Full Text:   <536>

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CLC number: O59; TN710

On-line Access: 2019-05-14

Received: 2018-08-21

Revision Accepted: 2018-10-22

Crosschecked: 2019-01-14

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Citations:  Bibtex RefMan EndNote GB/T7714


Jun Ma


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Frontiers of Information Technology & Electronic Engineering  2019 Vol.20 No.4 P.571-583


Differential coupling contributes to synchronization via a capacitor connection between chaotic circuits

Author(s):  Yu-meng Xu, Zhao Yao, Aatef Hobiny, Jun Ma

Affiliation(s):  Department of Physics, Lanzhou University of Technology, Lanzhou 730050, China; more

Corresponding email(s):   hyperchaos@163.com

Key Words:  Synchronization, Voltage coupling, Chaotic circuit, Capacitor coupling

Yu-meng Xu, Zhao Yao, Aatef Hobiny, Jun Ma. Differential coupling contributes to synchronization via a capacitor connection between chaotic circuits[J]. Frontiers of Information Technology & Electronic Engineering, 2019, 20(4): 571-583.

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DOI - 10.1631/FITEE.1800499

Nonlinear oscillators and circuits can be coupled to reach synchronization and consensus. The occurrence of complete synchronization means that all oscillators can maintain the same amplitude and phase, and it is often detected between identical oscillators. However, phase synchronization means that the coupled oscillators just keep pace in oscillation even though the amplitude of each node could be different. For dimensionless dynamical systems and oscillators, the synchronization approach depends a great deal on the selection of coupling variable and type. For nonlinear circuits, a resistor is often used to bridge the connection between two or more circuits, so voltage coupling can be activated to generate feedback on the coupled circuits. In this paper, capacitor coupling is applied between two Pikovsk-Rabinovich (PR) circuits, and electric field coupling explains the potential mechanism for differential coupling. Then symmetric coupling and cross coupling are activated to detect synchronization stability, separately. It is found that resistor-based voltage coupling via a single variable can stabilize the synchronization, and the energy flow of the controller is decreased when synchronization is realized. Furthermore, by applying appropriate intensity for the coupling capacitor, synchronization is also reached and the energy flow across the coupling capacitor is helpful in regulating the dynamical behaviors of coupled circuits, which are supported by a continuous energy exchange between capacitors and the inductor. It is also confirmed that the realization of synchronization is dependent on the selection of a coupling channel. The approach and stability of complete synchronization depend on symmetric coupling, which is activated between the same variables. Cross coupling between different variables just triggers phase synchronization. The capacitor coupling can avoid energy consumption for the case with resistor coupling, and it can also enhance the energy exchange between two coupled circuits.


摘要:非线性振子和电路常用于研究耦合同步和一致性问题。完全同步是指所有振子保持相同幅度和相位,主要发生在完全相同振子之间。相位同步是指振子保持步调节律同步而幅度不同。对于无维动力学系统和振子,同步依赖于耦合变量的选择和耦合方式。非线性电路中电阻常用于连接两个或以上电路,触发电压耦合可对耦合电路反馈调制。本文采用电容器耦合两个Pikovsk-Rabinovich (PR)电路,这种电场耦合机制为微分耦合提供了依据。讨论了对称性和错位耦合下两个混沌电路的同步稳定性问题。在电阻耦合下,两个混沌电路容易完全同步。进一步讨论电容器耦合,发现当耦合电容器选择合适电容值时,两个耦合电路同步可被有效控制,且耦合电容器能量流有助于对同步的调控。混沌电路的同步实现和耦合通道有关,如对称性耦合容易完全同步,错位耦合有利于相位同步。电容器对应电场耦合能降低耦合器件能量(焦耳热)消耗,加强两个耦合电路能量输运和交换,从而实现混沌电路同步。


Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article


[1]Adesnik H, Bruns W, Taniguchi H, et al., 2012. A neural circuit for spatial summation in visual cortex. Nature, 490(7419): 226-231.

[2]Andrievskii BR, Fradkov AL, 2004. Control of chaos: methods and applications. II. Applications. Autom Remote Contr, 65(4):505-533.

[3]Balenzuela P, García-Ojalvo J, 2005. Role of chemical synapses in coupled neurons with noise. Phys Rev E, 72: 021901.

[4]Bao BC, Jiang T, Xu Q, et al., 2016. Coexisting infinitely many attractors in active band-pass filter-based memristive circuit. Nonl Dynam, 86(3):1711-1723.

[5]Bao BC, Jiang T, Wang GY, et al., 2017. Two-memristor-based Chua’s hyperchaotic circuit with plane equilibrium and its extreme multistability. Nonl Dynam, 89(2):1157-1171.

[6]Bennett MVL, 1997. Gap junctions as electrical synapses. J Neurocytol, 26(6):349-366.

[7]Bennett MVL, 2000. Electrical synapses, a personal perspective (or history). Brain Res Rev, 32(1):16-28.

[8]Boccaletti S, Farini A, Arecchi FT, 1997. Adaptive synchronization of chaos for secure communication. Phys Rev E, 55(5):4979-4981.

[9]Budhathoki RK, Sah MP, Adhikari SP, et al., 2013. Composite behavior of multiple memristor circuits. IEEE Trans Circ Syst I, 60(10):2688-2700.

[10]Burić N, Todorović K, Vasović N, 2008. Synchronization of bursting neurons with delayed chemical synapses. Phys Rev E, 78:036211.

[11]Buscarino A, Fortuna L, Frasca M, 2009. Experimental robust synchronization of hyperchaotic circuits. Phys D, 238(18): 1917-1922.

[12]Buscarino A, Fortuna L, Frasca M, et al., 2012. A chaotic circuit based on Hewlett-Packard memristor. Chaos, 22(2):023136.

[13]Davison IG, Ehlers MD, 2011. Neural circuit mechanisms for pattern detection and feature combination in olfactory cortex. Neuron, 70(1):82-94.

[14]Eccles JC, 1982. The synapse: from electrical to chemical transmission. Ann Rev Neurosci, 5(1):325-339.

[15]Fell J, Axmacher N, 2011. The role of phase synchronization in memory processes. Nat Rev Neurosci, 12(2):105-118.

[16]Guo SL, Xu Y, Wang CN, et al., 2017. Collective response, synapse coupling and field coupling in neuronal network. Chaos Sol Fract, 105:120-127.

[17]Guo SL, Ma J, Alsaedi A, 2018. Suppression of chaos via control of energy flow. Pramana, 90(3):39.

[18]Hahn SL, 1996. Hilbert Transforms in Signal Processing. Artech House, Boston, USA.

[19]Hanias MP, Giannaris G, Spyridakis A, et al., 2006. Time series analysis in chaotic diode resonator circuit. Chaos Sol Fract, 27(2):569-573.

[20]He DH, Shi PL, Stone L, 2003. Noise-induced synchronization in realistic models. Phys Rev E, 67(2):027201.

[21]Ikezi H, deGrassie JS, Jensen TH, 1983. Observation of multiple-valued attractors and crises in a driven nonlinear circuit. Phys Rev A, 28(2):1207-1209.

[22]Kiliç R, Alçi M, Çam U, et al., 2002. Improved realization of mixed-mode chaotic circuit. Int J Bifurc Chaos, 12(6): 1429-1435.

[23]Kopell N, Ermentrout B, 2004. Chemical and electrical synapses perform complementary roles in the synchronization of interneuronal networks. PNAS, 101(43):15482-15487.

[24]Li XM, Wang J, Hu WH, 2007. Effects of chemical synapses on the enhancement of signal propagation in coupled neurons near the canard regime. Phys Rev E, 76:041902.

[25]Louodop P, Fotsin H, Kountchou M, et al., 2014. Finite-time synchronization of tunnel-diode-based chaotic oscillators. Phys Rev E, 89:032921.

[26]Lv M, Ma J, Yao YG, et al., 2018. Synchronization and wave propagation in neuronal network under field coupling. Sci China Technol Sci, in press.

[27]Ma J, Song XL, Tang J, et al., 2015. Wave emitting and propagation induced by autapse in a forward feedback neuronal network. Neurocomputing, 167:378-389.

[28]Ma J, Mi L, Zhou P, et al., 2017. Phase synchronization between two neurons induced by coupling of electromagnetic field. Appl Math Comput, 307:321-328.

[29]Muthuswamy B, Chua LO, 2010. Simplest chaotic circuit. Int J Bifurc Chaos, 20(5):1567-1580.

[30]Muthuswamy B, Kokate PP, 2009. Memristor-based chaotic circuits. IETE Tech Rev, 26(6):417-429.

[31]Nazzal JM, Natsheh AN, 2007. Chaos control using sliding-mode theory. Chaos Sol Fract, 33(2):695-702.

[32]Neiman A, Schimansky-Geier L, Cornell-Bell A, et al., 1999. Noise-enhanced phase synchronization in excitable media. Phys Rev Lett, 83(23):4896-4899.

[33]Parlitz U, Junge L, Lauterborn W, et al., 1996. Experimental observation of phase synchronization. Phys Rev E, 54(2): 2115-2117.

[34]Pikovsky AS, 1981. A dynamical model for periodic and chaotic oscillations in the Belousov-Zhabotinsky reaction. Phys Lett A, 85(1):13-16.

[35]Pikovsky AS, Rabinovich MI, 1978. A simple autogenerator with stochastic behaviour. Sov Phys Dokl, 23:183-185.

[36]Pikovsky A, Rosenblum M, Kurths J, 2000. Phase synchronization in regular and chaotic systems. Int J Bifurc Chaos, 10(10):2291-2305.

[37]Qin HX, Ma J, Jin WY, et al., 2014. Dynamics of electric activities in neuron and neurons of network induced by autapses. Sci China Technol Sci, 57(5):936-946.

[38]Ren GD, Zhou P, Ma J, et al., 2017. Dynamical response of electrical activities in digital neuron circuit driven by autapse. Int J Bifurc Chaos, 27(12):1750187.

[39]Ren GD, Xue YX, Li YW, et al., 2019. Field coupling benefits signal exchange between Colpitts systems. Appl Math Comput, 342:45-54.

[40]Schöll E, Schuster HG, 2008. Handbook of Chaos Control. John Wiley & Sons, Weinheim, Germany.

[41]Song XL, Wang CN, Ma J, et al., 2015. Transition of electric activity of neurons induced by chemical and electric autapses. Sci China Technol Sci, 58(6):1007-1014.

[42]Tang J, Zhang J, Ma J, et al., 2017. Astrocyte calcium wave induces seizure-like behavior in neuron network. Sci China Technol Sci, 60(7):1011-1018.

[43]Timmer J, Rust H, Horbelt W, et al., 2000. Parametric, non parametric and parametric modelling of a chaotic circuit time series. Phys Lett A, 274(3-4):123-134.

[44]Wang CN, Ma J, Liu Y, et al., 2012. Chaos control, spiral wave formation, and the emergence of spatiotemporal chaos in networked Chua circuits. Nonl Dynam, 67(1):139-146.

[45]Wang CN, Chu RT, Ma J, 2015. Controlling a chaotic resonator by means of dynamic track control. Complexity, 21(1): 370-378.

[46]Wu CW, Chua LO, 1993. A simple way to synchronize chaotic systems with applications to secure communication systems. Int J Bifurc Chaos, 3(6):1619-1627.

[47]Xu Y, Jia Y, Ma J, et al., 2018. Collective responses in electrical activities of neurons under field coupling. Sci Rep, 8(1):1349.

[48]Yu WT, Zhang J, Tang J, 2017. Effects of dynamic synapses, neuronal coupling, and time delay on firing of neuron. Acta Phys Sin, 66:200201.

[49]Zaher AA, Abu-Rezq A, 2011. On the design of chaos-based secure communication systems. Commun Nonl Sci Numer Simul, 16(9):3721-3737.

[50]Zhang G, Ma J, Alsaedi A, et al., 2018a. Dynamical behavior and application in Josephson junction coupled by memristor. Appl Math Comput, 321:290-299.

[51]Zhang G, Wu FQ, Hayat T, et al., 2018b. Selection of spatial pattern on resonant network of coupled memristor and Josephson junction. Commun Nonl Sci Numer Simul, 65:79-90.

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