Impact of bounded noise on the formation and instability of spiral wave in a 2D Lattice of neurons

Yuangen Yao,Jun Ma,Ming Yi,Haiyou Deng

doi:10.1038/srep43151

Abstract

Spiral waves in the neocortex may provide a spatial framework to organize cortical oscillations, thus help signal communication. However, noise influences spiral wave. Many previous theoretical studies about noise mainly focus on unbounded Gaussian noise, which contradicts that a real physical quantity is always bounded. Furthermore, non-Gaussian noise is also important for dynamical behaviors of excitable media. Nevertheless, there are no results concerning the effect of bounded noise on spiral wave till now. Based on Hodgkin-Huxley neuron model subjected to bounded noise with the form of Asin[ωt + σW(t)], the influences of bounded noise on the formation and instability of spiral wave in a two-dimensional (2D) square lattice of neurons are investigated in detail by separately adjusting the intensity σ, amplitude A, and frequency f of bounded noise. It is found that the increased intensity σ can facilitate the formation of spiral wave while the increased amplitude A tends to destroy spiral wave. Furthermore, frequency of bounded noise has the effect of facilitation or inhibition on pattern synchronization. Interestingly, for the appropriate intensity, amplitude and frequency can separately induce resonance-like phenomenon.

Highlights

Experimental work have revealed the counterintuitive influences of noise
We found that spiral wave is robust below a certain threshold of noise intensity; otherwise, the breakup of spiral wave occurs over this threshold[27]
Motivated by the previous findings and the importance of spiral wave, bounded noises with sine-function form are imposed on some neurons, whose local kinetics is described by the famous Hodgkin-Huxley (H-H) neuron model, while neurons are coupled with nearest-neighbor connection to form a two-dimensional (2D) square lattice

Summary

Main results

Influences of intensity on formation and instability of spiral wave. Firstly, we discuss how the intensity σ of the unit Wiener process changes the wave formation and instability in the network at the different frequencies of bounded noise. We investigate how the intensity σ of the unit Wiener process affects wave formation and instability in the network at the different amplitudes of bounded noise The bounded noise is dependent on the frequency, it is important to evaluate the influences of frequency on formation and instability of spiral wave In this case, we discuss how frequency influences wave formation and instability in the network, and the results are shown in Fig. 6 when we set A = 20. For lower amplitude, such as 10 or 15, the increased frequency almost has no effect on the pattern of spiral wave (Fig. 7) This conclusion may change for greater amplitude.

Discussions and Conclusions

Additional Information