Chaos in the fractional order logistic delay system: Circuit realization and synchronization

2016 ◽  
Author(s):  
Haci Mehmet Baskonus ◽  
Zakia Hammouch ◽  
Toufik Mekkaoui ◽  
Hasan Bulut
Keyword(s):  
Fractional Order ◽  
Delay System ◽  
Circuit Realization

An experimental analog circuit realization of Matsuda’s approximate fractional-order integral operators for industrial electronics

2021 ◽  
Author(s):  
Murat Koseoglu ◽  
Furkan Nur Deniz ◽  
Baris Baykant Alagoz ◽  
Ali Yuce ◽  
Nusret Tan
Keyword(s):  
Fractional Order ◽  
Analog Circuit ◽  
Low Cost ◽  
Electric Circuit ◽  
Partial Fraction ◽  
Circuit Realization ◽  
Pass Filter ◽  
Low Pass Filter ◽  
Performance Improvements ◽  
Low Pass

Abstract Analog circuit realization of fractional order (FO) elements is a significant step for the industrialization of FO control systems because of enabling a low-cost, electric circuit realization by means of standard industrial electronics components. This study demonstrates an effective operational amplifier-based analog circuit realization of approximate FO integral elements for industrial electronics. To this end, approximate transfer function models of FO integral elements, which are calculated by using Matsuda’s approximation method, are decomposed into the sum of low-pass filter forms according to the partial fraction expansion. Each partial fraction term is implemented by using low-pass filters and amplifier circuits, and these circuits are combined with a summing amplifier to compose the approximate FO integral circuits. Widely used low-cost industrial electronics components, which are LF347N opamps, resistor and capacitor components, are used to achieve a discrete, easy-to-build analog realization of the approximate FO integral elements. The performance of designed circuit is compared with performance of Krishna’s FO circuit design and performance improvements are shown. The study presents design, performance validation and experimental verification of this straightforward approximate FO integral realization method.

Hybrid Projective Synchronization for the Fractional-Order Chen-Lee System and its Circuit Realization

2013 ◽  
Vol 300-301 ◽  
pp. 1573-1578
Author(s):  
Seng Kin Lao ◽  
Hsien Keng Chen ◽  
Lap Mou Tam ◽  
Long Jye Sheu
Keyword(s):  
Fractional Order ◽  
Chaotic Systems ◽  
Body Motion ◽  
Projective Synchronization ◽  
Fractional Order Systems ◽  
Control Of Chaos ◽  
Circuit Realization ◽  
Hybrid Projective Synchronization ◽  
The Time Domain ◽  
Theoretical Analyses

The growing interest shows the importance of the control of chaos in fractional-order systems in recent years. This paper investigates in the hybrid projective synchronization of two chaotic systems with fractional-order, which were derived from Euler equations of rigid body motion. Theoretical analyses of the proposed methods are validated by numerical simulation in the time domain. Moreover, the synchronization system is realized using electronic circuits with fractance in the frequency domain.

Multistability and Coexisting Attractors in a New Circulant Chaotic System

2019 ◽  
Vol 29 (13) ◽  
pp. 1950174 ◽  
Author(s):  
Karthikeyan Rajagopal ◽  
Akif Akgul ◽  
Viet-Thanh Pham ◽  
Fawaz E. Alsaadi ◽  
Fahimeh Nazarimehr ◽  
...  
Keyword(s):  
Fractional Order ◽  
Order System ◽  
Cyclic Symmetry ◽  
Order Model ◽  
Coexisting Attractors ◽  
Circuit Realization ◽  
Chaotic Flow ◽  
Fractional Order Model ◽  
Dynamical Properties ◽  
Fractional Orders

In this paper, a new four-dimensional chaotic flow is proposed. The system has a cyclic symmetry in its structure and shows a complicated, chaotic attractor. The dynamical properties of the system are investigated. The system shows multistability in an interval of its parameter. Fractional order model of the proposed system is discussed in various fractional orders. Bifurcation analysis of the fractional order system shows that it has a kind of multistability like the integer order system, which is a very rare phenomenon. Circuit realization of the proposed system is also carried out to show that it is usable for engineering applications.

Bursting, Dynamics, and Circuit Implementation of a New Fractional-Order Chaotic System With Coexisting Hidden Attractors

2019 ◽  
Vol 14 (7) ◽  
Author(s):  
Meng Jiao Wang ◽  
Xiao Han Liao ◽  
Yong Deng ◽  
Zhi Jun Li ◽  
Yi Ceng Zeng ◽  
...  
Keyword(s):  
Numerical Simulation ◽  
Fractional Order ◽  
Chaotic System ◽  
Chaotic Systems ◽  
Equilibrium Points ◽  
Neuroendocrine Cells ◽  
Order System ◽  
Hidden Attractors ◽  
Main Mode ◽  
Circuit Realization

Systems with hidden attractors have been the hot research topic of recent years because of their striking features. Fractional-order systems with hidden attractors are newly introduced and barely investigated. In this paper, a new 4D fractional-order chaotic system with hidden attractors is proposed. The abundant and complex hidden dynamical behaviors are studied by nonlinear theory, numerical simulation, and circuit realization. As the main mode of electrical behavior in many neuroendocrine cells, bursting oscillations (BOs) exist in this system. This complicated phenomenon is seldom found in the chaotic systems, especially in the fractional-order chaotic systems without equilibrium points. With the view of practical application, the spectral entropy (SE) algorithm is chosen to estimate the complexity of this fractional-order system for selecting more appropriate parameters. Interestingly, there is a state variable correlated with offset boosting that can adjust the amplitude of the variable conveniently. In addition, the circuit of this fractional-order chaotic system is designed and verified by analog as well as hardware circuit. All the results are very consistent with those of numerical simulation.

On the Energy Stored in Fractional-Order Electrical Elements

2013 ◽  
Author(s):  
Tom T. Hartley ◽  
Robert J. Veillette ◽  
Carl F. Lorenzo ◽  
Jay L. Adams
Keyword(s):  
Fractional Order ◽  
Energy Input ◽  
Major Conclusion ◽  
Energy Storage Devices ◽  
Initial Current ◽  
Circuit Realization ◽  
External Work ◽  
Storage Devices ◽  
The Past ◽  
Order Element

In this paper, fractional-order electrical elements are considered as energy storage devices. They are studied by comparing the energy available from the element to do future external work, relative to the energy input into the element in the past. A standard circuit realization is used to represent the fractional-order element connected to an inductor with a given initial current. This circuit realization is used to determine the energy returned by both capacitive and inductive fractional-order elements of order between zero and one. Plots of the energy stored versus time are provided. The major conclusion is that fractional-order elements tend to rapidly dissipate much of their input energy leaving less energy for doing work in the future.

Robust Fractional Order Proportional Integral Control for Large Time-Delay System

2014 ◽  
Vol 716-717 ◽  
pp. 1614-1619
Author(s):  
Rui Hao Xin ◽  
Chun Yang Wang ◽  
Xue Lian Liu ◽  
Ming Qiu Li ◽  
Duan Yuan Bai
Keyword(s):  
Time Delay ◽  
Fractional Order ◽  
Delay Time ◽  
Large Time ◽  
Delay System ◽  
Order System ◽  
Time Delay System ◽  
Proportional Integral ◽  
Integral Controller ◽  
Proportional Integral Controller

In this paper, a new control method for large time delay system is proposed. Firstly, the decreasing time delay controller is used to remodel large delay time plant into small delay time plant. Then, a fractional robust proportional-integral controller (FOPI) is designed, using the phase margin and cut-off frequency at a specified point in the Bode plot of flat robust conditions, to guarantee the desired control performance and the robustness of the high order system to the gain order system. For comparison between the fractional order proportional integral controller and the traditional integer order PID (IOPID) controller, the IOPID controller is also designed following the same proposed tuning specifications. The simulation results indicates that the both designed controllers work efficiently. Furthermore, the FOPI controller makes the large time-delay system get better control effect, the system has high robustness, adaptive ability and anti-jamming ability.

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