scholarly journals On Chaos in the Fractional-Order Discrete-Time Unified System and Its Control Synchronization

Entropy ◽  
2018 ◽  
Vol 20 (7) ◽  
pp. 530 ◽  
Author(s):  
Amina-Aicha Khennaoui ◽  
Adel Ouannas ◽  
Samir Bendoukha ◽  
Xiong Wang ◽  
Viet-Thanh Pham
Keyword(s):  
Fractional Order ◽  
Discrete Time ◽  
Chaotic Behavior ◽  
Numerical Results ◽  
Complete Synchronization ◽  
Control Laws ◽  
Integer Order

In this paper, we propose a fractional map based on the integer-order unified map. The chaotic behavior of the proposed map is analyzed by means of bifurcations plots, and experimental bounds are placed on the parameters and fractional order. Different control laws are proposed to force the states to zero asymptotically and to achieve the complete synchronization of a pair of fractional unified maps with identical or nonidentical parameters. Numerical results are used throughout the paper to illustrate the findings.

OPCL Coupling of Mixed Integer-Fractional Order oscillators: Tree and Chain Implementation

2021 ◽  
Author(s):  
Adedayo Oke Adelakun
Keyword(s):  
Fractional Order ◽  
Mixed Integer ◽  
Complete Synchronization ◽  
Amplitude Death ◽  
Integer Order ◽  
Simulation Results ◽  
Coupled Circuits ◽  
Tree Type ◽  
Chain Type

Abstract OPCL Coupling of Integer-order and fractional-order Sprott-A systems using off-shelf components are constructed. Fractance configurations such as chain-type and tree-type were designed using a fractional-order capacitor and fractional-order resistor, respectively. The simulation results of the coupled circuits reveal the transition between complete synchronization (CS) to Anti-synchronization (AS) and vice versa via Amplitude death (AD).

Angular control of differential shape-memory alloy spring actuator for underactuated dynamic system

2021 ◽  
pp. 107754632110216
Author(s):  
M Banu Sundareswari ◽  
G Then Mozhi ◽  
K Dhanalakshmi
Keyword(s):  
Shape Memory Alloy ◽  
Shape Memory ◽  
Fractional Order ◽  
Position Control ◽  
Sliding Mode ◽  
Control Effort ◽  
Control Laws ◽  
Integer Order ◽  
Two Degree Of Freedom ◽  
Outer Primary

This article dwells on two technical aspects, the design and implementation of an upgraded version of the differential shape-memory alloy–based revolute actuator/rotary actuating mechanism for stabilization and position control of a two-degree-of-freedom centrally hinged ball on beam system. The actuator is configured with differential and inclined placement of shape-memory alloy springs to provide bidirectional angular shift. The shape-memory alloy spring actuator occupies a smaller space and provides more extensive reformation with justifiable actuation force than an equally able shape-memory alloy wire. The cross or diagonal architecture of shape-memory alloy springs provides force amplification and reduces the actuator’s control effort. The shape-memory alloy spring–embodied actuator’s function is exemplified by the highly dynamic underactuated custom-designed ball balancing system. The ball position control is experimentally demonstrated by cascade control using the control laws that have been unattempted for shape-memory alloy actuated systems; the ball is positioned with linear (integer-order and fractional-order) proportional–integral–derivative controllers optimized with genetic algorithm and particle swarm optimization at the outer/primary loop. Angular control of the shape-memory alloy actuated beam is obtained with nonlinear (integer-order and fractional-order sliding mode control) control algorithms in the inner/secondary loop.

scholarly journals Fractional-Order Discrete-Time SIR Epidemic Model with Vaccination: Chaos and Complexity

Mathematics ◽  
2022 ◽  
Vol 10 (2) ◽  
pp. 165
Author(s):  
Zai-Yin He ◽  
Abderrahmane Abbes ◽  
Hadi Jahanshahi ◽  
Naif D. Alotaibi ◽  
Ye Wang
Keyword(s):  
Fractional Order ◽  
Discrete Time ◽  
Epidemic Model ◽  
Chaotic Behavior ◽  
Dynamical Behavior ◽  
Maximum Lyapunov Exponent ◽  
Sir Epidemic Model ◽  
Sir Epidemic ◽  
Reasonable Range ◽  
Fractional Orders

This research presents a new fractional-order discrete-time susceptible-infected-recovered (SIR) epidemic model with vaccination. The dynamical behavior of the suggested model is examined analytically and numerically. Through using phase attractors, bifurcation diagrams, maximum Lyapunov exponent and the 0−1 test, it is verified that the newly introduced fractional discrete SIR epidemic model vaccination with both commensurate and incommensurate fractional orders has chaotic behavior. The discrete fractional model gives more complex dynamics for incommensurate fractional orders compared to commensurate fractional orders. The reasonable range of commensurate fractional orders is between γ = 0.8712 and γ = 1, while the reasonable range of incommensurate fractional orders is between γ2 = 0.77 and γ2 = 1. Furthermore, the complexity analysis is performed using approximate entropy (ApEn) and C0 complexity to confirm the existence of chaos. Finally, simulations were carried out on MATLAB to verify the efficacy of the given findings.

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 On fractional Liénard--type systems

2019 ◽  
Vol 65 (6 Nov-Dec) ◽  
pp. 618 ◽  
Author(s):  
A. Fleitas ◽  
J. A. Mendez-Bermudez ◽  
J. E. Napoles Valdes ◽  
J. M. Sigarreta Almira
Keyword(s):  
Fractional Order ◽  
Type Systems ◽  
Numerical Results ◽  
General Context ◽  
Integer Order ◽  
Global And Local

In this work we present numerical results of classical Li\'{e}nard--type systems in a very general context, since we consider several types of derivatives (integer order and fractional order, global and local). Additionally we made theoretical-methodological observations. En este trabajo presentamos resultados num´ericos de sistemas tipo Li´enard en un contexto muy general ya que consideramos varios tipos dederivadas (de orden entero y fraccionario, globales y locales). Adicionalmente hacemos observaciones te ´oricas y metodol´ogicas.

scholarly journals Chaos Suppression of an Electrically Actuated Microresonator Based on Fractional-Order Nonsingular Fast Terminal Sliding Mode Control

2017 ◽  
Vol 2017 ◽  
pp. 1-12
Author(s):  
Jianxin Han ◽  
Qichang Zhang ◽  
Wei Wang ◽  
Gang Jin ◽  
Houjun Qi ◽  
...  
Keyword(s):  
Fractional Order ◽  
Chaotic Motion ◽  
Sliding Mode ◽  
Period Doubling ◽  
Terminal Sliding Mode ◽  
Control Laws ◽  
Switching Law ◽  
Integer Order ◽  
Chaos Suppression ◽  
Fast Terminal Sliding Mode

This paper focuses on chaos suppression strategy of a microresonator actuated by two symmetrical electrodes. Dynamic behavior of this system under the case where the origin is the only stable equilibrium is investigated first. Numerical simulations reveal that system may exhibit chaotic motion under certain excitation conditions. Then, bifurcation diagrams versus amplitude or frequency of AC excitation are drawn to grasp system dynamics nearby its natural frequency. Results show that the vibration is complex and may exhibit period-doubling bifurcation, chaotic motion, or dynamic pull-in instability. For the suppression of chaos, a novel control algorithm, based on an integer-order nonsingular fast terminal sliding mode and a fractional-order switching law, is proposed. Fractional Lyapunov Stability Theorem is used to guarantee the asymptotic stability of the system. Finally, numerical results with both fractional-order and integer-order control laws show that our proposed control law is effective in controlling chaos with system uncertainties and external disturbances.

Synchronisation of integer-order and fractional-order discrete-time chaotic systems

Pramana ◽  
2019 ◽  
Vol 92 (4) ◽  
Author(s):  
Adel Ouannas ◽  
Amina-Aicha Khennaoui ◽  
Okba Zehrour ◽  
Samir Bendoukha ◽  
Giuseppe Grassi ◽  
...  
Keyword(s):  
Fractional Order ◽  
Discrete Time ◽  
Chaotic Systems ◽  
Integer Order

scholarly journals D3 Dihedral Logistic Map of Fractional Order

Mathematics ◽  
2022 ◽  
Vol 10 (2) ◽  
pp. 213
Author(s):  
Marius-F. Danca ◽  
Nikolay Kuznetsov
Keyword(s):  
Bifurcation Diagram ◽  
Fractional Order ◽  
Chaotic Attractor ◽  
Logistic Map ◽  
Numerical Results ◽  
System Stability ◽  
Hidden Attractors ◽  
Integer Order

In this paper, the D3 dihedral logistic map of fractional order is introduced. The map presents a dihedral symmetry D3. It is numerically shown that the construction and interpretation of the bifurcation diagram versus the fractional order requires special attention. The system stability is determined and the problem of hidden attractors is analyzed. Furthermore, analytical and numerical results show that the chaotic attractor of integer order, with D3 symmetries, looses its symmetry in the fractional-order variant.

Sliding mode projective synchronization for fractional-order coupled systems based on network without strong connectedness

2021 ◽  
pp. 014233122110009
Author(s):  
Xin Meng ◽  
Baoping Jiang ◽  
Cunchen Gao
Keyword(s):  
Fractional Order ◽  
Sliding Mode ◽  
Coupled Systems ◽  
Projective Synchronization ◽  
Slave System ◽  
Complete Synchronization ◽  
Synchronization Problem ◽  
Strong Connectedness ◽  
Master System ◽  
Error System

This paper considers the Mittag-Leffler projective synchronization problem of fractional-order coupled systems (FOCS) on the complex networks without strong connectedness by fractional sliding mode control (SMC). Combining the hierarchical algorithm with the graph theory, a new SMC strategy is designed to realize the projective synchronization between the master system and the slave system, which covers the globally complete synchronization and the globally anti-synchronization. In addition, some novel criteria are derived to guarantee the Mittag-Leffler stability of the projective synchronization error system. Finally, a numerical example is given to illustrate the validity of the proposed method.

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