Impact of Bounded Noise and Rewiring on the Formation and Instability of Spiral Waves in a Small-World Network of Hodgkin-Huxley Neurons

Abstract

Spiral waves are observed in the chemical, physical and biological systems, and the emergence of spiral waves in cardiac tissue is linked to some diseases such as heart ventricular fibrillation and epilepsy; thus it has importance in theoretical studies and potential medical applications. Noise is inevitable in neuronal systems and can change the electrical activities of neuron in different ways. Many previous theoretical studies about the impacts of noise on spiral waves focus an unbounded Gaussian noise and even colored noise. In this paper, the impacts of bounded noise and rewiring of network on the formation and instability of spiral waves are discussed in small-world (SW) network of Hodgkin-Huxley (HH) neurons through numerical simulations, and possible statistical analysis will be carried out. Firstly, we present SW network of HH neurons subjected to bounded noise. Then, it is numerically demonstrated that bounded noise with proper intensity σ, amplitude A, or frequency f can facilitate the formation of spiral waves when rewiring probability p is below certain thresholds. In other words, bounded noise-induced resonant behavior can occur in the SW network of neurons. In addition, rewiring probability p always impairs spiral waves, while spiral waves are confirmed to be robust for small p, thus shortcut-induced phase transition of spiral wave with the increase of p is induced. Furthermore, statistical factors of synchronization are calculated to discern the phase transition of spatial pattern, and it is confirmed that larger factor of synchronization is approached with increasing of rewiring probability p, and the stability of spiral wave is destroyed.

Breakup of Spiral Wave and Order‐Disorder Spatial Pattern Transition Induced by Spatially Uniform Cross‐Correlated Sine‐Wiener Noises in a Regular Network of Hodgkin‐Huxley Neurons

“…As reported previously, to measure spatial synchronization, a synchronization factor is introduced as follows [14,15,38]:…”

“…Hence, bounded stochastic processes are increasingly employed in various research fields involving electrical engineering, mechanical and structural engineering, and biological systems [13]. For example, impacts of bounded noise on the formation and instability of spiral waves in regular and small-world networks of Hodgkin-Huxley (HH) neurons were investigated in our previous works [14,15] and the constructive role of bounded noise in facilitating formation and stability of spiral waves was discovered [14,15].…”

Delay-induced synchronization transition in a small-world neuronal network of FitzHugh–Nagumo neurons subjected to sine-Wiener bounded noise

“…35 Based on these considerations, bounded noise attracts much attention and has been used widely in engineering, physical and biological systems. 36 Remarkably, some interesting phenomena have been observed, such as bounded noise-facilitated spiral formation and breakup, 37,38 and bounded noise-enhanced periodic signal detection. 39 Sine-Wiener (SW) bounded noise is usually represented as a sinusoidal function with a constant amplitude and a random phase caused by a standard Wiener process.…”

Subthreshold Periodic Signal Detection by Bounded Noise‐Induced Resonance in the FitzHugh–Nagumo Neuron

“…Gaussian noise is usually adopted in many cases for convenience of analysis. It is worth mentioning that the widely used Gaussian noise has the probability of taking very large values, which violates the notion that real physical quantities in real systems always take values in bounded intervals [34][35][36]. In fact, unbounded Gaussian noise is not always suitable for modeling all realistic random processes.…”

“…We have also investigated the effect of bounded noise on the formation and instability of spiral waves [35,36]. In particular, the combined effects of correlated bounded noises and weak periodic signal were investigated in a recent study, and related results suggest that bounded noise can enhance the detection of external signals [49,50].…”