method ◽  
Harmonic Excitation ◽  
Phase Portraits ◽  
Pipe Conveying Fluid ◽  
Bifurcation Diagrams ◽  
Dynamical Behaviors ◽  
Transition To Chaos ◽  
Subharmonic Bifurcations ◽  
Conveying Fluid

The subharmonic and chaotic behavior of a two end-fixed fluid conveying pipe whose base is subjected to a harmonic excitation are investigated. Melnikov method is applied for the system, and Melnikov criterions for subharmonic and homoclinic bifurcations are obtained analytically. The numerical simulations (including bifurcation diagrams, maximal Lyapunov exponents, phase portraits and Poincare map) confirm the analytical predictions and exhibit the complicated dynamical behaviors.

Nonlinear Modeling and Control of Overhead Crane Load Sway

1988 ◽  
Vol 110 (3) ◽  
pp. 266-271 ◽  
Author(s):  
Kamal A. F. Moustafa ◽  
A. M. Ebeid
Keyword(s):  
Control System ◽  
Feedback Control ◽  
Digital Computer ◽  
Nonlinear Modeling ◽  
Overhead Crane ◽  
Nonlinear Dynamical ◽  
Modeling And Control ◽  
Control Scheme ◽  
Rate Of Decay ◽  
And Control

In this paper, we derive a nonlinear dynamical model for an overhead crane. The model takes into account simultaneous travel and transverse motions of the crane. The aim is to transport an object along a specified transport route in such a way that the swing angles are suppressed as quickly as possible. We develop an antiswing control system which adopts a feedback control to specify the crane speed at every moment. The gain matrix is chosen such that a desired rate of decay of the swing angles is obtained. The model and control scheme are simulated on a digital computer and the results prove that the feedback control works well.

scholarly journals Dynamics Analysis and Control of a Five-Term Fractional-Order System

2018 ◽  
Vol 2018 ◽  
pp. 1-10
Author(s):  
Li-xin Yang ◽  
Xiao-jun Liu
Keyword(s):  
Fractional Order ◽  
Equilibrium Points ◽  
Fractional Order System ◽  
Phase Portraits ◽  
Order System ◽  
Bifurcation Diagrams ◽  
Compound Structure ◽  
Dynamical Properties ◽  
The Stability ◽  
And Control

This paper proposes a new fractional-order chaotic system with five terms. Firstly, basic dynamical properties of the fractional-order system are investigated in terms of the stability of equilibrium points, Jacobian matrices theoretically. Furthermore, rich dynamics with interesting characteristics are demonstrated by phase portraits, bifurcation diagrams numerically. Besides, the control problem of the new fractional-order system is discussed via numerical simulations. Our results demonstrate that the new fractional-order system has compound structure.

scholarly journals SYNTHESIS OF THE LAWS GOVERNING THE NON-HOLONOMIC MODEL OF A TWO-LINK ROAD TRAIN WITH REVERSE MOTION (OFF-AXLE HITCHING MODEL)

2018 ◽  
Vol 2 ◽  
pp. 40-51
Author(s):  
Dmitry Tatievskyi
Keyword(s):  
Rear Axle ◽  
Orientation Angle ◽  
Control Object ◽  
Phase Portraits ◽  
Rectilinear Motion ◽  
Control Laws ◽  
The Road ◽  
Automatic Control Systems ◽  
Lyapunov Function Method ◽  
And Control

The complexity of the control of the road train is due to the pronounced nonlinearities, as well as the instability of the control object during the movement in the backward motion (jackknifing). For the road trains, the location of the towing device behind the tractor's rear axle is quite typical. In this study, a synthesis of control laws for road trains with offset of coupling devices relative to the rear axle of the tractor (off-axle hitching) is proposed. The controllers have been implemented both to ensure a stable circular motion and for rectilinear motion with a given orientation angle, and the behavioral features of this model have been studied on the basis of them. Based on the analysis of the approaches to the synthesis of the laws governing the road train with the coupling out, it was decided to synthesize the required control laws using the Lyapunov function method. Synthesized controllers can be directly used to program the robotic systems of the respective models. It is also possible to use them for the development of the Dubins machine for the investigated model. They can be used to build automatic control systems that would help the driver to drive a car with a trailer while driving backward. In this research, a study was made of the state of the solution of the problem associated with the reverse movement of a road train consisting of a tractor and a semitrailer with a coupling, synthesized laws made it possible to study the features of such model, determined by its linear dimensions. For comparison of the synthesized laws, the analysis of phase portraits of trajectories, angles of folding and control, orientation angles was carried out, and also the analysis of the quality of transient processes with the change in the speed of the road train was performed.

Chaos Behavior and Control of Stay-Cables

2012 ◽  
Vol 446-449 ◽  
pp. 1109-1114
Author(s):  
Jin Hai Li ◽  
Qing Li Yan ◽  
Jin Shuan Liu
Keyword(s):  
Dynamic Behavior ◽  
Chaotic Motion ◽  
Nonlinear Dynamical System ◽  
Melnikov Method ◽  
Periodic Excitation ◽  
Stay Cable ◽  
Nonlinear Dynamical ◽  
Infinite Dimensional ◽  
First Order ◽  
And Control

Stay-cable is infinite dimensional nonlinear dynamical system with a very complex vibration types and mechanism which are not described reasonably yet. In order to better control its dynamic behavior, it is necessary to study complex dynamic behavior carefully. Fistly, partial differential equation of the cable motion is established based on the parabolic initial configuration and is simplified into n Duffing-equations by using Galerkin method. Secondly, the chaos behaviors of the first order Duffing-equation under periodic excitation are studied by taking advantage of Melnikov method. At last , parameters may lead to chaotic motion of a true cable in laboratory are calculated and the methods of chaos control are discussed briefly. The study shows that: 1. First order vibration of cable under periodic excitation has much more complex behaviors than the freedom vibration; 2. The Melnikov method can be very effective and convenient for the analysis of chaotic motion of cable.

On the Dynamics and Control of a Fractional Form of the Discrete Double Scroll

2019 ◽  
Vol 29 (06) ◽  
pp. 1950078 ◽  
Author(s):  
Adel Ouannas ◽  
Amina-Aicha Khennaoui ◽  
Samir Bendoukha ◽  
Giuseppe Grassi
Keyword(s):  
Fractional Order ◽  
Numerical Results ◽  
Phase Portraits ◽  
Bifurcation Diagrams ◽  
Complete Synchronization ◽  
General Behavior ◽  
Control Schemes ◽  
Dynamics And Control ◽  
And Control

This paper is concerned with the dynamics and control of the fractional version of the discrete double scroll hyperchaotic map. Using phase portraits and bifurcation diagrams, we show that the general behavior of the proposed map depends on the fractional order. We also present two control schemes for the proposed map, one that adaptively stabilizes the map, and another to achieve the complete synchronization of a pair of maps. Numerical results are presented to illustrate the findings.

scholarly journals Bifurcations, Hidden Chaos and Control in Fractional Maps

Symmetry ◽  
2020 ◽  
Vol 12 (6) ◽  
pp. 879 ◽  
Author(s):  
Adel Ouannas ◽  
Othman Abdullah Almatroud ◽  
Amina Aicha Khennaoui ◽  
Mohammad Mossa Alsawalha ◽  
Dumitru Baleanu ◽  
...  
Keyword(s):  
Nonlinear Dynamical Systems ◽  
Initial Conditions ◽  
Three Dimensional ◽  
Phase Portraits ◽  
Discrete Fractional Calculus ◽  
Hidden Attractors ◽  
Nonlinear Dynamical ◽  
Control Schemes ◽  
Stable Equilibria ◽  
And Control

Recently, hidden attractors with stable equilibria have received considerable attention in chaos theory and nonlinear dynamical systems. Based on discrete fractional calculus, this paper proposes a simple two-dimensional and three-dimensional fractional maps. Both fractional maps are chaotic and have a unique equilibrium point. Results show that the dynamics of the proposed fractional maps are sensitive to both initial conditions and fractional order. There are coexisting attractors which have been displayed in terms of bifurcation diagrams, phase portraits and a 0-1 test. Furthermore, control schemes are introduced to stabilize the chaotic trajectories of the two novel systems.

scholarly journals Codimension-2 Bifurcation Analysis and Control of a Discrete Mosquito Model with a Proportional Release Rate of Sterile Mosquitoes

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-18
Author(s):  
Qiaoling Chen ◽  
Zhidong Teng ◽  
Junli Liu ◽  
Feng Wang
Keyword(s):  
Release Rate ◽  
Discrete Model ◽  
Bifurcation Theory ◽  
Control Strategies ◽  
Phase Portraits ◽  
Bifurcation Diagrams ◽  
Dynamical Behaviors ◽  
And Control ◽  
Theoretical Results ◽  
Maximum Lyapunov Exponents

This paper concerns a discrete wild and sterile mosquito model with a proportional release rate of sterile mosquitoes. It is shown that the discrete model undergoes codimension-2 bifurcations with 1 : 2, 1 : 3, and 1 : 4 strong resonances by applying the bifurcation theory. Some numerical simulations, including codimension-2 bifurcation diagrams, maximum Lyapunov exponents diagrams, and phase portraits, are also presented to illustrate the validity of theoretical results and display the complex dynamical behaviors. Moreover, two control strategies are applied to the model.

Chaotic Motions in Forced Mixed Rayleigh–Liénard Oscillator with External and Parametric Periodic-Excitations

2018 ◽  
Vol 28 (03) ◽  
pp. 1830005 ◽  
Author(s):  
C. H. Miwadinou ◽  
A. V. Monwanou ◽  
A. A. Koukpemedji ◽  
Y. J. F. Kpomahou ◽  
J. B. Chabi Orou
Keyword(s):  
Numerical Simulations ◽  
Lyapunov Exponents ◽  
Melnikov Method ◽  
Phase Portraits ◽  
Chaotic Motions ◽  
Poincaré Sections ◽  
Routes To Chaos ◽  
Domain Boundaries ◽  
Bifurcation Structures ◽  
Poincare Sections

This paper addresses the issue of a mixed Rayleigh–Liénard oscillator with external and parametric periodic-excitations. The Melnikov method is utilized to analytically determine the domain boundaries where horseshoe chaos appears. Routes to chaos are investigated through bifurcation structures, Lyapunov exponents, phase portraits and Poincaré sections. The effects of Rayleigh and Liénard parameters are analyzed. Results of analytical investigations are validated and complemented by numerical simulations.

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