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

Abstract

Spatially uniform cross-correlated sine-Wiener (CCSW) noises are imposed on each Hodgkin-Huxley (HH) neuron in a twodimensional (2D) regular network. Noise-induced spiral wave destruction and order-disorder spatial pattern transition can be observed by adjusting cross-correlation time or cross-correlation intensity of CCSW noises. The sudden change of the curve of synchronization factor and the time series of average membrane voltage F can be used to semiquantitatively assess this spatial pattern transition and spiral wave destruction induced by CCSW noises, respectively. In addition, moderate cross-correlation time and strong cross-correlation intensity of CCSW noises are both detrimental to survival of spiral wave. Comparing with non-crosscorrelated sine-Wiener noises, CCSW noises can destroy organized spiral wave with lesser noise amplitude.

Properties of bounded stochastic processes employed in biophysics

“…Moreover, both µ (1) and σ (1) are bounded and continuous, as per their definition in (17), (18). Hence, Proposition B.6 ensures that a weak solution to (16) exists.…”

“…In the last two decades, a large literature has been devoted to the application of bounded stochastic processes to many scientific areas. For example: noise-induced transitions [4], stochastic resonance [5], Kramers problem [6], bifurcation theory [7], parametric resonance [8], fractional mechanics [9], nonlinear mechanics [10], chaotic systems [11], tumor biophysics [2,12], cell biology [13], ecology [14], environmental sciences [15], interacting cellular populations [16], delayed systems [17], neurosciences [18], chemistry [19], and population genetics [20]. However, the best known and oldest example of bounded stochastic process is probably the dichotomous Markov noise, also known as telegraph noise [15].…”

Stochastic Dynamics of Gene Switching and Energy Dissipation for Gene Expression

“…In our work, a double-deck loop model is constructed. Due to the stochastic nature of bio-processes (Wang et al, 2017 ; Yao et al, 2018a , b ), we have calculated the steady-state probability distributions of ROCK protein through the method of probability-generating functions for chemical master equations. The crucial factors in the stochastic dynamics of gene switching are identified.…”

Spike propagation by synchronization and vibrational resonance in feedforward Izhikevich neural network

“…Furthermore, the topology of the network and the self−induced stochastic resonance of one layer to control the coherent resonance (CR) of the other layer [18]. Moreover, the amplification effect of weak signals in the nervous system is studied, and the statistical characteristics of the emission process and the dependence of the helical wave destruction on noise are explored [19][20][21].…”