Dynamics Analysis of Firing Patterns in Pre-Bötzinger Complex Neurons Model

Pre-Bötzinger complex (PBC) neurons located in mammalian brain are the necessary conditions to produce respiratory rhythm, which has been widely verified experimentally and numerically. At present, one of the two different types of bursting mechanisms found in PBC mainly depends on the calcium-activated of non-specific cation current (ICaN). In order to study the influence of ICaN and stimulus current Iexc in PBC inspiratory neurons, a single compartment model was simplified, and firing patterns of the model was discussed by using stability theory, bifurcation analysis, fast, and slow decomposition technology combined with numerical simulation. Under the stimulation of different somatic applied currents, the firing behavior of neurons are studied and exhibit multiple mix bursting patterns, which is helpful to further understand the mechanism of respiratory rhythms of PBC neurons.

Influence of Electric Current and Magnetic Flow on Firing Patterns of Pre-Bötzinger Complex Model

The dynamics of neuronal firing activity is vital for understanding the pathological respiratory rhythm. Studies on electrophysiology show that the magnetic flow is an essential factor that modulates the firing activities of neurons. By adding the magnetic flow to Butera’s neuron model, we investigate how the electric current and magnetic flow influence neuronal activities under certain parametric restrictions. Using fast-slow decomposition and bifurcation analysis, we show that the variation of external electric current and magnetic flow leads to the change of the bistable structure of the system and hence results in the switch of neuronal firing pattern from one type to another.

Θ-SEIHRD mathematical model of Covid19-stability analysis using fast-slow decomposition

In general, a mathematical model that contains many linear/nonlinear differential equations, describing a phenomenon, does not have an explicit hierarchy of system variables. That is, the identification of the fast variables and the slow variables of the system is not explicitly clear. The decomposition of a system into fast and slow subsystems is usually based on intuitive ideas and knowledge of the mathematical model being investigated. In this study, we apply the singular perturbed vector field (SPVF) method to the COVID-19 mathematical model of to expose the hierarchy of the model. This decomposition enables us to rewrite the model in new coordinates in the form of fast and slow subsystems and, hence, to investigate only the fast subsystem with different asymptotic methods. In addition, this decomposition enables us to investigate the stability analysis of the model, which is important in case of COVID-19. We found the stable equilibrium points of the mathematical model and compared the results of the model with those reported by the Chinese authorities and found a fit of approximately 96 percent.

Cost-Effective Remediation Using Microscale Zvi: Comparison of Commercially Available Products

Zero-valent iron is very effective in the treatment of groundwater contaminated with chlorinated hydrocarbons and solvents broadly used in industrial production. In terms of its sustainability and cost, a legitimate effort has been devoted to the optimization of the remediation process, which can be demanding and expensive. In this study, the application potential and fundamental properties of several commercial micro-sized zero-valent iron (μZVI) were investigated. Although the manufacturers report the basic parameters of μZVI, it has been shown that the actual reactivity of apparently similar products varies notably. This work was focused on monitoring of frequently occurring contaminants. The actual contaminated water from the Pisecna locality -former landfill of industrial waste, with high levels of chlorinated ethenes and ethanes (PCE, TCE, cis-1,2-DCE and 1,2-DCA) was used for the experiment. The degree of dechlorination reached over 85 % 32 days after the application of μZVI in several samples and a far higher reaction rate for smaller particles was observed. Also, the amount of cis-1,2-DCE, which is characterized by slow decomposition, decreased by more than 95 % over the course of the experiment. Smaller particles showed a much longer sedimentation rate and gradual fractionation was also observed. Monitoring of ORP and pH also suggested that the smaller particles possessed a reduction capacity that was sufficiently high even at the end of the experiment. Laboratory tests with apparently similar μZVI samples indicated considerable differences in their reaction rate and efficiency.