Chaos, Solitons and Fractals: X最新文献

Asymptomatic carriers serve as a potential source of transmission of epidemic diseases. Exposed people who develop symptoms only get tested and remain isolated in their homes or sometimes in hospitals when needed. In contrast, the asymptomatic individuals go untested and spread the disease silently as they roam freely throughout their entire infectious lifetime. The work intends to explore the role of asymptomatic carriers in the transmission of epidemic diseases and investigate suitable optimal control strategies. We propose a SEIAQR compartmental model subdividing the total population into six different compartments. To illustrate the model’s implication, we estimate the number of asymptomatic individuals using COVID-19 data during June 9–July 18, 2021 from Bangladesh. We then analyze the model to explore whether the epidemic subsides if the asymptomatic individuals are tested randomly and isolated. Finally, to gain a better understanding of the potential of this unidentified transmission route, we propose an optimal control model considering two different control strategies: personal protective measures and isolation of asymptomatic carriers through random testing. Our results show that simultaneous implementation of both control strategies can reduce the epidemic early. Most importantly, sustained effort in identifying and isolation of asymptotic individuals allows relaxation in personal protective measures.

In this investigation, the dynamical model of social media addiction is considered in the spirit of the Caputo differential operator. The main utilization is to elucidate the importance of nonclassical derivatives order in the implementation of social media addiction complex phenomena. Herein, we first developed the model using the Caputo scheme and discussed some fundamental mathematical computations. Secondly, we adapt the Hilbert reproducing scheme to generate numerical appropriate solutions via Mathematica 12 software. The utilized fractional social media problem was formulated and configured to solve it by fitting two subspaces from the space of Hilbert. The convergence-error behavior results are established using functional analysis techniques. After utilizing several computational algorithms, the considered model results are tabularly and graphically demonstrated with different choices of arbitrary order parameter values. The outcomes show that when applying the fractional Caputo differential operator, such complicated events become more realistic and convincing. The summary of the presented work and various scientific recommendations in addition to the future work that complements this analysis has been utilized in the last part.

In 1982 in a series of works Vielliefosse [1, 2] discussed a nonlinear homogeneous evolution equation for the velocity gradient tensor in fluid dynamics. Later Cantwell [3] extended this formalism to the non-homogeneous case including the effects of viscous diffusion and cross derivatives of pressure field. Here, we derive the evolution equations of the geometrical invariants of the magnetic and velocity field gradient tensors in the case of magneto-hydrodynamics for both non-homogeneous and homogeneous cases, i.e., considering or neglecting viscous effects and source terms. The inclusion of dissipation effects and higher-order gradient terms introduces a non trivial evolution of invariants, which can be treated as a stochastic evolution equation. Conversely, in the homogeneous case, the magnetic field invariants do not evolve, i.e., the magnetic field line topology is conserved, while the corresponding velocity invariants are affected by magnetic forces. By writing the equations of the velocity field invariants as a dynamical system we can identify the role of the different terms in the evolution equations. In detail, in the homogenous case we show that the term associated with the current density drives transitions between hyperbolic and elliptical structures. Evolution equations are also discussed in the perspective of an application to the analysis of magneto-hydrodynamic turbulence.

In this research, we study the fetal heart rate from abdominal signals using multi-fractal spectra and fractal analysis. We use the Abdominal and Direct Fetal Electrocardiogram Database contains multichannel fetal electrocardiogram (FECG) recordings obtained from 5 different women in labor, between 38 and 41 weeks of gestation. We apply autocorrelation or power spectral densities (PSD) analysis on these five FECG recordings to estimate the exponent from realizations of these processes and to find out if the signal of interest exhibits a power-law PSD. We perform multi-fractal analysis to discover whether some type of power-law scaling exists for various statistical moments at different scales of these FECG signals. We plot the multi-fractal spectra of this database to compare the width of the scaling exponent for each spectrum. A quantitative analysis commonly known as the Fractal Dimension (FD) using the Higuchi algorithm has been carried out to illustrate the fractal complexity of input signals. Our finding shows that the fractal geometry can be used as a mathematical model and computational framework to further analysis and classification of clinical database. Moreover, it can be considered as a framework to compare the complexity of FECG signals and a useful tool to differentiate between their patterns.

In this study, we explore the possibility that ECG recordings belong to class of multifractal process for which a large number of scaling exponents are required to characterize their scaling structures. We use the BIDMC Congestive Heart Failure database including long term ECG recordings from 11 men, aged 22 to 71, and 4 women, aged 54 to 63 with severe congestive heart failure and the MIT-BIH Arrhythmia database that contains 48 half-hour excerpts of two-channel ambulatory ECG recordings, obtained from 47 subjects studied by the BIH Arrhythmia Laboratory between 1975 and 1979. We compare these two chronic heart diseases with the control people in the MIT-BIH Normal Sinus Rhythm database which includes 18 long-term ECG recordings of 5 men, aged 26 to 45, and 13 women, aged 20 to 50 without significant arrhythmia. The vibration analysis such as power spectral densities (PSD) analysis has been performed for differentiating the time series. Multifractal dynamics of heartbeat interval signals have been assessed by multifractal spectrum analysis to differentiate normal signals with arrhythmia and severe congestive heart failure patients. We apply Higuchi algorithm to find the fractal complexity of each cardiac rhythm and then compare the signals for different time intervals. According to our analysis, we investigate that neither the power spectral densities nor the Higuchi algorithm to find the fractal dimension alone were sufficient to separate different classes of patients and healthy people. However, when multifractal analysis and scaling exponent were used as a classifier, the three classes were well separated. In addition, multifractal analysis revealed that we have a narrow range of exponents for arrhythmia and congestive heart failure subjects and as a result, a clear loss of multifractality for them. It was of great significance to show that we have a narrower range of exponents for arrhythmia subject compared to congestive heart failure subject which is useful to recognize these two classes of patients with heart disease. Our findings provide a comprehensive framework for diagnostic and classifying different patients with cardiac disease such as arrhythmia and congestive heart failure and differentiate them with normal people without heart disease which is crucial in finding the best diagnostic and controlling strategy in fight against chronic heart disease.

The present study examines the nonlinear relationship between the bitcoin prices and total bitcoin energy consumption over the period November 2010 and October 2021. A discrete threshold regression (TR) model is deployed to estimate the unknown thresholds that trigger the Bitcoin prices regime change. The designated TR model identifies six regimes of change for Bitcoin price movements. The estimated critical threshold specifications (total bitcoin energy consumption) that trigger the regime change of Bitcoin prices are estimated as 0.13, 2.52, 14.06, 43.17, and 146.29 respectively. The study finds that the impact of total bitcoin energy consumption on bitcoin prices are only statistically significant in the higher (4^th and 6^th) regimes respectively. The message here is that the impact of total bitcoin energy consumption on bitcoin prices is not uniform.

This paper presents a model of a finite population of agents constrained to strategies that alternate between activity and inactivity (a.k.a. temporal partitioning) in a social environment where multiple one-shot prisoner's dilemma games occur across discrete, intra-generational time points. Evolutionary selection acts on agents’ behavioral dispositions to cooperate/defect and the schedules that determine when agents periodically implement that behavior. Numerical simulation of the model indicates that cooperators reach fixation with far greater frequency when using schedules with prime-number period lengths. These findings reinforce recent analytic findings that indicate a connection between the evolution of cooperation and the prime numbers, plus they offer new empirical predictions about the timing of social behavior.

In this article, we study time-fractional non-linear Kawahara and modified Kawahara equations with Caputos fractional derivative. A variety of integral transforms with Adomian decomposition are applied to obtain the general series solutions of the considered models. The efficiency of the proposed methods is confirmed by numerical examples under suitable initial conditions. From the numerical results, one can see that the attained series solutions converge to the exact solutions of the systems. The stability of the applied methods is investigated using the principle of Banach contraction and $S$-stable mapping. For the Kawahara Equation, it is observed that the amplitude of the system enhances as time increases for fixed values of fractional orders. Similarly, for stable temporal variables, when the fractional-order increases, the amplitude of the solitary wave solution also increases. Similarly, for the modified system, the wave amplitude is also enhanced with variations in time $\left(t\right)$. It infers that when $\left(\alpha \right)$ increases, it significantly decreases the wave amplitude. It is also observed that uniform changes take place in the wave amplitude with time $\left(t\right)$. However, non-uniform changes in wave amplitude occur for different values of $\alpha$. The absolute error between the exact and obtained series solutions is presented. It is revealed that the absolute error in the systems reduces promptly when $x$ increases at a comparatively small time $t$, whereas the increment in iterations decreases the error in the systems.

The development of methods to identify prime numbers spans centuries and includes models of physical and biological systems that spot primes. This paper adds to the latter research genre by reporting a prisoner's dilemma model that identifies prime numbers greater than 2. Albeit containing unconventional features and arguable assumptions, the model nonetheless confirms a previously hypothesized connection between prime numbers and the cross-disciplinary puzzle of how cooperation evolved. In a companion paper (part II), the features and assumptions of the analytic model reported here are explored in a finite-population, computational model.

Odor disturbance and group defense generally play an important role in ecosystem stability. By incorporating odor disturbances and group defenses into the traditional three-species food chain system, where the preys are disturbed by the odor of predators, and group together to defend. We proved the boundedness of solutions of the system, and discussed the existence of equilibrium points. By Lyapunov’s first method and Routh-Hurwitz criterion, the sufficient conditions for stability of equilibrium points are obtained. It is found that, with the increasing of group defense, the density of the preys increases, while the odor disturbance of predators decreases the density of preys. Interestingly, the group defense induces a transition from a boundary equilibrium point to a positive equilibrium one, or from no Hopf-bifurcation to a Hopf-bifurcation. Furthermore, we demonstrated that the system undergoes a saddle-node bifurcation at $m_c=0.3362$, below which the system has a stable node and a saddle point, suggesting that the less odor disturbance avail system stability; while above which the system has no equilibrium point, indicating that the greater odor disturbance causes the collapse of the system. To reveal the underlying mechanisms of the interplay of odor disturbance and group defense, the bifurcation diagrams of the preys with two factors are given respectively.