Optimal time-varying coupling function can enhance synchronization in complex networks.

In this paper, we propose a time-varying coupling function that results in enhanced synchronization in complex networks of oscillators. The stability of synchronization can be analyzed by applying the master stability approach, which considers the largest Lyapunov exponent of the linearized variational equations as a function of the network eigenvalues as the master stability function. Here, it is assumed that the oscillators have diffusive single-variable coupling. All possible single-variable couplings are studied for each time interval, and the one with the smallest local Lyapunov exponent is selected. The obtained coupling function leads to a decrease in the critical coupling parameter, resulting in enhanced synchronization. Moreover, synchronization is achieved faster, and its robustness is increased. For illustration, the optimum coupling function is found for three networks of chaotic Rössler, Chen, and Chua systems, revealing enhanced synchronization.

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.

A simple one-dimensional map-based model of spiking neurons with wide ranges of firing rates and complexities.

This paper introduces a simple 1-dimensional map-based model of spiking neurons. During the past decades, dynamical models of neurons have been used to investigate the biology of human nervous systems. The models simulate experimental records of neurons' voltages using difference or differential equations. Difference neuronal models have some advantages besides the differential ones. They are usually simpler, and considering the cost of needed computations, they are more efficient. In this paper, a simple 1-dimensional map-based model of spiking neurons is introduced. Sample entropy is applied to analyze the complexity of the model's dynamics. The model can generate a wide range of time series with different firing rates and different levels of complexities. Besides, using some tools like bifurcation diagrams and cobwebs, the introduced model is analyzed.

Multimedia Cryptosystem for IoT Applications Based on a Novel Chaotic System around a Predefined Manifold.

Multimedia data play an important role in our daily lives. The evolution of internet technologies means that multimedia data can easily participate amongst various users for specific purposes, in which multimedia data confidentiality and integrity have serious security issues. Chaos models play an important role in designing robust multimedia data cryptosystems. In this paper, a novel chaotic oscillator is presented. The oscillator has a particular property in which the chaotic dynamics are around pre-located manifolds. Various dynamics of the oscillator are studied. After analyzing the complex dynamics of the oscillator, it is applied to designing a new image cryptosystem, in which the results of the presented cryptosystem are tested from various viewpoints such as randomness, time encryption, correlation, plain image sensitivity, key-space, key sensitivity, histogram, entropy, resistance to classical types of attacks, and data loss analyses. The goal of the paper is proposing an applicable encryption method based on a novel chaotic oscillator with an attractor around a pre-located manifold. All the investigations confirm the reliability of using the presented cryptosystem for various IoT applications from image capture to use it.

Chaos in memory function of sleep: A nonlinear dynamical analysis in thalamocortical study.

Studying the dynamical behaviors of neuronal models may help in better understanding of real nervous system. In addition, it can help researchers to understand some specific phenomena in neuronal system. The thalamocortical network is made of neurons in the thalamus and cortex. In it, the memory function is consolidated in sleep by creating up and down state oscillations (1 Hz) and fast (13-17 Hz) - slow (8-12 Hz) spindles. Recently, a nonlinear biological model for up-down oscillations and fast-slow spindles of the thalamocortical network has been proposed. In this research, the power spectral for the fast-slow spindle of the model is extracted. Dynamical properties of the model, such as the bifurcation diagrams, and attractors are investigated. The results show that the variation of the synaptic power between the excitatory neurons of the cortex and the reticular neurons in the thalamus changes the spindles' activity. According to previous experimental findings, it is an essential rule for consolidating the memory function during sleep. It is also pointed out that when the fast-slow spindles of the brain increase, the dynamics of the thalamocortical system tend to chaos.

Investigation of Early Warning Indexes in a Three-Dimensional Chaotic System with Zero Eigenvalues.

A rare three-dimensional chaotic system with all eigenvalues equal to zero is proposed, and its dynamical properties are investigated. The chaotic system has one equilibrium point at the origin. Numerical analysis shows that the equilibrium point is unstable. Bifurcation analysis of the system shows various dynamics in a period-doubling route to chaos. We highlight that from the evaluation of the entropy, bifurcation points can be predicted by identifying early warning signals. In this manner, bifurcation points of the system are analyzed using Shannon and Kolmogorov-Sinai entropy. The results are compared with Lyapunov exponents.

Prediction of bifurcations by varying critical parameters of COVID-19.

Coronavirus disease 2019 is a recent strong challenge for the world. In this paper, an epidemiology model is investigated as a model for the development of COVID-19. The propagation of COVID-19 through various sub-groups of society is studied. Some critical parameters, such as the background of mortality without considering the disease state and the speed of moving people from infected to resistance, affect the conditions of society. In this paper, early warning indicators are used to predict the bifurcation points in the system. In the interaction of various sub-groups of society, each sub-group can have various parameters. Six cases of the sub-groups interactions are studied. By coupling these sub-groups, various dynamics of the whole society are investigated.

Predicting tipping points of dynamical systems during a period-doubling route to chaos.

Classical indicators of tipping points have limitations when they are applied to an ecological and a biological model. For example, they cannot correctly predict tipping points during a period-doubling route to chaos. To counter this limitation, we here try to modify four well-known indicators of tipping points, namely the autocorrelation function, the variance, the kurtosis, and the skewness. In particular, our proposed modification has two steps. First, the dynamic of the considered system is estimated using its time-series. Second, the original time-series is divided into some sub-time-series. In other words, we separate the time-series into different period-components. Then, the four different tipping point indicators are applied to the extracted sub-time-series. We test our approach on an ecological model that describes the logistic growth of populations and on an attention-deficit-disorder model. Both models show different tipping points in a period-doubling route to chaos, and our approach yields excellent results in predicting these tipping points.