Fractal analyses of networks of integrate-and-fire stochastic spiking neurons
arXiv:1801.08087 · doi:10.1007/978-3-319-73198-8_14
Abstract
Although there is increasing evidence of criticality in the brain, the processes that guide neuronal networks to reach or maintain criticality remain unclear. The present research examines the role of neuronal gain plasticity in time-series of simulated neuronal networks composed of integrate-and-fire stochastic spiking neurons, and the utility of fractal methods in assessing network criticality. Simulated time-series were derived from a network model of fully connected discrete-time stochastic excitable neurons. Monofractal and multifractal analyses were applied to neuronal gain time-series. Fractal scaling was greatest in networks with a mid-range of neuronal plasticity, versus extremely high or low levels of plasticity. Peak fractal scaling corresponded closely to additional indices of criticality, including average branching ratio. Networks exhibited multifractal structure, or multiple scaling relationships. Multifractal spectra around peak criticality exhibited elongated right tails, suggesting that the fractal structure is relatively insensitive to high-amplitude local fluctuations. Networks near critical states exhibited mid-range multifractal spectra width and tail length, which is consistent with literature suggesting that networks poised at quasi-critical states must be stable enough to maintain organization but unstable enough to be adaptable. Lastly, fractal analyses may offer additional information about critical state dynamics of networks by indicating scales of influence as networks approach critical states.
arXiv comment11 pages, 3 subfigures divided into 2 figures
References in corpus (13)
- Optimal Dynamical Range of Excitable Networks at Criticality
- Dynamical synapses causing self-organized criticality in neural networks
- Critical brain networks
- Self-Organized Criticality model for Brain Plasticity
- 25 Years of Self-Organized Criticality: Concepts and Controversies
- Infinite systems of interacting chains with memory of variable length - a stochastic model for biological neural nets
- Inhibition causes ceaseless dynamics in networks of excitable nodes
- Hydrodynamic limit for interacting neurons
- Markers of criticality in phase synchronisation
- Can dynamical synapses produce true self-organized criticality?
- Self-Organized Supercriticality and Oscillations in Networks of Stochastic Spiking Neurons
- Correlations Induced by Depressing Synapses in Critically Self-Organized Networks with Quenched Dynamics
- A model for neural activity in the absence of external stimuli