Spatiotemporal pattern in a neural network with non-smooth memristor

Xuerong Shi; Zuolei Wang; Lizhou Zhuang; Xuerong Shi; Zuolei Wang; Lizhou Zhuang

doi:10.3934/era.2022038

Electronic Research Archive

2022, Volume 30, Issue 2: 715-731. doi: 10.3934/era.2022038

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Research article

Spatiotemporal pattern in a neural network with non-smooth memristor

1.
School of Mathematics and Statistics, Yancheng Teachers University, Yancheng 224002, China
2.
School of Chemical and Environmental, Yancheng Teachers University, Yancheng 224007, China

Received: 23 September 2021 Revised: 01 November 2021 Accepted: 02 November 2021 Published: 25 February 2022

Considering complicated dynamics of non-smooth memductance function, an improved Hindmarsh-Rose neuron model is introduced by coupling with non-smooth memristor and dynamics of the improved model are discussed. Simulation results suggest that dynamics of the proposed neuron model depends on the external stimuli but not on the initial value for the magnetic flux. Furthermore, a network composed of the improved Hindmarsh-Rose neuron is addressed via single channel coupling method and spatiotemporal patterns of the network are investigated via numerical simulations with no-flux boundary condition. Firstly, development of spiral wave are discussed for different coupling strengths, different external stimuli and various initial value for the magnetic flux. Results suggest that spiral wave can be developed for coupling strength $ 0 < D < 1 $ when the nodes are provided with period-1 dynamics, especially, double-arm spiral wave appear for $ D = 0.4 $.External stimuli changing can make spiral wave collapse and the network demonstrates chaotic state. Alternation of initial value for the magnetic flux hardly has effect on the developed spiral wave. Secondly, formation of target wave are studied for different coupling strengths, different sizes of center area with parameter diversity and various initial value for the magnetic flux. It can be obtained that, for certain size of center area with parameter diversity, target wave can be formed for coupling strength $ 0 < D < 1 $, while for too small size of center area with parameter diversity, target wave can hardly be formed. Change of initial value for the magnetic flux has no effect on the formation of target wave. Research results reveal the spatiotemporal patterns of neuron network to some extent and may provide some suggestions for exploring some disease of neural system.
- spatiotemporal pattern,
- non-smooth memristor,
- Hindmarsh-Rose neuron,
- single channel coupling method,
- neuron network
Citation: Xuerong Shi, Zuolei Wang, Lizhou Zhuang. Spatiotemporal pattern in a neural network with non-smooth memristor[J]. Electronic Research Archive, 2022, 30(2): 715-731. doi: 10.3934/era.2022038

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Abstract

Considering complicated dynamics of non-smooth memductance function, an improved Hindmarsh-Rose neuron model is introduced by coupling with non-smooth memristor and dynamics of the improved model are discussed. Simulation results suggest that dynamics of the proposed neuron model depends on the external stimuli but not on the initial value for the magnetic flux. Furthermore, a network composed of the improved Hindmarsh-Rose neuron is addressed via single channel coupling method and spatiotemporal patterns of the network are investigated via numerical simulations with no-flux boundary condition. Firstly, development of spiral wave are discussed for different coupling strengths, different external stimuli and various initial value for the magnetic flux. Results suggest that spiral wave can be developed for coupling strength $ 0 < D < 1 $ when the nodes are provided with period-1 dynamics, especially, double-arm spiral wave appear for $ D = 0.4 $.External stimuli changing can make spiral wave collapse and the network demonstrates chaotic state. Alternation of initial value for the magnetic flux hardly has effect on the developed spiral wave. Secondly, formation of target wave are studied for different coupling strengths, different sizes of center area with parameter diversity and various initial value for the magnetic flux. It can be obtained that, for certain size of center area with parameter diversity, target wave can be formed for coupling strength $ 0 < D < 1 $, while for too small size of center area with parameter diversity, target wave can hardly be formed. Change of initial value for the magnetic flux has no effect on the formation of target wave. Research results reveal the spatiotemporal patterns of neuron network to some extent and may provide some suggestions for exploring some disease of neural system.

References

[1]	Q. Y. Wang, M. Perc, Z. S. Duan, G. R. Chen, Synchronization transitions on scale-free neuronal networks due to finite information transmission delays, Phys. Rev. E, 80 (2009), 026206. https://doi.org/10.1103/PhysRevE.80.026206 doi: 10.1103/PhysRevE.80.026206
[2]	F. Han, M. Wiercigroch, J. A. Fang, Z. J. Wang, Excitement and synchronization of small-world neuronal networks with short-term synaptic plasticity, Int. J. Neural Syst., 21 (2011), 415-425. https://doi.org/10.1142/S0129065711002924 doi: 10.1142/S0129065711002924
[3]	Q. Y. Wang, G. R. Chen, M. Perc, Synchronous bursts on scale-free neuronal networks with attractive and repulsive coupling, Plos One, 6 (2011), e15851. https://doi.org/10.1371/journal.pone.0015851 doi: 10.1371/journal.pone.0015851
[4]	F. Han, Z.J. Wang, Y. Du, X.J. Sun, B. Zhang, Robust synchronization of bursting Hodgkin- Huxley neuronal systems coupled by delayed chemical synapses, Int. J. Nonlin. Mech., 70 (2015), 105-111. https://doi.org/10.1016/j.ijnonlinmec.2014.10.010 doi: 10.1016/j.ijnonlinmec.2014.10.010
[5]	X. L. Qin, C. Wang, L. X. Li, H. P. Peng, Y. X. Yang, L. Ye, Finite-time projective synchronization of memristor-based neural networks with leakage and time-varying delays, Physica A, 531 (2019), 121788. https://doi.org/10.1016/j.physa.2019.121788 doi: 10.1016/j.physa.2019.121788
[6]	F. Han, X. C. Gu, Z. J. Wang, H. Fan, J. F. Cao, Q.S. Lu, Global firing rate contrast enhancement in E/I neuronal networks by recurrent synchronized inhibition, Chaos, 28 (2018), 106324. https://doi.org/10.1063/1.5037207 doi: 10.1063/1.5037207
[7]	D. H. He, G. Hu, M. Zhan, W. Ren, Z. Gao, Pattern formation of spiral waves in an inhomogeneous medium with small-world connections, Phys. Rev. E, 65 (2002), 055204. https://doi.org/10.1103/PhysRevE.65.055204 doi: 10.1103/PhysRevE.65.055204
[8]	H. X. Qin, J. Ma, C. N. Wang, Y. Wu, Autapse-induced spiral wave in network of neurons under noise, Plos One, 9 (2014), e100849. https://doi.org/10.1371/journal.pone.0100849 doi: 10.1371/journal.pone.0100849
[9]	H. X. Qin, Y. Wu, C. N. Wang, J. Ma, Emitting waves from defects in network with autapses, Commun. Nonlinear Sci., 23 (2015), 164-174. https://doi.org/10.1016/j.cnsns.2014.11.008 doi: 10.1016/j.cnsns.2014.11.008
[10]	X.Y. Wu, J. Ma, The formation mechanism of defects, spiral wave in the network of neurons, Plos One, 8 (2013), e55403. https://doi.org/10.1371/journal.pone.0055403 doi: 10.1371/journal.pone.0055403
[11]	J. Ma, Y. Wu, N. J. Wu, H. Y. Guo, Detection of ordered wave in the networks of neurons with changeable connection, Sci. China Phys. Mech., 56 (2013), 952-959. https://doi.org/10.1007/s11433-013-5070-0 doi: 10.1007/s11433-013-5070-0
[12]	P. Wang, Q. Y. Li, G. N. Tang, Spontaneous generation of spiral wave in the array of Hindmarsh- Rose neurons, Acta Phys. Sin-Ch Ed., 67 (2018), 030502. https://doi.org/10.7498/aps.67.20172140 doi: 10.7498/aps.67.20172140
[13]	C. N. Wang, J. Ma, J. Tang, Y. L. Li, Instability and death of spiral wave in a two-dimensional array of Hindmarsh-Rose neurons, Commun. Theor. Phys., 53 (2010), 382-388. https://doi.org/10.1088/0253-6102/53/2/32 doi: 10.1088/0253-6102/53/2/32
[14]	Y. Xu, W. Y. Jin, J. Ma, Emergence and robustness of target waves in a neuronal network, Int. J. Mod. Phys. B, 29 (2015), 1550164. https://doi.org/10.1142/S0217979215501647 doi: 10.1142/S0217979215501647
[15]	H. X. Qin, J. Ma, C. N. Wang, R. T. Chu, Autapse-induced target wave, spiral wave in regular network of neurons, Sci. China Phys. Mech., 57 (2014), 1918-1926. https://doi.org/10.1007/s11433-014-5466-5 doi: 10.1007/s11433-014-5466-5
[16]	Q. Y. Wang, M. Perc, Z. S. Duan, G. R. Chen, Delay-enhanced coherence of spiral waves in noisy Hodgkin-Huxley neuronal networks, Phys. Lett. A, 372 (2008), 5681-5687. https://doi.org/10.1016/j.physleta.2008.07.005 doi: 10.1016/j.physleta.2008.07.005
[17]	C. N. Takembo, A. Mvogo, H. P. E. Fouda, T. C. Kofane, Effect of electromagnetic radiation on the dynamics of spatiotemporal patterns in memristor-based neuronal network, Nonlinear Dynam., 95 (2019), 1067-1078. https://doi.org/10.1007/s11071-018-4616-0 doi: 10.1007/s11071-018-4616-0
[18]	K. Rajagopal, A. Karthikeyan, S. Jafari, F. Parastesh, C. Volos, I. Hussain, Wave propagation and spiral wave formation in a Hindmarsh-Rose neuron model with fractional-order threshold memristor synaps, Int. J. Mod. Phys. B, 34 (2020), 2050157. https://doi.org/10.1142/S021797922050157X doi: 10.1142/S021797922050157X
[19]	H. Bao, B. C. Bao, Y. Lin, J. Wang, H. G. Wu, Hidden attractor and its dynamical characteristic in memristive self-oscillating system, Acta Phys. Sin-Ch. Ed., 65 (2016), 180501. https://doi.org/10.7498/aps.65.180501 doi: 10.7498/aps.65.180501
[20]	L. Chua, Resistance switching memories are memristors, Appl. Phys. A-Mater., 102 (2011), 765-783. https://doi.org/10.1007/s00339-011-6264-9 doi: 10.1007/s00339-011-6264-9

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