Chaotic Synchronization
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Author(s):  
О.И. Москаленко ◽  
А.А. Короновский ◽  
А.О. Сельский ◽  
Е.В. Евстифеев

Method to define the characteristic phases in the behavior of unidirectionally coupled systems being near the boundary of the generalized chaotic synchronization regime onset, based on calculation of the probability of the synchronous regime observation in ensemble of coupled systems is proposed. Using the example of unidirectionally coupled Rössler systems in the band chaos regime we show its efficiency in comparison with the other known methods for detection the characteristics of intermittent generalized synchronization.


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 ◽  
Vol 58 (4) ◽  
pp. 55-68
Author(s):  
F. Capligins ◽  
A. Litvinenko ◽  
A. Aboltins ◽  
E. Austrums ◽  
A. Rusins ◽  
...  

Abstract The paper presents a study of the chaotic jerk circuit (CJC) employment capabilities for digital communications. The concept of coherent chaos shift keying (CSK) communication system with controlled error feedback chaotic synchronization is proposed for a specific CJC in two modifications. The stability of chaotic synchronization between the two CJCs was evaluated in terms of voltage drop at the input of the slave circuit and the impact of channel noise using simulations and experimental studies.


Author(s):  
Yi-You Hou ◽  
Cheng-Shun Fang ◽  
Chang-Hua Lien ◽  
Sundarapandian Vaidyanathan ◽  
Aceng Sambas ◽  
...  

2021 ◽  
Vol 31 (6) ◽  
pp. 061107
Author(s):  
Dawid Dudkowski ◽  
Jerzy Wojewoda ◽  
Krzysztof Czołczyński ◽  
Tomasz Kapitaniak

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.


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