Dynamic analysis of the discrete fractional-order Rulkov neuron map.

Human evolution is carried out by two genetic systems based on DNA and another based on the transmission of information through the functions of the nervous system. In computational neuroscience, mathematical neural models are used to describe the biological function of the brain. Discrete-time neural models have received particular attention due to their simple analysis and low computational costs. From the concept of neuroscience, discrete fractional order neuron models incorporate the memory in a dynamic model. This paper introduces the fractional order discrete Rulkov neuron map. The presented model is analyzed dynamically and also in terms of synchronization ability. First, the Rulkov neuron map is examined in terms of phase plane, bifurcation diagram, and Lyapunov exponent. The biological behaviors of the Rulkov neuron map, such as silence, bursting, and chaotic firing, also exist in its discrete fractional-order version. The bifurcation diagrams of the proposed model are investigated under the effect of the neuron model's parameters and the fractional order. The stability regions of the system are theoretically and numerically obtained, and it is shown that increasing the order of the fractional order decreases the stable areas. Finally, the synchronization behavior of two fractional-order models is investigated. The results represent that the fractional-order systems cannot reach complete synchronization.

Applying machine learning techniques to detect the deployment of spatial working memory from the spiking activity of MT neurons.

Neural signatures of working memory have been frequently identified in the spiking activity of different brain areas. However, some studies reported no memory-related change in the spiking activity of the middle temporal (MT) area in the visual cortex. However, recently it was shown that the content of working memory is reflected as an increase in the dimensionality of the average spiking activity of the MT neurons. This study aimed to find the features that can reveal memory-related changes with the help of machine-learning algorithms. In this regard, different linear and nonlinear features were obtained from the neuronal spiking activity during the presence and absence of working memory. To select the optimum features, the Genetic algorithm, Particle Swarm Optimization, and Ant Colony Optimization methods were employed. The classification was performed using the Support Vector Machine (SVM) and the K-Nearest Neighbor (KNN) classifiers. Our results suggest that the deployment of spatial working memory can be perfectly detected from spiking patterns of MT neurons with an accuracy of 99.65±0.12 using the KNN and 99.50±0.26 using the SVM classifiers.

Higuchi fractal dimension is a unique indicator of working memory content represented in spiking activity of visual neurons in extrastriate cortex.

Working memory has been identified as a top-down modulation of the average spiking activity in different brain parts. However, such modification has not yet been reported in the middle temporal (MT) cortex. A recent study showed that the dimensionality of the spiking activity of MT neurons increases after deployment of spatial working memory. This study is devoted to analyzing the ability of nonlinear and classical features to capture the content of the working memory from the spiking activity of MT neurons. The results suggest that only the Higuchi fractal dimension can be considered as a unique indicator of working memory while the Margaos-Sun fractal dimension, Shannon entropy, corrected conditional entropy, and skewness are perhaps indicators of other cognitive factors such as vigilance, awareness, and arousal as well as working memory.

Investigation of vaccination game approach in spreading covid-19 epidemic model with considering the birth and death rates.

In this study, an epidemic model for spreading COVID-19 is presented. This model considers the birth and death rates in the dynamics of spreading COVID-19. The birth and death rates are assumed to be the same, so the population remains constant. The dynamics of the model are explained in two phases. The first is the epidemic phase, which spreads during a season based on the proposed SIR/V model and reaches a stable state at the end of the season. The other one is the "vaccination campaign", which takes place between two seasons based on the rules of the vaccination game. In this stage, each individual in the population decides whether to be vaccinated or not. Investigating the dynamics of the studied model during a single epidemic season without consideration of the vaccination game shows waves in the model as experimental knowledge. In addition, the impact of the parameters is studied via the rules of the vaccination game using three update strategies. The result shows that the pandemic speeding can be changed by varying parameters such as efficiency and cost of vaccination, defense against contagious, and birth and death rates. The final epidemic size decreases when the vaccination coverage increases and the average social payoff is modified.