Neurons and Near-Death Spikes
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termination (SIST) [18]. In SIST, a strong external impulse or a strong synaptic coupling in network of excitatory neurons caused hyper synchronization and subsequent
cessation of neuronal firings. It is responsible for spontaneous termination of epileptic seizures. Whereas in a ‘wave of death’ hyper synchronization is not playing a role
[19].
The analysis on ‘the spatiotemporal activities of a pulse-coupled biological neural
network’ which discusses near-death spikes when the neurons are chaotic can be
extended to explore the underlying reason for such behaviour, through dynamical
analysis.
Under optimal conditions, noise can induce synchronization, coherence resonance, stochastic resonance and vibrational resonance in nonlinear systems [20]. It is
demonstrated that Gaussian noise of particular intensity can induce spatial coherence
resonance in a two-dimensional network of FitzHugh-Nagumo neurons. Fractionalorder Gaussian noise can also enhance information carrying capacity of neurons.
In another study, it is found that long-range connections can destroy noise-induced
spatial coherence resonance (or cause decoherence). Influence of external electric
or magnetic fields or both on the neuronal environment can also be treated as noise.
Strong external electric field can influence the firing rate and synchronization of
neural networks. Many theoretical and experimental studies have proved that both
static and dynamic magnetic fields can suppress neuronal activities and cell growth
[21–24].
Unlike Gaussian white noise, Lévy noise or Lévy distribution is characterized by
small fluctuations, random large jumps and heavy tail. From predicting the path of a
bacteria in a swarm to game theory [25], Lévy process finds applications in almost all
fields of life, be it mathematics, finance, sociology, biology, physics, astronomy or
meteorology. In finance, it is used to study the stock market, options pricing, etc. In
physics, it finds applications in modelling turbulence, modelling chaos in Josephson
Junction and in quantum group theory.
Like channel noise and membrane noise, there are different types of noises present
in the neural system. Lévy noise is used to model the noisy environment of neuronal
network [26]. Neuron models involving Lévy noise can display all the dynamical
variations of membrane potential, be it diffusion, jumps in membrane voltage or
jump-diffusion.
In a recent study, it was revealed that Lévy noise can improve electrical activity
in a neuron under electromagnetic radiation. By adjusting appropriate parameters
of noise, firing modes of the neuron can be varied. Influence of Lévy noise on the
Izhikevich neuron, an all-to all coupled network and two excitatory coupled network
are studied recently [27], and it is shown that when the Lévy noise’s characteristic
exponent is 0.5, the individual neuronal level firing activity and the network dynamics
become irregular.
The study presented here gives the spatiotemporal activities of C. elegans neural
network under the influence of Lévy noise [28]. It is relevant to find the influence
of Lévy noise in ceasing or enhancing ‘wave of death’ activity and identify different parameter regions of noise at which the network makes transitions from one
synchronous state to another and the mechanism behind them. Because during such
143
termination (SIST) [18]. In SIST, a strong external impulse or a strong synaptic coupling in network of excitatory neurons caused hyper synchronization and subsequent
cessation of neuronal firings. It is responsible for spontaneous termination of epileptic seizures. Whereas in a ‘wave of death’ hyper synchronization is not playing a role
[19].
The analysis on ‘the spatiotemporal activities of a pulse-coupled biological neural
network’ which discusses near-death spikes when the neurons are chaotic can be
extended to explore the underlying reason for such behaviour, through dynamical
analysis.
Under optimal conditions, noise can induce synchronization, coherence resonance, stochastic resonance and vibrational resonance in nonlinear systems [20]. It is
demonstrated that Gaussian noise of particular intensity can induce spatial coherence
resonance in a two-dimensional network of FitzHugh-Nagumo neurons. Fractionalorder Gaussian noise can also enhance information carrying capacity of neurons.
In another study, it is found that long-range connections can destroy noise-induced
spatial coherence resonance (or cause decoherence). Influence of external electric
or magnetic fields or both on the neuronal environment can also be treated as noise.
Strong external electric field can influence the firing rate and synchronization of
neural networks. Many theoretical and experimental studies have proved that both
static and dynamic magnetic fields can suppress neuronal activities and cell growth
[21–24].
Unlike Gaussian white noise, Lévy noise or Lévy distribution is characterized by
small fluctuations, random large jumps and heavy tail. From predicting the path of a
bacteria in a swarm to game theory [25], Lévy process finds applications in almost all
fields of life, be it mathematics, finance, sociology, biology, physics, astronomy or
meteorology. In finance, it is used to study the stock market, options pricing, etc. In
physics, it finds applications in modelling turbulence, modelling chaos in Josephson
Junction and in quantum group theory.
Like channel noise and membrane noise, there are different types of noises present
in the neural system. Lévy noise is used to model the noisy environment of neuronal
network [26]. Neuron models involving Lévy noise can display all the dynamical
variations of membrane potential, be it diffusion, jumps in membrane voltage or
jump-diffusion.
In a recent study, it was revealed that Lévy noise can improve electrical activity
in a neuron under electromagnetic radiation. By adjusting appropriate parameters
of noise, firing modes of the neuron can be varied. Influence of Lévy noise on the
Izhikevich neuron, an all-to all coupled network and two excitatory coupled network
are studied recently [27], and it is shown that when the Lévy noise’s characteristic
exponent is 0.5, the individual neuronal level firing activity and the network dynamics
become irregular.
The study presented here gives the spatiotemporal activities of C. elegans neural
network under the influence of Lévy noise [28]. It is relevant to find the influence
of Lévy noise in ceasing or enhancing ‘wave of death’ activity and identify different parameter regions of noise at which the network makes transitions from one
synchronous state to another and the mechanism behind them. Because during such