PHASE AND LAG SYNCHRONIZATION IN COUPLED FRACTIONAL ORDER CHAOTIC OSCILLATORS

2007 ◽  
Vol 21 (30) ◽  
pp. 5159-5166 ◽  
Author(s):  
CHUNGUANG LI
Keyword(s):  
Fractional Order ◽  
Coupling Strength ◽  
Chaotic Dynamics ◽  
Phase Synchronization ◽  
Lag Synchronization ◽  
Chaotic Oscillators ◽  
Integer Order

Chaotic dynamics of fractional (non-integer) order systems have begun to attract much attention in recent years. In this paper, we study the phase and lag synchronization in coupled two fractional order chaotic oscillators. It is shown that with the increase of coupling strength, the system first undergoes a transition to phase synchronization, and when the coupling strength is increased further, another transition to lag synchronization occurs. It is further shown that the system with two chaotic oscillators of different orders can also exhibit phase synchronization phenomena, although the identical synchronization is impossible in this case.

STIMULUS-INDUCED CHAOTIC SYNCHRONIZATION OF CHUA'S OSCILLATORS

2006 ◽  
Vol 16 (10) ◽  
pp. 2843-2853
Author(s):  
V. V. KLINSHOV ◽  
V. B. KAZANTSEV ◽  
V. I. NEKORKIN
Keyword(s):  
Initial Phase ◽  
Chaotic Dynamics ◽  
Phase Synchronization ◽  
Cluster Formation ◽  
Time Moment ◽  
Chaotic Oscillation ◽  
Single Pulse ◽  
Chaotic Synchronization ◽  
Phase Reset ◽  
Chaotic Oscillators

The problem of phase synchronization of Chua's chaotic oscillators is investigated. We consider Chua's circuit when it exhibits a chaotic attractor and apply a single pulse stimulus. It is shown that under certain conditions the system displays self-referential phase reset (SPR) phenomenon. This is a case when the reset phase of the chaotic oscillation is independent on the initial phase, hence on the time moment when the stimulus has been applied. In an ensemble of chaotic oscillators simultaneously stimulated, the SPR yields mutual phase coherence or synchronization between the units. We describe basic dynamical mechanisms of the effect and show how it can be used for controllable cluster formation and for the control of chaotic dynamics.

Bifurcation analysis of a fractional order time-delay Chua’s circuit based on coupled memristors

2019 ◽  
Vol 33 (30) ◽  
pp. 1950366
Author(s):  
Dawei Ding ◽  
Yecui Weng ◽  
Yongbing Hu ◽  
Zongli Yang
Keyword(s):  
Time Delay ◽  
Fractional Order ◽  
Coupling Strength ◽  
Coupling Effect ◽  
Phase Portraits ◽  
Chua’S Circuit ◽  
Chua's Circuit ◽  
Integer Order ◽  
Dynamical Characteristics ◽  
Memristive System

In this paper, a fractional-order (and an integer-order) chaotic system, obtained from Chua’s circuit by substituting Chua’s diode with two active coupled memristors (MRs) characterized by quadratic nonlinearity, is introduced to probe the memristive coupling effect. Two MRs connected in parallel are coupled by the flux. For the integer-order memristive system, the dynamical characteristics depending on the coupling strength coefficient between MRs without changing the circuit parameters are illustrated theoretically and numerically by using phase portraits, time domain diagram, bifurcation diagram and the Lyapunov diagram. Then based on the Adams–Bashforth–Moulton algorithm, the study of dynamic behavior of the fractional-order memristive system containing the time-delay reveals that appropriately setting the coupling strength between MRs generates more interesting attractors that differ from its integer-order counterpart. Besides, the effects of the order and the time-delay on dynamics are discussed briefly. Finally, the simulation results verify the validity of the theoretical analysis.

scholarly journals The Synchronization Behaviors of Coupled Fractional-Order Neuronal Networks under Electromagnetic Radiation

Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2204
Author(s):  
Xin Yang ◽  
Guangjun Zhang ◽  
Xueren Li ◽  
Dong Wang
Keyword(s):  
Electromagnetic Radiation ◽  
Fractional Order ◽  
Neuronal Network ◽  
Neuronal Networks ◽  
Phase Synchronization ◽  
Chaotic Synchronization ◽  
Feedback Gain ◽  
Integer Order ◽  
Conductance Parameter ◽  
Simulation Results

Previous studies on the synchronization behaviors of neuronal networks were constructed by integer-order neuronal models. In contrast, this paper proposes that the above topics of symmetrical neuronal networks are constructed by fractional-order Hindmarsh–Rose (HR) models under electromagnetic radiation. They are then investigated numerically. From the research results, several novel phenomena and conclusions can be drawn. First, for the two symmetrical coupled neuronal models, the synchronization degree is influenced by the fractional-order q and the feedback gain parameter k1. In addition, the fractional-order or the parameter k1 can induce the synchronization transitions of bursting synchronization, perfect synchronization and phase synchronization. For perfect synchronization, the synchronization transitions of chaotic synchronization and periodic synchronization induced by q or parameter k1 are also observed. In particular, when the fractional-order is small, such as 0.6, the synchronization transitions are more complex. Then, for a symmetrical ring neuronal network under electromagnetic radiation, with the change in the memory-conductance parameter β of the electromagnetic radiation, k1 and q, compared with the fractional-order HR model’s ring neuronal network without electromagnetic radiation, the synchronization behaviors are more complex. According to the simulation results, the influence of k1 and q can be summarized into three cases: β>0.02, −0.06<β<0.02 and β<−0.06. The influence rules and some interesting phenomena are investigated.

scholarly journals Invariant Image Representation Using Novel Fractional-Order Polar Harmonic Fourier Moments

Sensors ◽  
2021 ◽  
Vol 21 (4) ◽  
pp. 1544
Author(s):  
Chunpeng Wang ◽  
Hongling Gao ◽  
Meihong Yang ◽  
Jian Li ◽  
Bin Ma ◽  
...  
Keyword(s):  
Image Reconstruction ◽  
Fractional Order ◽  
Continuous Functions ◽  
Kernel Functions ◽  
Superior Performance ◽  
Image Description ◽  
Orthogonal Moments ◽  
Integer Order ◽  
Geometric Invariance ◽  
Order Continuous

Continuous orthogonal moments, for which continuous functions are used as kernel functions, are invariant to rotation and scaling, and they have been greatly developed over the recent years. Among continuous orthogonal moments, polar harmonic Fourier moments (PHFMs) have superior performance and strong image description ability. In order to improve the performance of PHFMs in noise resistance and image reconstruction, PHFMs, which can only take integer numbers, are extended to fractional-order polar harmonic Fourier moments (FrPHFMs) in this paper. Firstly, the radial polynomials of integer-order PHFMs are modified to obtain fractional-order radial polynomials, and FrPHFMs are constructed based on the fractional-order radial polynomials; subsequently, the strong reconstruction ability, orthogonality, and geometric invariance of the proposed FrPHFMs are proven; and, finally, the performance of the proposed FrPHFMs is compared with that of integer-order PHFMs, fractional-order radial harmonic Fourier moments (FrRHFMs), fractional-order polar harmonic transforms (FrPHTs), and fractional-order Zernike moments (FrZMs). The experimental results show that the FrPHFMs constructed in this paper are superior to integer-order PHFMs and other fractional-order continuous orthogonal moments in terms of performance in image reconstruction and object recognition, as well as that the proposed FrPHFMs have strong image description ability and good stability.

Analysis of a New Class of Impulsive Implicit Sequential Fractional Differential Equations

2020 ◽  
Vol 21 (6) ◽  
pp. 571-587 ◽  
Author(s):  
Akbar Zada ◽  
Sartaj Ali ◽  
Tongxing Li
Keyword(s):  
Differential Equations ◽  
Fractional Order ◽  
Fractional Differential Equations ◽  
Sufficient Conditions ◽  
Uniqueness Of Solutions ◽  
Integer Order ◽  
New Class ◽  
Proposed Model ◽  
Fractional Differential ◽  
Sequential Fractional Differential Equations

AbstractIn this paper, we study an implicit sequential fractional order differential equation with non-instantaneous impulses and multi-point boundary conditions. The article comprehensively elaborate four different types of Ulam’s stability in the lights of generalized Diaz Margolis’s fixed point theorem. Moreover, some sufficient conditions are constructed to observe the existence and uniqueness of solutions for the proposed model. The proposed model contains both the integer order and fractional order derivatives. Thus, the exponential function appearers in the solution of the proposed model which will lead researchers to study fractional differential equations with well known methods of integer order differential equations. In the last, few examples are provided to show the applicability of our main results.

Complex projection synchronization of fractional order uncertain complex-valued networks with time-varying coupling

2019 ◽  
Vol 33 (29) ◽  
pp. 1950351 ◽  
Author(s):  
Dawei Ding ◽  
Xiaolei Yao ◽  
Hongwei Zhang
Keyword(s):  
Fractional Order ◽  
Coupling Strength ◽  
Dynamic Networks ◽  
Sufficient Conditions ◽  
Feedback Gain ◽  
Time Varying ◽  
Order Complex ◽  
Unknown Parameters ◽  
Synchronization Problem ◽  
Complex Valued

In this paper, the complex projection synchronization problem of fractional complex-valued dynamic networks is investigated. Considering the time-varying coupling and unknown parameters of the fractional order complex network, several decentralized adaptive strategies are designed to adjust the coupling strength and controller feedback gain in order to investigate the complex projection synchronization problem of the system. Moreover, based on the designed identification law, the uncertain parameters in the network can be estimated. Using adaptive law which balances the time-varying coupling strength and the feedback gain of the controller, some sufficient conditions are obtained for the complex projection synchronization of complex networks. Finally, numerical simulation examples are provided to illustrate the efficiency of the complex projection synchronization strategies of the fractional order complex dynamic networks.

Phase synchronization of chaotic oscillators by external driving

1997 ◽  
Vol 104 (3-4) ◽  
pp. 219-238 ◽  
Author(s):  
Arkady S. Pikovsky ◽  
Michael G. Rosenblum ◽  
Grigory V. Osipov ◽  
Jürgen Kurths
Keyword(s):  
Phase Synchronization ◽  
Chaotic Oscillators ◽  
External Driving

Exploiting Fractional Order PID Controller Methods in Improving the Performance of Integer Order PID Controllers: A GA Based Approach

2009 ◽  
Author(s):  
Bijoy K. Mukherjee ◽  
Santanu Metia ◽  
Sio-Iong Ao ◽  
Alan Hoi-Shou Chan ◽  
Hideki Katagiri ◽  
...  
Keyword(s):  
Fractional Order ◽  
Pid Controller ◽  
Pid Controllers ◽  
Integer Order ◽  
Fractional Order Pid ◽  
Fractional Order Pid Controller

TWOFOLD IMPACT OF DELAYED FEEDBACK ON COUPLED OSCILLATORS

2007 ◽  
Vol 17 (07) ◽  
pp. 2517-2530 ◽  
Author(s):  
OLEKSANDR V. POPOVYCH ◽  
VALERII KRACHKOVSKYI ◽  
PETER A. TASS
Keyword(s):  
Time Delay ◽  
Coupling Strength ◽  
Coupled Oscillators ◽  
Phase Synchronization ◽  
Threshold Value ◽  
Phase Oscillators ◽  
Intermediate Coupling ◽  
Rich Variety ◽  
Dynamical Regimes ◽  
The Impact

We present a detailed bifurcation analysis of desynchronization transitions in a system of two coupled phase oscillators with delay. The coupling between the oscillators combines a delayed self-feedback of each oscillator with an instantaneous mutual interaction. The delayed self-feedback leads to a rich variety of dynamical regimes, ranging from phase-locked and periodically modulated synchronized states to chaotic phase synchronization and desynchronization. We show that an increase of the coupling strength between oscillators may lead to a loss of synchronization. Intriguingly, the delay has a twofold influence on the oscillations: synchronizing for small and intermediate coupling strength and desynchronizing if the coupling strength exceeds a certain threshold value. We show that the desynchronization transition has the form of a crisis bifurcation of a chaotic attractor of chaotic phase synchronization. This study contributes to a better understanding of the impact of time delay on interacting oscillators.

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