Neurons and Near-Death Spikes
151
within the network. When most of the neurons of the network are converted to
chaotic ones, their activities become independent of each other.
The ‘near-death’-like surges had not been reported earlier by the theoretical study
of biological neuron network. The present study indicates that to soothe an overactive
brain, some neurons of the network can be turned into chaotic. Further, experimental
studies are to be performed before its use in treatment of diseases like stress, over
anxiety, ADHD, Alzheimer’s disease, etc. This study can be extended to the complete
neural network of the C. elegans. A detailed mean field approximation of the present
network can also be included in the future study.
This article also examines the influence of Lévy noise on the neural network of
C. elegans through the dynamics of average firing rate and bursting synchronization.
It is found that characteristic exponent of noise (α) influences the network dynamics
more compared to scale parameter of noise (D) and coupling strength of synapse
(G syn ). The present study identified that at α nearly equal to 0.7 the network makes
transitions from one state of relatively high degree of synchronization to a state of
almost complete asynchronization. It is known that with increase in α values, magnitude of noise changes from very high and random values to small and regular values.
It is found that with increase in α values, the feedback current received by a neuron
from the network peaks around α ≈ 0.7 and then decreases gradually. Consequently,
for α < 0.8, neurons displayed synchronizations and near-death spikes. With further
increase in characteristic exponent of noise, firings of the neurons become asynchronous, sustains longer and the near-death spikes gradually get disappeared.
This work identifies the various parameter regions which helps in the control of the
network dynamics. It is found that the network even displayed gamma oscillations
for large values of α. The study also recognized α values, at which the network
displayed the generation of waves of other frequencies. This result suggests a new
method for neurostimulation in the case of traumatic brain injury [33].
In most of the studied parameter regions, noise enhanced bursting synchronization of the non-chaotic network of C. elegans. Compared to G syn , D influences the
network dynamics more. In the presence of Lévy noise, for some values of α, even
the non-chaotic neurons of the network displayed near death like surges of firing.
This observation is not yet reported in the literature.
Similar to that of the noise free case, chaotic neurons reduced the firing rate of
the network from Beta range to Delta and Theta ranges. This reduction is a different
feature in comparison to that of the non-chaotic ones for all values of α. The spiking
rate and synchronization of the network are decreased due to decrease in value of
average feedback current received by a neuron.
The results of the works support the observation of transitions between states of
different degrees of synchronization in cortical regions of brain of rats. The model
also enables to give the theoretical background for biological observation that during
the transition period between asynchronous and synchronous firing state, network is
more susceptible to changes in firing patterns of individual neurons.
151
within the network. When most of the neurons of the network are converted to
chaotic ones, their activities become independent of each other.
The ‘near-death’-like surges had not been reported earlier by the theoretical study
of biological neuron network. The present study indicates that to soothe an overactive
brain, some neurons of the network can be turned into chaotic. Further, experimental
studies are to be performed before its use in treatment of diseases like stress, over
anxiety, ADHD, Alzheimer’s disease, etc. This study can be extended to the complete
neural network of the C. elegans. A detailed mean field approximation of the present
network can also be included in the future study.
This article also examines the influence of Lévy noise on the neural network of
C. elegans through the dynamics of average firing rate and bursting synchronization.
It is found that characteristic exponent of noise (α) influences the network dynamics
more compared to scale parameter of noise (D) and coupling strength of synapse
(G syn ). The present study identified that at α nearly equal to 0.7 the network makes
transitions from one state of relatively high degree of synchronization to a state of
almost complete asynchronization. It is known that with increase in α values, magnitude of noise changes from very high and random values to small and regular values.
It is found that with increase in α values, the feedback current received by a neuron
from the network peaks around α ≈ 0.7 and then decreases gradually. Consequently,
for α < 0.8, neurons displayed synchronizations and near-death spikes. With further
increase in characteristic exponent of noise, firings of the neurons become asynchronous, sustains longer and the near-death spikes gradually get disappeared.
This work identifies the various parameter regions which helps in the control of the
network dynamics. It is found that the network even displayed gamma oscillations
for large values of α. The study also recognized α values, at which the network
displayed the generation of waves of other frequencies. This result suggests a new
method for neurostimulation in the case of traumatic brain injury [33].
In most of the studied parameter regions, noise enhanced bursting synchronization of the non-chaotic network of C. elegans. Compared to G syn , D influences the
network dynamics more. In the presence of Lévy noise, for some values of α, even
the non-chaotic neurons of the network displayed near death like surges of firing.
This observation is not yet reported in the literature.
Similar to that of the noise free case, chaotic neurons reduced the firing rate of
the network from Beta range to Delta and Theta ranges. This reduction is a different
feature in comparison to that of the non-chaotic ones for all values of α. The spiking
rate and synchronization of the network are decreased due to decrease in value of
average feedback current received by a neuron.
The results of the works support the observation of transitions between states of
different degrees of synchronization in cortical regions of brain of rats. The model
also enables to give the theoretical background for biological observation that during
the transition period between asynchronous and synchronous firing state, network is
more susceptible to changes in firing patterns of individual neurons.