136
R. P. Ignatius
1 Introduction
Neurons communicate between each other through chemical and electrical synapses.
Individual neurons show different firing patterns such as spiking, bursting, chaotic
firing patterns and a mix of them [1]. When more than two neurons are coupled
together, which is the case of real biological neuronal networks, their behaviour
becomes still more interesting and complex due to the involvement of a large number
of parameters pertaining to individual neurons, network and external factors. Such
networks display complex phenomena like amplitude death, oscillation death, neardeath-like spikes [2, 3], synchronization, coherence resonance, stochastic resonance,
chimeras, spatiotemporal pattern formation and pattern selection [4].
In an undirected, homogenous Caenorhabditis elegans (C. elegans) neuronal network, due to the interplay of chemical and electrical synapses, chimera-like synchronization [5] pattern was observed. In a heterogeneous network of integrate-and-fire
neurons, the macroscopic dynamics was found to be irregular, whereas the microscopic dynamics is linearly stable. Spatiotemporal activities of neuronal network are
an important feature of brain dynamics like cognitive process, visual object detection, memory formation [6] and of seizures [7]. Parameters like coupling strength,
network topology, network size, delays, type of neurons and external factors like
electric fields and noise affect the spatiotemporal activities of neural networks [8, 9].
It was shown that single-neuron spiking in sensorimotor cortex of humans and
monkeys can be predicted using the spiking history of small random ensembles.
Interplay between time constants of active ionic currents and interspike interval
causes differences in synchrony of excitatory networks, and hence, the difference in
corresponding spatiotemporal pattern is formed.
Recently, it has been shown that a random perturbation at the boundary neurons
induces spiral waves in a regular excitatory neuronal network. In another study, it
was revealed that Lévy noise can induce the mode transition in firing activities of
neurons under electromagnetic radiation.
Astrocytes are star-shaped glial cells of nervous tissues. Astroglia is the main
power source of neurons. Astrocytes on receiving the neurotransmitters change the
intracellular calcium concentration and hence modulate the electrical activities of
neurons connected to it. Thus, they facilitate the communication between neurons.
Firing patterns of neurons and spatiotemporal dynamics of neuronal network can
be understood clearly from the dynamics of connected astrocytes. For example, the
network of neuron–astrocyte displayed different modes of electrical activities under
autaptic(self-feedback) driving, when calcium and inositol triphosphate concentrations of astrocytes are under control [10]. Seizure-like firings in neuronal network is
attributed to dysfunction of neurons. It has been shown that astrocytes and neurons
support each other in the propagation of seizure-like firings in neuronal network [11].
R. P. Ignatius
1 Introduction
Neurons communicate between each other through chemical and electrical synapses.
Individual neurons show different firing patterns such as spiking, bursting, chaotic
firing patterns and a mix of them [1]. When more than two neurons are coupled
together, which is the case of real biological neuronal networks, their behaviour
becomes still more interesting and complex due to the involvement of a large number
of parameters pertaining to individual neurons, network and external factors. Such
networks display complex phenomena like amplitude death, oscillation death, neardeath-like spikes [2, 3], synchronization, coherence resonance, stochastic resonance,
chimeras, spatiotemporal pattern formation and pattern selection [4].
In an undirected, homogenous Caenorhabditis elegans (C. elegans) neuronal network, due to the interplay of chemical and electrical synapses, chimera-like synchronization [5] pattern was observed. In a heterogeneous network of integrate-and-fire
neurons, the macroscopic dynamics was found to be irregular, whereas the microscopic dynamics is linearly stable. Spatiotemporal activities of neuronal network are
an important feature of brain dynamics like cognitive process, visual object detection, memory formation [6] and of seizures [7]. Parameters like coupling strength,
network topology, network size, delays, type of neurons and external factors like
electric fields and noise affect the spatiotemporal activities of neural networks [8, 9].
It was shown that single-neuron spiking in sensorimotor cortex of humans and
monkeys can be predicted using the spiking history of small random ensembles.
Interplay between time constants of active ionic currents and interspike interval
causes differences in synchrony of excitatory networks, and hence, the difference in
corresponding spatiotemporal pattern is formed.
Recently, it has been shown that a random perturbation at the boundary neurons
induces spiral waves in a regular excitatory neuronal network. In another study, it
was revealed that Lévy noise can induce the mode transition in firing activities of
neurons under electromagnetic radiation.
Astrocytes are star-shaped glial cells of nervous tissues. Astroglia is the main
power source of neurons. Astrocytes on receiving the neurotransmitters change the
intracellular calcium concentration and hence modulate the electrical activities of
neurons connected to it. Thus, they facilitate the communication between neurons.
Firing patterns of neurons and spatiotemporal dynamics of neuronal network can
be understood clearly from the dynamics of connected astrocytes. For example, the
network of neuron–astrocyte displayed different modes of electrical activities under
autaptic(self-feedback) driving, when calcium and inositol triphosphate concentrations of astrocytes are under control [10]. Seizure-like firings in neuronal network is
attributed to dysfunction of neurons. It has been shown that astrocytes and neurons
support each other in the propagation of seizure-like firings in neuronal network [11].