Chaos, Solitons and Fractals: X最新文献

Reaction-diffusion systems with cross-diffusion terms in addition to, or instead of, the usual self-diffusion demonstrate interesting features which motivate their further study. The present work is aimed at designing a toy reaction-cross-diffusion model with exact solutions in the form of propagating fronts. We propose a minimal model of this kind which involves two species linked by cross-diffusion, one of which governed by a linear equation and the other having a polynomial kinetic term. We classify the resulting exact propagating front solutions. Some of them have some features of the Fisher-KPP fronts and some features of the ZFK-Nagumo fronts.

A topic in the Sina-Microblog consists of multiple Weibos sharing a specific set of key words. Therefore, a reader of a Weibo may be susceptible to other Weibos of the same topic, and hence may undergo multiple transitions between the susceptible and the exposed states before eventually becoming infectious. This complicates the reading dynamics that traditional epidemic susceptible-exposed-infectious compartmental models cannot capture, and requires a different setting than a single Weibo forwarding dynamics model. Here we formulate a topic reading dynamics model; introduce some summative indices characterizing the reading “outbreak” potential; derive analytic formulae to calculate these indices; and examine the sensitivity of these indices and the ability of prediction on model parameters and on sampling frequencies. We conduct some numerical experiments based on historical data of popular reading topics in the Chinese Sina-Microblog. In our experiments, different sampling frequencies (4 h, 8 h or 12 h) nearcasting the turning points are feasible, in particular, a good nearcasting prediction for the accumulated R-users are 72 h with the sampling frequencies of every 4 h and every 12 h and 78 h with the sampling frequency of every 8 h.

The complex organization of gait variability, or fractal dynamics, theoretically represents the adaptive capacity of the locomotor system. Prior studies suggest that fractal dynamics are sensitive to various individual constraints (e.g., age, neurological disease) and task constraints (e.g., walking speed or novel gait tasks). The purpose of this study was to determine if physical activity levels represent an additional individual constraint during walking. Fifteen young and 15 older adults walked on a treadmill at their preferred walking speed and at half of their preferred speed. Detrended fluctuation analysis was used to estimate the statistical persistence of stride time variability. Volume of physical activity was determined using a wearable monitor for 3-7 days. Habitual physical activity levels did not appear to have an effect on the fractal nature of stride-to-stride fluctuations in young adults. However, the least active older adults displayed higher scaling exponents compared to the more active older adults during slow walking. That is, less active older adults responded to the slow walking task by increasing fractal scaling, suggesting this task is more challenging and complex. These findings suggest that lower levels of habitual physical activity may represent an additional individual constraint in older but not young adults. When age and physical activity constraints are combined with a challenging slow walking task, the locomotor system of older adults may be more highly taxed, ultimately manifesting as stronger statistical persistence.

We show that, among all smooth one-dimensional maps conjugated to an N-ary shift (a Bernoulli shift of N symbols), Chebyshev maps are distinguished in the sense that they have least higher-order correlations. We generalise our consideration and study a family of shifted Chebyshev maps, presenting analytic results for two-point and higher-order correlation functions. We also review results for the eigenvalues and eigenfunctions of the Perron-Frobenius operator of Nth order Chebyshev maps and their shifted generalisations. The spectrum is degenerate for odd N. Finally, we consider coupled map lattices (CMLs) of shifted Chebyshev maps and numerically investigate zeros of the temporal and spatial nearest-neighbour correlations, which are of interest in chaotically quantized field theories.

This comment shows that data regarding cumulative confirmed cases from the coronavirus COVID-19 disease outbreak, in the period December 31, 2019–June 29, 2020 of some countries reported by the European Centre for Disease Prevention and Control, can be adjusted by the exact solution of the Kermack – McKendrick approximation of the SIR epidemiological model.

In this paper, we study Hyers-Ulam stability and generalized Hyers-Ulam stability of linear equations with weighted Caputo-Fabrizio fractional derivative. We establish existence and uniqueness of solutions for nonlinear equations using Schaefer’s fixed point theorem. In addition, we present a generalized Hyers-Ulam stability result via the Gronwall inequality. Finally, two examples are given to illustrate our main results.

Some ideas are presented about a geometric motivation of the apparent capacity of generalized logistic equations to describe the outbreak of quite many epidemics, possibly including that of the COVID-19 infection. This interpretation pivots on the complex, possibly fractal, structure of the locus describing the “contagion event set”, and on what can be learnt from the models of trophic webs with “herd behaviour”.

Under the hypothesis that the total number of cases, as a function of time, is fitted by a solution of the Generalized Richards Model, it is argued that the exponents appearing in that differential equation, usually determined empirically, represent the geometric signature of the non-space filling, network-like locus on which contagious contacts take place.

Chaotic entanglement is a new method used to deliver chaotic physical process, as suggested in this work. Primary rationale is to entangle more than two mathematical product stationery linear schemes by means of entanglement functions to make a chaotic system that develops in a chaotic manner.Existence of Hopf bifurcation is looked into by selecting the set aside bifurcation parameter. More accurately, we consider the stableness and bifurcations of sense of equilibrium in the modern chaotic system. In addition, there is involvement of chaos in mathematical systems that have one positive Lyapunov exponent. Furthermore, there are four requirements that are needed to achieve chaos entanglement. In that way through dissimilar linear schemes and dissimilar entanglement functions, a collection of fresh chaotic attractors has been created and abundant coordination compound dynamics are exhibited. The breakthrough suggests that it is not difficult any longer to construct new obviously planned chaotic systems/networks for applied science practical application such as chaos-based secure communication.

Chaotic system has been widely used in the design of pseudorandom sequence generators. However, the performance of pseudorandom sequence generators is greatly affected by the chaotic degradation, which is caused by computational accuracy. In this paper, we propose a self-perturbed pseudorandom sequence generator based on hyper-chaotic system to overcome this problem. A novel hyper-chaotic system is constructed to achieve a complex dynamic behavior. One of the feedback controllers is used to disturb the other dimensions so that the short period can be avoided. Based on the proposed hyper-chaotic system, a pseudorandom number generator is designed. The dynamic behavior of the hyper-chaotic system is analyzed. The randomness and the security of the pseudorandom sequence generated by the proposed scheme are tested and analyzed. The results show that this scheme has a larger key space and a higher level of randomness. It is suitable to be used in privacy encryption and secure communication.