Analysis of Spatially Extended Excitable Izhikevich Neuron Model near Instability

The article focuses on the issue of a spatiotemporal excitable biophysical model that describes the propagation of electrical potential called spikes to model the diffusion induced dynamics based on an analytical development of amplitude equations. Considering the Izhikevich neuron model consisting of coupled systems of ODEs , we demonstrate various results of spatiotemporal architecture ( PDEs ) using a suitable parameter regime. We analytically perform the saddle node bifurcation and Hopf bifurcation analysis with bifurcating periodic solutions that show the transition phases in the system dynamics. We study different types of firing patterns both analytically and numerically by the formation of Riccati differential equation. To examine the characteristics of diffusive instabilities, we use Turing amplitude equations by multiscaling method and then expansion in powers of a small control parameter. The instabilities and Turing bifurcation are established using the theoretical analysis and numerical simulations. The spatial system has potential effects on the deterministic system as a result of the diffusive matrices with various couplings and the coupled oscillators with this nearest neighbor coupling show synchronization measured by the synchronization factor analysis. Our results qualitatively reproduce different phenomena of the extended excitable system based with an efficient analytical scheme.

Retraction: Five papers from Open Access Maced J Med Sci. Vol. 7 No. 18 (2019): Sep 30 (Global Dermatology)

Editor-in-Chief has retracted the following articles from the special issue Vol. 7 No. 18 (2019): Sep 30 (Global Dermatology): (1) DNA Waves and Their Applications in Biology - Massimo Fioranelli et al. - Open Access Macedonian Journal of Medical Sciences (2019) - DOI: 10.3889/oamjms.2019.767; (2) Recovery of Brain in Chick Embryos by Growing Second Heart and Brain - Massimo Fioranelli et al. - Open Access Macedonian Journal of Medical Sciences (2019) - DOI: 10.3889/oamjms.2019.777; (3) A Mathematical Model for the Signal of Death and Emergence of Mind Out of Brain in Izhikevich Neuron Model - Massimo Fioranelli et al. - Open Access Macedonian Journal of Medical Sciences (2019) - DOI: 10.3889/oamjms.2019.774; (4) A Black Hole at the Center of Earth Plays the Role of the Biggest System of Telecommunication for Connecting DNAs, Dark DNAs and Molecules of Water on 4+N- Dimensional Manifold - Massimo Fioranelli et al. - Open Access Macedonian Journal of Medical Sciences (2019) - DOI: 10.3889/oamjms.2019.776 (5) New System Delivering Microwaves Energy for Inducing Subcutaneous Fat Reduction: In - Vivo Histological and Ultrastructural Evidence - Nicola Zerbinati et al., Open Access Macedonian Journal of Medical Sciences (2019) - DOI: 10.3889/oamjms.2019.778 An internal investigation has raised sufficient evidence that they are not directly connected with the special issue Global Dermatology and contain inconsistent results. As such, we retract these articles from the literature and by guidelines and best editorial practices from the Committee on Publication Ethics. We apologize to our audience about this unfortunate situation.

A Mathematical Model for the Signal of Death and Emergence of Mind Out of Brain in Izhikevich Neuron Model

AIM: In this paper, using a mathematical model, we will show that for special exchanged photons, the Hamiltonian of a collection of neurons tends to a constant number and all activities is stopped. These photons could be called as the dead photons. To this aim, we use concepts of Bio-BIon in Izhikevich Neuron model. METHODS: In a neuron, there is a page of Dendrite, a page of axon's terminals and a tube of Schwann cells, axon and Myelin Sheath that connects them. These two pages and tube form a Bio-Bion. In a Bio-Bion, exchanging photons and some charged particles between terminals of dendrite and terminals of axon leads to the oscillation of neurons and transferring information. This Bion produces the Hamiltonian, wave equation and action potential of Izhikevich Neuron model. Also, this Bion determines the type of dependency of parameters of Izhikevich model on temperature and frequency and obtains the exact shape of membrane capacitance, resting membrane potential and instantaneous threshold potential. RESULTS: Under some conditions, waves of neurons in this BIon join to each other and potential shrinks to a delta function. Consequently, total Hamiltonian of the system tends to a constant number and system of neuron act like a dead system. Finally, this model indicates that all neurons have the ability to produce similar waves and signals like waves of the mind. CONCLUSION: Generalizing this to biology, we can claim that neurons out of the brain can produce signals of minding and imaging and thus mind isn’t confined to the brain.