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

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.

2021 ◽  
Author(s):  
Xin Yang ◽  
GuangJun Zhang ◽  
XueRen Li ◽  
Dong Wang

Abstract Different from the previous researches on the synchronization and synchronization transition of neuronal networks constructed by integer-order neuronal models, the synchronization and synchronization transition of fractional-order neuronal network are investigated in this paper. The fractional-order ring neuronal network constructed by fractional-order HindmarshRose (HR) neuronal models without electromagnetic radiation are proposed, and it’s synchronization behaviors are investigated numerically. The synchronization behaviors of two coupled fractional-order neuronal models and ring neuronal network under electromagnetic radiation are studied numerically. By research results, several novel phenomena and conclusions can be drawn. First, for the fractional-order HR model’s ring neuronal network without electromagnetic radiation, if the fractional-order q is changed, the threshold of the coupling strength when the network is in perfect synchronization will change. Furthermore, the change of fractional-order can induce the transition of periodic synchronization and chaotic synchronization. Second, for the two coupled neurons under electromagnetic radiation, the synchronization degree is influenced by fractional-order and the feedback gain parameter k1 . In addition, the fractional-order and parameter k1 can induce the synchronization transition of bursting synchronization, perfect synchronization and phase synchronization. For the perfect synchronization, the synchronization transition of chaotic synchronization and periodic synchronization induced by q and parameter k1 is also observed. Especially, When the fractionalorder is small, like 0.6, the synchronization behavior will be more complex. Third, for the ring neuronal network under electromagnetic radiation, with the change of memory-conductance parameter β, parameter k1 and fractional-order q of electromagnetic radiation, the synchronization behaviors are different. When β > 0.02 , the synchronization will be strengthened with the decreasing of fractional-order. The parameter k1 can induce the synchronization transition of perfect periodic10 synchronization, perfect periodic-7 synchronization, perfect periodic-5 synchronization and perfect periodic4 synchronization. It is hard for the system to synchronize and q has little effect on the synchronization when −0.06 < β < 0.02 . When β < −0.06 , the network moves directly from asynchronization to perfect synchronization, and the synchronization factor goes from 0.1 to 1 with the small change of fractional-order. Larger the factional-order is, larger the range of synchronization is. The synchronization degree increases with the increasing of k1.


2021 ◽  
Author(s):  
Adedayo Oke Adelakun

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).


2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
Jun Liu ◽  
Kaiyu Qin ◽  
Wei Chen ◽  
Ping Li ◽  
Mengji Shi

Due to the complex external environment, many multiagent systems cannot be precisely described or even cannot be described by an integer-order dynamical model and can only be described by a fractional-order dynamical model. In this paper, consensus problems are investigated for two types of fractional-order multiagent systems (FOMASs) with nonuniform time delays: FOMAS with symmetric time delays and undirected topology and FOMAS with asymmetric time delays and directed topology. Employing the Laplace transform and the frequency-domain theory, two delay margins are obtained to guarantee the consensus for the two types of FOMAS, respectively. These results are also suitable for the integer-order dynamical model. Finally, simulation results are provided to illustrate the effectiveness of our theoretical results.


Author(s):  
Xing-Yuan Wang ◽  
Hao Zhang

Based on the classic Lorenz system, this paper studies the problem of bivariate module-phase synchronizations in a fractional-order Lorenz system, bivariate module-phase synchronizations in a fractional-order spatiotemporal coupled Lorenz system, and malposed module-phase synchronization in a fractional-order spatiotemporal coupled Lorenz system. It is the first time, to our knowledge, that module-phase synchronization in fractional-order high-dimensional systems is applied. According to the fractional calculus techniques and spatiotemporal theory, we design controllers and achieve synchronizations both in module space and phase space at the same time. In the simulation, we discuss the bivariate module-phase synchronization and malposed module-phase synchronization. The numerical simulation results demonstrate the validity of controllers.


2009 ◽  
Vol 23 (31) ◽  
pp. 5769-5777 ◽  
Author(s):  
XINGYUAN WANG ◽  
YIJIE HE

This paper studies the problem of chaotic synchronization of the fractional-order modified coupled dynamos system, designs the activate controllers, and then proves that the self-synchronization of the fractional-order modified coupled dynamos system and the fractional-order modified coupled dynamos system's different structure synchronization with the fractional-order Lorenz system can both arrive theoretically. The simulation results demonstrate the validity of the activate controller.


2007 ◽  
Vol 21 (30) ◽  
pp. 5159-5166 ◽  
Author(s):  
CHUNGUANG LI

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.


2012 ◽  
Vol 23 (10) ◽  
pp. 1250067 ◽  
Author(s):  
XING-YUAN WANG ◽  
HAO ZHANG

By utilizing the fractional calculus techniques and spatiotemporal chaos theory, this paper brings Lorenz system to fractional-order spatiotemporal coupled differential equation for the first time, and proposes the fractional-order spatiotemporal coupled Lorenz system. Based on that, we study the problem of chaotic synchronization of fractional-order spatiotemporal coupled Lorenz systems, design the linear controller and nonlinear controller by utilizing the Lyapunov stability theory and prove the correctness in theory. The numerical simulation results demonstrate the validity of controllers in high-dimension fractional-order spatiotemporal coupled Lorenz system.


Author(s):  
Yongshun Jin ◽  
YangQuan Chen ◽  
Chunyang Wang ◽  
Ying Luo

This paper considers the fractional order proportional derivative (FOPD) controller and fractional order [proportional derivative] (FO[PD]) controller for networked position servo systems. The systematic design schemes of the networked position servo system with a time delay are presented. It follows from the Bode plot of the FOPD system and the FO[PD] that the given gain crossover frequency and phase margin are fulfilled. Moreover, the phase derivative w.r.t. the frequency is zero, which means that the closed-loop system is robust to gain variations at the given gain crossover frequency. However, sometimes we can not get the controller parameters to meet our robustness requirement. In this paper, we have studied on this situation and presented the requirement of the gain cross frequency, and phase margin in the designing process. For the comparison of fractional order controllers with traditional integer order controller, the integer order proportional integral differential (IOPID) was also designed by using the same proposed method. The simulation results have verified that FOPD and FO[PD] are effective for networked position servo. The simulation results also reveal that both FOPD controller and FO[PD] controller outperform IO-PID controller for this type of system.


Author(s):  
Riccardo Caponetto ◽  
Salvatore Graziani ◽  
Emanuele Murgano

AbstractIn the paper, a fractional-order RLC circuit is presented. The circuit is realized by using a fractional-order capacitor. This is realized by using carbon black dispersed in a polymeric matrix. Simulation results are compared with the experimental data, confirming the suitability of applying this new device in the circuital implementation of fractional-order systems.


Sensors ◽  
2021 ◽  
Vol 21 (4) ◽  
pp. 1544
Author(s):  
Chunpeng Wang ◽  
Hongling Gao ◽  
Meihong Yang ◽  
Jian Li ◽  
Bin Ma ◽  
...  

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.


Sign in / Sign up

Export Citation Format

Share Document