Multiple modes of electrical activities in a new neuron model under electromagnetic radiation

Dynamical responses to external stimuli for both cases of excitatory and inhibitory synchronization in a complex neuronal network

For studying how dynamical responses to external stimuli depend on the synaptic-coupling type, we consider two types of excitatory and inhibitory synchronization (i.e., synchronization via synaptic excitation and inhibition) in complex small-world networks of excitatory regular spiking (RS) pyramidal neurons and inhibitory fast spiking (FS) interneurons. For both cases of excitatory and inhibitory synchronization, effects of synaptic couplings on dynamical responses to external time-periodic stimuli S(t) (applied to a fraction of neurons) are investigated by varying the driving amplitude A of S(t). Stimulated neurons are phase-locked to external stimuli for both cases of excitatory and inhibitory couplings. On the other hand, the stimulation effect on non-stimulated neurons depends on the type of synaptic coupling. The external stimulus S(t) makes a constructive effect on excitatory non-stimulated RS neurons (i.e., it causes external phase lockings in the non-stimulated sub-population), while S(t) makes a destructive effect on inhibitory non-stimulated FS interneurons (i.e., it breaks up original inhibitory synchronization in the non-stimulated sub-population). As results of these different effects of S(t), the type and degree of dynamical response (e.g., synchronization enhancement or suppression), characterized by the dynamical response factor [Formula: see text] (given by the ratio of synchronization degree in the presence and absence of stimulus), are found to vary in a distinctly different way, depending on the synaptic-coupling type. Furthermore, we also measure the matching degree between the dynamics of the two sub-populations of stimulated and non-stimulated neurons in terms of a "cross-correlation" measure [Formula: see text]. With increasing A, based on [Formula: see text], we discuss the cross-correlations between the two sub-populations, affecting the dynamical responses to S(t).

Modeling of inter-neuronal coupling medium and its impact on neuronal synchronization

In this paper, modeling of the coupling medium between two neurons, the effects of the model parameters on the synchronization of those neurons, and compensation of coupling strength deficiency in synchronization are studied. Our study exploits the inter-neuronal coupling medium and investigates its intrinsic properties in order to get insight into neuronal-information transmittance and, there from, brain-information processing. A novel electrical model of the coupling medium that represents a well-known RLC circuit attributable to the coupling medium’s intrinsic resistive, inductive, and capacitive properties is derived. Surprisingly, the integration of such properties reveals the existence of a natural three-term control strategy, referred to in the literature as the proportional integral derivative (PID) controller, which can be responsible for synchronization between two neurons. Consequently, brain-information processing can rely on a large number of PID controllers based on the coupling medium properties responsible for the coherent behavior of neurons in a neural network. Herein, the effects of the coupling model (or natural PID controller) parameters are studied and, further, a supervisory mechanism is proposed that follows a learning and adaptation policy based on the particle swarm optimization algorithm for compensation of the coupling strength deficiency.

Calculation of Hamilton energy and control of dynamical systems with different types of attractors

Strange attractors can be observed in chaotic and hyperchaotic systems. Most of the dynamical systems hold a finite number of attractors, while some chaotic systems can be controlled to present an infinite number of attractors by generating infinite equilibria. Chaos can also be triggered in some dynamical systems that can present hidden attractors, and the attractors in these dynamical systems find no equilibria and the basin of attraction is not connected with any equilibrium (the equilibria position meets certain restriction function). In this paper, Hamilton energy is calculated on the chaotic systems with different types of attractors, and energy modulation is used to control the chaos in these systems. The potential mechanism could be that negative feedback in energy can suppress the phase space and oscillating behaviors, and thus, the chaotic, periodical oscillators can be controlled. It could be effective to control other chaotic, hyperchaotic and even periodical oscillating systems as well.

Lévy noise improves the electrical activity in a neuron under electromagnetic radiation

As the fluctuations of the internal bioelectricity of nervous system is various and complex, the external electromagnetic radiation induced by magnet flux on membrane can be described by the non-Gaussian type distribution of Lévy noise. Thus, the electrical activities in an improved Hindmarsh-Rose model excited by the external electromagnetic radiation of Lévy noise are investigated and some interesting modes of the electrical activities are exhibited. The external electromagnetic radiation of Lévy noise leads to the mode transition of the electrical activities and spatial phase, such as from the rest state to the firing state, from the spiking state to the spiking state with more spikes, and from the spiking state to the bursting state. Then the time points of the firing state versus Lévy noise intensity are depicted. The increasing of Lévy noise intensity heightens the neuron firing. Also the stationary probability distribution functions of the membrane potential of the neuron induced by the external electromagnetic radiation of Lévy noise with different intensity, stability index and skewness papremeters are analyzed. Moreover, through the positive largest Lyapunov exponent, the parameter regions of chaotic electrical mode of the neuron induced by the external electromagnetic radiation of Lévy noise distribution are detected.

Autaptic regulation of electrical activities in neuron under electromagnetic induction

Realistic neurons may hold complex anatomical structure, for example, autapse connection to some internuncial neurons, which this specific synapse can connect to its body via a close loop. Continuous exchanges of charged ions across the membrane can induce complex distribution fluctuation of intracellular and extracellular charged ions of cell, and a time-varying electromagnetic field is set to modulate the membrane potential of neuron. In this paper, an autapse-modulated neuron model is presented and the effect of electromagnetic induction is considered by using magnetic flux. Bifurcation analysis and sampled time series for membrane potentials are calculated to investigate the mode transition in electrical activities and the biological function of autapse connection is discussed. Furthermore, the Gaussian white noise and electromagnetic radiation are considered on the improved neuron model, it is found appropriate setting and selection for feedback gain and time delay in autapse can suppress the bursting in neuronal behaviors. It indicates the formation of autapse can enhance the self-adaption of neuron so that appropriate response to external forcing can be selected, this biological function is helpful for encoding and signal propagation of neurons. It can be useful for investigation about collective behaviors in neuronal networks exposed to electromagnetic radiation.

A basic bifurcation structure from bursting to spiking of injured nerve fibers in a two-dimensional parameter space

Two different bifurcation scenarios of firing patterns with decreasing extracellular calcium concentrations were observed in identical sciatic nerve fibers of a chronic constriction injury (CCI) model when the extracellular 4-aminopyridine concentrations were fixed at two different levels. Both processes proceeded from period-1 bursting to period-1 spiking via complex or simple processes. Multiple typical experimental examples manifested dynamics closely matching those simulated in a recently proposed 4-dimensional model to describe the nonlinear dynamics of the CCI model, which included most cases of the bifurcation scenarios. As the extracellular 4-aminopyridine concentrations is increased, the structure of the bifurcation scenario becomes more complex. The results provide a basic framework for identifying the relationships between different neural firing patterns and different bifurcation scenarios and for revealing the complex nonlinear dynamics of neural firing patterns. The potential roles of the basic bifurcation structures in identifying the information process mechanism are discussed.

Model of electrical activity in cardiac tissue under electromagnetic induction

Complex electrical activities in cardiac tissue can set up time-varying electromagnetic field. Magnetic flux is introduced into the Fitzhugh-Nagumo model to describe the effect of electromagnetic induction, and then memristor is used to realize the feedback of magnetic flux on the membrane potential in cardiac tissue. It is found that a spiral wave can be triggered and developed by setting specific initials in the media, that is to say, the media still support the survival of standing spiral waves under electromagnetic induction. Furthermore, electromagnetic radiation is considered on this model as external stimuli, it is found that spiral waves encounter breakup and turbulent electrical activities are observed, and it can give guidance to understand the occurrence of sudden heart disorder subjected to heavily electromagnetic radiation.

Dynamic transition of neuronal firing induced by abnormal astrocytic glutamate oscillation

The gliotransmitter glutamate released from astrocytes can modulate neuronal firing by activating neuronal N-methyl-D-aspartic acid (NMDA) receptors. This enables astrocytic glutamate(AG) to be involved in neuronal physiological and pathological functions. Based on empirical results and classical neuron-glial "tripartite synapse" model, we propose a practical model to describe extracellular AG oscillation, in which the fluctuation of AG depends on the threshold of calcium concentration, and the effect of AG degradation is considered as well. We predict the seizure-like discharges under the dysfunction of AG degradation duration. Consistent with our prediction, the suppression of AG uptake by astrocytic transporters, which operates by modulating the AG degradation process, can account for the emergence of epilepsy.