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In this study, the dynamic behavior of fractional order co-infection model with human immunodeficiency virus type 1 (HIV-1) and human T-lymphotropic virus type I (HTLV-I) is analyzed using operational matrix of Hermite wavelet collocation method. Also, the uniqueness and existence of solutions are calculated based on the fixed point hypothesis. For the fractional order co-infection model, its positivity and boundedness are demonstrated. Furthermore, different types of Ulam-Hyres stability are also discussed. The numerical solution of the model are obtained by using the operational matrix of the Hermite wavelet approach. This scheme is used to solve the system of nonlinear equations that are very fruitful and easy to implement. Additionally, the stability analysis of the numerical scheme is explained. The mathematical model taken in this work incorporates the biological characteristics of both HIV-1 and HTLV-I. After that all the equilibrium points of the fractional order co-infection model are found and their existence conditions are explored with the help of the Caputo derivative. The global stability of all equilibrium points of this model are determined with the help of Lyapunov functions and the LaSalle invariance principle. Convergence analysis is also discussed. Hermite wavelet operational matrix methods are more accurate and convergent than other numerical methods. Lastly, variations in model dynamics are found when examining different fractional order values. These findings will be valuable to biologists in the treatment of HIV-1/HTLV-I.

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In public opinion triggered by rumors, the authenticity of the information remains uncertain, and the main topic oscillates between diverse opinions. In this paper, a nonlinear oscillator model is proposed to demonstrate the public opinion triggered by rumors. Based on the model and actual data of one case, it is found that a continuous flow of new information about rumors acts as external forces on the system, probably leading to the chaotic behavior of public opinion. Moreover, similar features are observed in three other cases, and the same model is also applicable to these cases. Based on these results, it is shown that our model possesses generality, revealing the evolutionary trends of a certain type of public opinion in real-world scenarios.

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In December 2019, China reported a new virus identified as SARS-CoV-2, causing COVID-19, which soon spread to other countries and led to a global pandemic. Although many countries imposed strict actions to control the spread of the virus, the COVID-19 pandemic resulted in unprecedented economic and social consequences in 2020 and early 2021. To understand the dynamics of the spread of the virus, we evaluated its chaotic behavior in Japan. A 0-1 test was applied to the time-series data of daily COVID-19 cases from January 26, 2020 to August 5, 2021 (3 days before the end of the Tokyo Olympic Games). Additionally, the influence of hosting the Olympic Games in Tokyo was assessed in data including the post-Olympic period until October 8, 2021. Even with these extended time period data, although the time-series data for the daily infections across Japan were not found to be chaotic, more than 76.6% and 55.3% of the prefectures in Japan showed chaotic behavior in the pre- and post-Olympic Games periods, respectively. Notably, Tokyo and Kanagawa, the two most populous cities in Japan, did not show chaotic behavior in their time-series data of daily COVID-19 confirmed cases. Overall, the prefectures with the largest population centers showed non-chaotic behavior, whereas the prefectures with smaller populations showed chaotic behavior. This phenomenon was observed in both of the analyzed time periods (pre- and post-Olympic Games); therefore, more attention should be paid to prefectures with smaller populations, in which controlling and preventing the current pandemic is more difficult.

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Nonlinear dynamics have become a new perspective on model human movement variability; however, it is still a debate whether chaotic behavior is indeed possible to present during a rhythmic movement. This paper reports on the nonlinear dynamical behavior of coupled and synchronization models of a planar rhythmic arm movement. Two coupling schemes between a planar arm and an extended Duffing-Van der Pol (DVP) oscillator are investigated. Chaos tools, namely phase space, Poincare section, Lyapunov Exponent (LE), and heuristic approach are applied to observe the dynamical behavior of orbit solutions. For the synchronization, an orientation angle is modeled as a single well DVP oscillator implementing a Proportional Derivative (PD)-scheme. The extended DVP oscillator is used as a drive system, while the orientation angle of the planar arm is a response system. The results show that the coupled system exhibits very rich dynamical behavior where a variety of solutions from periodic, quasi-periodic, to chaotic orbits exist. An advanced coupling scheme is necessary to yield the route to chaos. By modeling the orientation angle as the single well DVP oscillator, which can synchronize with other dynamical systems, the synchronization can be achieved through the PD-scheme approach.

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In December 2019, China announced the breakout of a new virus identified as coronavirus SARS-CoV-2 (COVID-19), which soon grew exponentially and resulted in a global pandemic. Despite strict actions to mitigate the spread of the virus in various countries, COVID-19 resulted in a significant loss of human life in 2020 and early 2021. To better understand the dynamics of the spread of COVID-19, evidence of its chaotic behavior in the US and globally was evaluated. A 0-1 test was used to analyze the time-series data of confirmed daily COVID-19 cases from 1/22/2020 to 12/13/2020. The results show that the behavior of the COVID-19 pandemic was chaotic in 55% of the investigated countries. Although the time-series data for the entire US was not chaotic, 39% of individual states displayed chaotic infection spread behavior based on the reported daily cases. Overall, there is evidence of chaotic behavior of the spread of COVID-19 infection worldwide, which adds to the difficulty in controlling and preventing the current pandemic.

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The effectiveness of control measures against the diffusion of the COVID-19 pandemic is grounded on the assumption that people are prepared and disposed to cooperate. From a strategic decision point of view, cooperation is the unreachable strategy of the prisoner's dilemma game, where the temptation to exploit the others and the fear to be betrayed by them drives the people behavior, which eventually results fully defective. In this work, we integrate the SIRS epidemic model with the replicator equation of evolutionary games in order to study the interplay between the infection spreading and the propensity of people to become cooperative under the pressure of the epidemic. We find that the developed model possesses several steady states, including fully or partially cooperative ones and that the presence of such states allows to take the disease under control. Moreover, assuming a seasonal variation of the infection rate, the system presents rich dynamics, including chaotic behavior and epidemic extinction.

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The present work introduces an analysis framework to comprehend the dynamics of a 3D plasma model, which has been proposed to describe the pellet injection in tokamaks. The analysis of the system reveals the existence of a complex transition from transient chaos to steady periodic behavior. Additionally, without adding any kind of forcing term or controllers, we demonstrate that the system can be changed to become a multi-stable model by injecting more power input. In this regard, we observe that increasing the power input can fluctuate the numerical solution of the system from coexisting symmetric chaotic attractors to the coexistence of infinitely many quasi-periodic attractors. Besides that, complexity analyses based on Sample entropy are conducted, and they show that boosting power input spreads the trajectory to occupy a larger range in the phase space, thus enhancing the time series to be more complex and random. Therefore, our analysis could be important to further understand the dynamics of such models, and it can demonstrate the possibility of applying this system for generating pseudorandom sequences.

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Despite numerous studies of epidemiological systems, the role of seasonality in the recurrent epidemics is not entirely understood. During certain periods of the year incidence rates of a number of endemic infectious diseases may fluctuate dramatically. This influences the dynamics of mathematical models describing the spread of infection and often leads to chaotic oscillations. In this paper, we are concerned with a generalization of a classical Susceptible-Infected-Recovered epidemic model which accounts for seasonal effects. Combining numerical and analytic techniques, we gain new insights into the complex dynamics of a recurrent disease influenced by the seasonality. Computation of the Lyapunov spectrum allows us to identify different chaotic regimes, determine the fractal dimension and estimate the predictability of the appearance of attractors in the system. Applying the homotopy analysis method, we obtain series solutions to the original nonautonomous SIR model with a high level of accuracy and use these approximations to analyze the dynamics of the system. The efficiency of the method is guaranteed by the optimal choice of an auxiliary control parameter which ensures the rapid convergence of the series to the exact solution of the forced SIR epidemic model.

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The balance between excitatory and inhibitory inputs is critical for the proper functioning of neural circuits. Landau and colleagues show that, in the presence of cell-type-specific connectivity, this balance is difficult to achieve without either synaptic plasticity or spike-frequency adaptation to fine-tune the connection strengths.

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