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 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.

Generating Fully Bounded Chaotic Attractors

2013 ◽  
pp. 148-153
Author(s):  
Zeraoulia Elhadj
Keyword(s):  
Dynamical Systems ◽  
Nonlinear Dynamical Systems ◽  
Dynamical Behavior ◽  
Phase Portraits ◽  
Chaotic Attractors ◽  
Nonlinear Dynamical ◽  
Dynamical Properties ◽  
The Given

Generating chaotic attractors from nonlinear dynamical systems is quite important because of their applicability in sciences and engineering. This paper considers a class of 2-D mappings displaying fully bounded chaotic attractors for all bifurcation parameters. It describes in detail the dynamical behavior of this map, along with some other dynamical phenomena. Also presented are some phase portraits and some dynamical properties of the given simple family of 2-D discrete mappings.

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.

Coexistence of Chaos with Hyperchaos, Period-3 Doubling Bifurcation, and Transient Chaos in the Hyperchaotic Oscillator with Gyrators

2015 ◽  
Vol 25 (04) ◽  
pp. 1550052 ◽  
Author(s):  
J. Kengne
Keyword(s):  
Integrated Circuit ◽  
Nonlinear Dynamical Systems ◽  
Piecewise Linear ◽  
Phase Portraits ◽  
Piecewise Linear Approximation ◽  
Transient Chaos ◽  
Frequency Spectra ◽  
Nonlinear Dynamical ◽  
System Parameters ◽  
Coexistence Of Attractors

In this paper, the dynamics of the paradigmatic hyperchaotic oscillator with gyrators introduced by Tamasevicius and co-workers (referred to as the TCMNL oscillator hereafter) is considered. This well known hyperchaotic oscillator with active RC realization of inductors is suitable for integrated circuit implementation. Unlike previous literature based on piecewise-linear approximation methods, I derive a new (smooth) mathematical model based on the Shockley diode equation to explore the dynamics of the oscillator. Various tools for detecting chaos including bifurcation diagrams, Lyapunov exponents, frequency spectra, phase portraits and Poincaré sections are exploited to establish the connection between the system parameters and various complex dynamic regimes (e.g. hyperchaos, period-3 doubling bifurcation, coexistence of attractors, transient chaos) of the hyperchaotic oscillator. One of the most interesting and striking features of this oscillator discovered/revealed in this work is the coexistence of a hyperchaotic attractor with a chaotic one over a broad range of system parameters. This phenomenon was not reported previously and therefore represents a meaningful contribution to the understanding of the behavior of nonlinear dynamical systems in general. A close agreement is observed between theoretical and experimental analyses.

scholarly journals Application of numerical modeling to reservoir immersion assessment and control in dual-formation hydrogeological unit

2021 ◽  
Author(s):  
Yun Yang ◽  
Wengui Nan ◽  
Shenggen Guo ◽  
Dan Jin ◽  
Jianhui Wu ◽  
...  
Keyword(s):  
Three Dimensional ◽  
Scientific Basis ◽  
Mitigation Measures ◽  
Scale Model ◽  
Jiangxi Province ◽  
Dynamic Surface ◽  
Control Schemes ◽  
Engineering Measures ◽  
Total Study Area ◽  
And Control

Abstract Reservoir immersion is a serious environmental geological issue in a dual-formation structural reservoir bank (DFB) induced by dynamic surface water impoundment (SWI) that has implications for low-lying farmland and buried infrastructure. It is a major challenge to identify the dynamic immersion process and make economic and scientific joint mitigation measures for controlling groundwater immersion. Here, we develop a three-dimensional groundwater flow model and apply it to evaluate and control reservoir immersion in the typical low-lying DFB of Xingan Navigation and Power Junction Project (XGNPJ) across Ganjiang River in Jiangxi Province, China. The field-scale model is well calibrated to predict where the groundwater immersion could potentially occur. Furthermore, the effectiveness of the countermeasures adopted for the reduction of reservoir immersion areas were analysed based on the simulation model by considering the projected future combination scenarios of engineering measures. Results indicate that without engineering mitigation measures, SWI generates groundwater inundation across 23% of the total study area. Comprehensive comparative analysis on different seepage control schemes reveals that the joint engineering measures can effectively control the immersion range to 5% of the total area. The findings can provide scientific basis for groundwater immersion assessment and guide immersion control of XGNPJ project.

scholarly journals Three-Dimensional Modeling and Control of a Tethered UAV-Buoy System

2021 ◽  
Author(s):  
Ahmad Kourani ◽  
Naseem Daher
Keyword(s):  
Control System ◽  
Three Dimensional ◽  
Vertical Motion ◽  
Robotic System ◽  
Three Dimensions ◽  
Spherical Coordinate ◽  
Nonlinear Dynamical ◽  
Modeling And Control ◽  
Three Dimensional Modeling ◽  
And Control

Abstract This work presents the nonlinear dynamical model and motion controller of a system consisting of an unmanned aerial vehicle (UAV) that is tethered to a floating buoy in the three-dimensional (3D) space. Detailed models of the UAV, buoy, and the coupled tethered system dynamics are presented in a marine environment that includes surface-water currents and oscillating gravity waves, in addition to wind gusts. This work extends the previously modeled planar (vertical) motion of this novel robotic system to allow its free motion in all three dimensions. Furthermore, a Directional Surge Velocity Control System (DSVCS) is hereby proposed to allow both the free movement of the UAV around the buoy when the cable is slack, and the manipulation of the buoy’s surge velocity when the cable is taut. Using a spherical coordinate system centered at the buoy, the control system commands the UAV to apply forces on the buoy at specific azimuth and elevation angles via the tether, which yields a more appropriate realization of the control problem as compared to the Cartesian coordinates where the traditional x- , y- , and z -coordinates do not intuitively describe the tether’s tension and orientation. The proposed robotic system and controller offer a new method of interaction and collaboration between UAVs and marine systems from a locomotion perspective. The system is validated in a virtual high-fidelity simulation environment, which was specifically developed for this purpose, while considering various settings and wave scenarios.

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