Dynamical behavior and synchronization in time-delay fractional-order coupled neurons under electromagnetic radiation

Meng, Fanqi; Zeng, Xin; Wang, Zuolei

doi:10.1007/s11071-018-4648-5

Cited by 23 publications

(20 citation statements)

References 48 publications

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“…This paper investigates the synchronization behavior and synchronization transition in three cases, which are the fractional-order HR model's ring neuronal network without electromagnetic radiation, two coupled fractional-order neuronal models under electromagnetic radiation and fractional-order ring neuronal network under electromagnetic radiation. First, for the fractionalorder model's ring neuronal network without electromagnetic radiation, like other influence factors reported in [21][22][23][24][25][26][27][28][29][30][31][32][33], the fractional-order can also change the threshold of the coupling strength. And the transition of periodic synchronization and chaotic synchronization induced by the fractional-order is found.…”

Section: Discussionmentioning

confidence: 99%

“…The fractional-order HR neuron under electromagnetic radiation is investigated in [27], and two neurons reach perfect synchronization through adaptive control. But the synchronization behavior and synchronization transition induce by the fractional-order and other parameter are not reported in [27]. In this section, the synchronization behavior and synchronization transition induced by fractional-order and parameter k 1 are studied.…”

Section: The Synchronization Behavior Of Two Fractional-order Coupled Neurons Under Electromagnetic Radiationmentioning

confidence: 99%

“…For the fractional-order coupled neurons and neuronal networks, there are few studies. For the fractional-order coupled neurons, the two neurons reach the perfect synchronization through the design of the controller in most of the literature [25][26][27]. In [28], it is found that the change of fractional-order can change the synchronization mode.…”

Section: Introductionmentioning

confidence: 99%

“…In [33], it is found that the rhythm synchronization will happen under appropriate coupling strength and electromagnetic radiation. In [26] and [27], the two coupled neurons with and without time-delay were in perfect synchronization by designing appropriate controller, but they didn't investigate the effects of parameter and the synchronization transition. From the above analysis, the synchronization and synchronization transition of coupled neurons and neuronal network under electromagnetic radiation are not investigated in the previous researches.…”

Section: Introductionmentioning

confidence: 99%

“…First, the ring network for fractionalorder HR model without electromagnetic radiation is constructed, and the synchronization transition induced by the fractional-order is investigated. Then, different from [25][26][27], the synchronization transition of two coupled neurons under electromagnetic radiation induced by the fractional-order, coupling strength and parameter k 1 is studied. Finally, this paper investigates the synchronization behavior of the ring neuronal network under electromagnetic radiation.…”

Section: Introductionmentioning

confidence: 99%

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

Xin

Zhang

et al. 2021

Preprint

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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.

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Section: Discussionmentioning

confidence: 99%

Section: The Synchronization Behavior Of Two Fractional-order Coupled Neurons Under Electromagnetic Radiationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

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

Xin

Zhang

et al. 2021

Preprint

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Pinning and self‐adaptive control to the couple‐group consensus of heterogeneous fractional multi‐agent systems with cooperative‐competitive relation

Cheng

2022

Adaptive Control & Signal

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In this article, the couple-group consensus of a class of heterogeneous fractional multi-agent systems with time-varying delay (HFMASs) has been studied.Based on cooperative-competitive interaction, pinning and self-adaptive controller has been designed to realize the couple-group consensus for this system with single integrator and double integrator fractional-order dynamics. By using Lyapunov function, mode-dependent average dwell time (MDADT) technology, stability theory and delta operator method, some sufficient conditions have been obtained to guard the success of couple-consensus for this HFMASs with fixed or switching topologies. According to these sufficient conditions, the related feasible solutions can be solved by using liner matrix inequality (LMI). In addition, these results are also applicable to the system with weakly connected topology without containing a spanning tree or meeting the demand of equilibrium of degree. Finally, several simulation experiments have been presented to prove the validity of the related results.

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Noise-induced collective dynamics in the small-world network of photosensitive neurons

Fan

Ren

2022

J Biol Phys

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Dynamical behavior and synchronization in time-delay fractional-order coupled neurons under electromagnetic radiation

Cited by 23 publications

References 48 publications

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

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

Pinning and self‐adaptive control to the couple‐group consensus of heterogeneous fractional multi‐agent systems with cooperative‐competitive relation

Noise-induced collective dynamics in the small-world network of photosensitive neurons

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