Hopf bifurcation, antimonotonicity and amplitude controls in the chaotic Toda jerk oscillator: analysis, circuit realization and combination synchronization in its fractional-order form

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.

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Solution of HIV and Malaria Coinfection Model Using Msgdtm

Journal of Mathematics Research ◽

10.5539/jmr.v7n4p181 ◽

2015 ◽

Vol 7 (4) ◽

pp. 181

Author(s):

Bonyah Ebenezer ◽

Kwasi Awuah-Werekoh ◽

Joseph Acquah

Keyword(s):

Approximate Solution ◽

Fractional Order ◽

Epidemic Model ◽

Unique Positive Solution ◽

Transform Method ◽

Order Form ◽

Differential Transform ◽

Infection Disease ◽

Generalized Differential ◽

Order Four

<p>In this paper, we investigate an epidemic model of HIV and Malaria co-infection using fractional order Calculus (FOC). The multistep generalized differential transform method (MSGDTM) is employed to obtain an accurate approximate solution to the epidemic model of HIV and Malaria co-infection disease in fractional order. A unique positive solution for HIV and Malaria co-infection is presented in fractional order form. For the integer case derivatives, the approximate solution of MSGDTM and the Runge–Kutta–order four scheme are compared. Numerical results are produced for the justification for this method.</p>

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An exponential jerk system, its fractional-order form with dynamical analysis and engineering application

Soft Computing ◽

10.1007/s00500-019-04373-w ◽

2019 ◽

Vol 24 (10) ◽

pp. 7469-7479 ◽

Cited By ~ 4

Author(s):

Karthikeyan Rajagopal ◽

Akif Akgul ◽

Sajad Jafari ◽

Anitha Karthikeyan ◽

Unal Cavusoglu ◽

...

Keyword(s):

Fractional Order ◽

Engineering Application ◽

Dynamical Analysis ◽

Order Form ◽

Jerk System

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

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.300-301.1573 ◽

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.

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Hopf bifurcation, chaos control and synchronization of a chaotic fractional-order system with chaos entanglement function

Mathematics and Computers in Simulation ◽

10.1016/j.matcom.2019.11.009 ◽

2020 ◽

Vol 172 ◽

pp. 321-340 ◽

Cited By ~ 9

Author(s):

Shiva Eshaghi ◽

Reza Khoshsiar Ghaziani ◽

Alireza Ansari

Keyword(s):

Hopf Bifurcation ◽

Fractional Order ◽

Chaos Control ◽

Fractional Order System ◽

Order System ◽

Control And Synchronization ◽

Bifurcation Chaos

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Multistability and Coexisting Attractors in a New Circulant Chaotic System

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127419501748 ◽

2019 ◽

Vol 29 (13) ◽

pp. 1950174 ◽

Cited By ~ 6

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.

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

Journal of Computational and Nonlinear Dynamics ◽

10.1115/1.4043003 ◽

2019 ◽

Vol 14 (7) ◽

Cited By ~ 3

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.

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