scholarly journals The Synchronization and Synchronization Transition of Coupled Fractional-order Neuronal Networks

2021 ◽  
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 ◽  
Synchronization Transition ◽  
Conductance Parameter ◽  
Small Change

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.

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.

Effects of Time Delay on Burst Synchronization Transition of Neuronal Networks

2018 ◽  
Vol 28 (12) ◽  
pp. 1850143 ◽  
Author(s):  
Xiaojuan Sun ◽  
Tianshu Xue
Keyword(s):  
Time Delay ◽  
Neuronal Network ◽  
Coupling Strength ◽  
Neuronal Networks ◽  
The Other ◽  
Electrical Synapses ◽  
Synchronization Transition ◽  
Burst Synchronization ◽  
Chemical Synapses ◽  
Bursting Activity

In this paper, we focus on investigating the effects of time delay on burst synchronization transitions of a neuronal network which is locally modeled by Hindmarsh–Rose neurons. Here, neurons inside the neuronal network are connected through electrical synapses or chemical synapses. With the numerical results, it is revealed that burst synchronization transitions of both electrically and chemically coupled neuronal networks could be induced by time delay just when the coupling strength is large enough. Meanwhile, it is found that, in electrically and excitatory chemically coupled neuronal networks, burst synchronization transitions are observed through change of spiking number per burst when coupling strength is large enough; while in inhibitory chemically coupled neuronal network, burst synchronization transitions are observed for large enough coupling strength through changing fold-Hopf bursting activity to fold-homoclinic bursting activity and vice versa. Namely, two types of burst synchronization transitions are observed. One type of burst synchronization transitions occurs through change of spiking numbers per burst and the other type of burst synchronization transition occurs through change of bursting types.

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.

scholarly journals Soft-wired long-term memory in a natural recurrent neuronal network

2020 ◽  
Author(s):  
Miguel A. Casal ◽  
Santiago Galella ◽  
Oscar Vilarroya ◽  
Jordi Garcia-Ojalvo
Keyword(s):  
Neuronal Network ◽  
Neuronal Networks ◽  
Initial Conditions ◽  
Permutation Entropy ◽  
Long Term Memory ◽  
Term Memory ◽  
C Elegans ◽  
Living Organisms ◽  
Recurrent Connections

Neuronal networks provide living organisms with the ability to process information. They are also characterized by abundant recurrent connections, which give rise to strong feed-back that dictates their dynamics and endows them with fading (short-term) memory. The role of recurrence in long-term memory, on the other hand, is still unclear. Here we use the neuronal network of the roundworm C. elegans to show that recurrent architectures in living organisms can exhibit long-term memory without relying on specific hard-wired modules. A genetic algorithm reveals that the experimentally observed dynamics of the worm’s neuronal network exhibits maximal complexity (as measured by permutation entropy). In that complex regime, the response of the system to repeated presentations of a time-varying stimulus reveals a consistent behavior that can be interpreted as soft-wired long-term memory.A common manifestation of our ability to remember the past is the consistence of our responses to repeated presentations of stimuli across time. Complex chaotic dynamics is known to produce such reliable responses in spite of its characteristic sensitive dependence on initial conditions. In neuronal networks, complex behavior is known to result from a combination of (i) recurrent connections and (ii) a balance between excitation and inhibition. Here we show that those features concur in the neuronal network of a living organism, namely C. elegans. This enables long-term memory to arise in an on-line manner, without having to be hard-wired in the brain.

Adaptive Synchronization of Fractional-Order Coupled Neurons Under Electromagnetic Radiation

2020 ◽  
Vol 30 (03) ◽  
pp. 2050044
Author(s):  
Fanqi Meng ◽  
Xiaoqin Zeng ◽  
Zuolei Wang ◽  
Xinjun Wang
Keyword(s):  
Electromagnetic Radiation ◽  
Fractional Order ◽  
Dynamical Behavior ◽  
Lyapunov Stability Theory ◽  
Neuronal Model ◽  
Adaptive Synchronization ◽  
Dynamical Characteristics ◽  
Single Controller ◽  
Improved Model ◽  
Complex Dynamical Behavior

In this paper, we investigate the dynamical characteristics of four-variable fractional-order Hindmarsh–Rose neuronal model under electromagnetic radiation. The numerical results show that the improved model exhibits more complex dynamical behavior with more bifurcation parameters. Meanwhile, based on the fractional-order Lyapunov stability theory, we propose two adaptive control methods with a single controller to realize chaotic synchronization between two coupled neurons. Finally, numerical simulations show the feasibility and effectiveness of the presented method.

scholarly journals Delay-induced synchronization transition in a small-world neuronal network of FitzHugh–Nagumo neurons subjected to sine-Wiener bounded noise

2019 ◽  
Vol 33 (08) ◽  
pp. 1950053 ◽  
Author(s):  
Yuangen Yao ◽  
Ming Yi ◽  
Dejia Hou
Keyword(s):  
Neuronal Network ◽  
Correlation Time ◽  
Small World ◽  
Nearest Neighbors ◽  
Spatiotemporal Patterns ◽  
Small World Network ◽  
Bounded Noise ◽  
Future Studies ◽  
Synchronization Transition ◽  
Brain Functions

Noise and delay are ubiquitous in brain and they have significant effects on neuronal network synchronization and even brain functions. Based on a small-world neuronal network of delayed FitzHugh–Nagumo (FHN) neurons subjected to sine-Wiener (SW) bounded noise, the effects of delay and SW noise on synchronization and synchronization transition are numerically investigated by calculating a synchronization measure R and plotting spatiotemporal patterns. The phenomenon of delay-induced synchronization transition is observed as delay [Formula: see text] is increased. And large self-correlation time and strength of SW noise can increase the number of delay-induced synchronization transition. In addition, delay-induced synchronization transition is robust against the change of topology structure of neuronal network and this phenomenon becomes much easier to see for small nearest neighbors k in the small-world network. Since synchronization transition may imply functional switch, our results may have important implications, and inspire future studies.

Module-phase synchronization of fractional-order complex chaotic systems based on RBF neural network and sliding mode control

2020 ◽  
Vol 34 (07) ◽  
pp. 2050050 ◽  
Author(s):  
Fuzhong Nian ◽  
Xinmeng Liu ◽  
Yaqiong Zhang ◽  
Xuelong Yu
Keyword(s):  
Neural Network ◽  
Sliding Mode Control ◽  
Fractional Order ◽  
Chaotic Systems ◽  
Phase Synchronization ◽  
Sliding Mode ◽  
Rbf Neural Network ◽  
Order Complex ◽  
Mode Control ◽  
Complex Chaotic Systems

Combined with RBF neural network and sliding mode control, the synchronization between drive system and response system was achieved in module space and phase space, respectively (module-phase synchronization). The RBF neural network is used to estimate the unknown nonlinear function in the system. The module-phase synchronization of two fractional-order complex chaotic systems is implemented by the Lyapunov stability theory of fractional-order systems. Numerical simulations are provided to show the effectiveness of the analytical results.

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