20,668 research outputs found
Distinct dynamical behavior in Erd\H{o}s-R\'enyi networks, regular random networks, ring lattices, and all-to-all neuronal networks
Neuronal network dynamics depends on network structure. In this paper we
study how network topology underpins the emergence of different dynamical
behaviors in neuronal networks. In particular, we consider neuronal network
dynamics on Erd\H{o}s-R\'enyi (ER) networks, regular random (RR) networks, ring
lattices, and all-to-all networks. We solve analytically a neuronal network
model with stochastic binary-state neurons in all the network topologies,
except ring lattices. Given that apart from network structure, all four models
are equivalent, this allows us to understand the role of network structure in
neuronal network dynamics. Whilst ER and RR networks are characterized by
similar phase diagrams, we find strikingly different phase diagrams in the
all-to-all network. Neuronal network dynamics is not only different within
certain parameter ranges, but it also undergoes different bifurcations (with a
richer repertoire of bifurcations in ER and RR compared to all-to-all
networks). This suggests that local heterogeneity in the ratio between
excitation and inhibition plays a crucial role on emergent dynamics.
Furthermore, we also observe one subtle discrepancy between ER and RR networks,
namely ER networks undergo a neuronal activity jump at lower noise levels
compared to RR networks, presumably due to the degree heterogeneity in ER
networks that is absent in RR networks. Finally, a comparison between network
oscillations in RR networks and ring lattices shows the importance of
small-world properties in sustaining stable network oscillations.Comment: 9 pages, 4 figure
Majorana Fermions Signatures in Macroscopic Quantum Tunneling
Thermodynamic measurements of magnetic fluxes and I-V characteristics in
SQUIDs offer promising paths to the characterization of topological
superconducting phases. We consider the problem of macroscopic quantum
tunneling in an rf-SQUID in a topological superconducting phase. We show that
the topological order shifts the tunneling rates and quantum levels, both in
the parity conserving and fluctuating cases. The latter case is argued to
actually enhance the signatures in the slowly fluctuating limit, which is
expected to take place in the quantum regime of the circuit. In view of recent
advances, we also discuss how our results affect a -junction loop.Comment: 10 pages, 11 figure
Neural networks with dynamical synapses: from mixed-mode oscillations and spindles to chaos
Understanding of short-term synaptic depression (STSD) and other forms of
synaptic plasticity is a topical problem in neuroscience. Here we study the
role of STSD in the formation of complex patterns of brain rhythms. We use a
cortical circuit model of neural networks composed of irregular spiking
excitatory and inhibitory neurons having type 1 and 2 excitability and
stochastic dynamics. In the model, neurons form a sparsely connected network
and their spontaneous activity is driven by random spikes representing synaptic
noise. Using simulations and analytical calculations, we found that if the STSD
is absent, the neural network shows either asynchronous behavior or regular
network oscillations depending on the noise level. In networks with STSD,
changing parameters of synaptic plasticity and the noise level, we observed
transitions to complex patters of collective activity: mixed-mode and spindle
oscillations, bursts of collective activity, and chaotic behaviour.
Interestingly, these patterns are stable in a certain range of the parameters
and separated by critical boundaries. Thus, the parameters of synaptic
plasticity can play a role of control parameters or switchers between different
network states. However, changes of the parameters caused by a disease may lead
to dramatic impairment of ongoing neural activity. We analyze the chaotic
neural activity by use of the 0-1 test for chaos (Gottwald, G. & Melbourne, I.,
2004) and show that it has a collective nature.Comment: 7 pages, Proceedings of 12th Granada Seminar, September 17-21, 201
Critical and resonance phenomena in neural networks
Brain rhythms contribute to every aspect of brain function. Here, we study
critical and resonance phenomena that precede the emergence of brain rhythms.
Using an analytical approach and simulations of a cortical circuit model of
neural networks with stochastic neurons in the presence of noise, we show that
spontaneous appearance of network oscillations occurs as a dynamical
(non-equilibrium) phase transition at a critical point determined by the noise
level, network structure, the balance between excitatory and inhibitory
neurons, and other parameters. We find that the relaxation time of neural
activity to a steady state, response to periodic stimuli at the frequency of
the oscillations, amplitude of damped oscillations, and stochastic fluctuations
of neural activity are dramatically increased when approaching the critical
point of the transition.Comment: 8 pages, Proceedings of 12th Granada Seminar, September 17-21, 201
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