Multi-switching combination synchronization of chaotic systems

A novel synchronization scheme is proposed for a class of chaotic systems, extending the concept of multi-switching synchronization to combination synchronization such that the state variables of two or more driving systems synchronize with different state variables of the response system, simultaneously. The new scheme, multi-switching combination synchronization (MSCS), represents a significant extension of earlier multi-switching schemes in which two chaotic systems, in a driver-response configuration, are multi-switched to synchronize up to a scaling factor. In MSCS, the chaotic driving systems multi-switch a response chaotic system in combination synchronization. For certain choices of the scaling factors, MSCS reduces to multi-switching synchronization, implying that the latter is a special case of MSCS. A theoretical approach to control design, based on backstepping, is presented and validated using numerical simulations

Nonlinear growth and mathematical modelling of COVID-19 in some African countries with the Atangana-Baleanu fractional derivative

We analyse the time-series evolution of the cumulative number of confirmed cases of COVID-19, the novel coronavirus disease, for some African countries. We propose a mathematical model, incorporating non-pharmaceutical interventions to unravel the disease transmission dynamics. Analysis of the stability of the model’s steady states was carried out, and the reproduction number R0, a vital key for flattening the time-evolution of COVID-19 cases, was obtained by means of the next generation matrix technique. By dividing the time evolution of the pandemic for the cumulative number of confirmed infected cases into different regimes or intervals, hereafter referred to as phases, numerical simulations were performed to fit the proposed model to the cumulative number of confirmed infections for different phases of COVID-19 during its first wave. The estimated R0 declined from 2.452 – 9.179 during the first phase of the infection to 1.374 – 2.417 in the last phase. Using the Atangana-Baleanu fractional derivative, a fractional COVID-19 model is proposed and numerical simulations performed to establish the dependence of the disease dynamics on the order of the fractional derivatives. An elasticity and sensitivity analysis of R0 was carried out to determine the most significant parameters for combating the disease outbreak. These were found to be the effective disease transmission rate, the disease diagnosis or case detection rate, the proportion of susceptible individuals taking precautions, and the disease infection rate. Our results show that if the disease infection rate is less than 0.082/day, then R0 is always less than 1; and if at least 55.29% of the susceptible population take precautions such as regular hand washing with soap, use of sanitizers, and the wearing of face masks, then the reproduction number R0 remains below unity irrespective of the disease infection rate. Keeping R0 values below unity leads to a decrease in COVID-19 prevalence

Hyperchaos and bifurcations in a driven Van der Pol–Duffing oscillator circuit

We investigate the dynamics of a driven Van der Pol–Duffing oscillator circuit and show the existence of higher-dimensional chaotic orbits (or hyperchaos), transient chaos, strange-nonchaotic attractors, as well as quasiperiodic orbits born from Hopf bifurcating orbits. By computing all the Lyapunov exponent spectra, scanning a wide range of the driving frequency and driving amplitude parameter space, we explore in two-parameter space the regimes of different dynamical behaviours

Vibrational and stochastic resonances in driven nonlinear systems

Nonlinear systems are abundant in nature. Their dynamics have been extensively investigated due to their multidisciplinary applicability, ranging from all branches of physical and mathematical sciences to engineering as well as to life sciences and medicine. When driven by external forces, nonlinear systems can exhibit plethora of interesting and important properties - one of the most prominent being resonance. In the presence of a second, higher frequency, driving force, whether stochastic or deterministic/periodic, a resonance phenomenon arises that can generally be termed stochastic resonance or vibrational resonance. Operating a system in or out of resonance promises applications in several advanced technologies, such as the creation of novel materials at the nano, micro and macroscales including, but not limited to, materials having photonic band gaps, quantum control of atoms and molecules as well as miniature condensed matter systems. Motivated in part by these potential applications, this Theme Issue provides a concrete up-to-date overview of vibrational and stochastic resonances in driven nonlinear systems. It assembles state-of-the-art, original contributions on such induced resonances - addressing their analysis, occurrence, and applications from either the theoretical, numerical and experimental perspectives, or through combinations of these

Vibrational and stochastic resonances in driven nonlinear systems:part two

Nonlinearity is ubiquitous in both natural and engineering systems. The resultant dynamics has emerged as a multidisciplinary field that has been very extensively investigated, due partly to the potential occurrence of nonlinear phenomena in all branches of sciences, engineering and medicine. Driving nonlinear systems with external excitations can yield a plethora of intriguing and important phenomena – one of the most prominent being that of resonance. In the presence of additional harmonic or stochastic excitation, two exotic forms of resonance can arise: vibrational resonance or stochastic resonance, respectively. Several promising state-of-the-art technologies that were not covered in Part One of this Theme Issue are discussed here. They include inter alia the improvement of image quality, the design of machines and devices that exert vibrations on materials, the harvesting of energy from various forms of ambient vibration, and control of aerodynamic instabilities. They form an important part of the Theme Issue as a whole, which is dedicated to an overview of vibrational and stochastic resonances in driven nonlinear systems. resonances in driven nonlinear systems

Comparative Assessment of Adaptability and Agronomic Traits of Seventeen Tomato Varieties on Coarse-Textured Soil in Tropical Dry and Rainy Seasons

Though tomato is sensitive to humidity, tomato lines introduced to humid tropical environments are rarely assessed for relative performance in the prevailing seasons. The agronomic traits of 17 tomato varieties grown on a sandy-loam soil in the derived savannah were assessed in successive dry and rainy seasons. The varieties generally performed poorer in the dry than the rainy season, mostly showing incongruent trends in the two seasons. ‘Ekwunato’ and ‘Tomato Mmiri’ were the tallest with the most nodes in the dry and rainy seasons, respectively. ‘Ekwunato’ and ‘Yolince’ attained 1st flowering earliest, whereas ‘Ekwunato’ and NACGRAB-5 produced the most flowers and fruits in the dry and rainy seasons, respectively; ‘Starke Aryes’ had the fewest in both seasons. However, ‘Ronata’ and NACGRAB-9 gave the highest fruit weight per plant (3892 and 3820 g, respectively) in the dry season, before ‘Tropimech’ (3245 g). NACGRAB-9 gave the highest (8,475g) weight in the rainy season, before ‘Ekwunato’ and ‘Ronata’ (7632 and 7513 g, respectively). Positive character associations prevailed among numbers of nodes, leaves, trusses, flowers and fruits per plant in both seasons. Numbers of days to 1st and 50% flowering were negatively correlated to the number of fruits per plant. However, fruit weight per plant had no correlations with the other traits. ‘Ekwunato’ and NACGRAB-5 could serve as gene donors in breeding for enhanced flowering/fruiting in dry and rainy seasons, respectively. To increase tomato fruit yields, NACGRAB-9 or ‘Ronata’ is recommended, otherwise ‘Tropimech’ and ‘Ekwunato’ should be grown specifically in dry and rainy seasons, respectively

Comparative Assessment of Adaptability and Agronomic Traits of Seventeen Tomato Varieties on Coarse-Textured Soil in Tropical Dry and Rainy Seasons

Though tomato is sensitive to humidity, tomato lines introduced to humid tropical environments are rarely assessed for relative performance in the prevailing seasons. The agronomic traits of 17 tomato varieties grown on a sandy-loam soil in the derived savannah were assessed in successive dry and rainy seasons. The varieties generally performed poorer in the dry than the rainy season, mostly showing incongruent trends in the two seasons. ‘Ekwunato’ and ‘Tomato Mmiri’ were the tallest with the most nodes in the dry and rainy seasons, respectively. ‘Ekwunato’ and ‘Yolince’ attained 1st flowering earliest, whereas ‘Ekwunato’ and NACGRAB-5 produced the most flowers and fruits in the dry and rainy seasons, respectively; ‘Starke Aryes’ had the fewest in both seasons. However, ‘Ronata’ and NACGRAB-9 gave the highest fruit weight per plant (3892 and 3820 g, respectively) in the dry season, before ‘Tropimech’ (3245 g). NACGRAB-9 gave the highest (8,475g) weight in the rainy season, before ‘Ekwunato’ and ‘Ronata’ (7632 and 7513 g, respectively). Positive character associations prevailed among numbers of nodes, leaves, trusses, flowers and fruits per plant in both seasons. Numbers of days to 1st and 50% flowering were negatively correlated to the number of fruits per plant. However, fruit weight per plant had no correlations with the other traits. ‘Ekwunato’ and NACGRAB-5 could serve as gene donors in breeding for enhanced flowering/fruiting in dry and rainy seasons, respectively. To increase tomato fruit yields, NACGRAB-9 or ‘Ronata’ is recommended, otherwise ‘Tropimech’ and ‘Ekwunato’ should be grown specifically in dry and rainy seasons, respectively

Acoustic vibrational resonance in a Rayleigh-Plesset bubble oscillator

The phenomenon of vibrational resonance (VR) has been investigated in a Rayleigh-Plesset oscillator for a gas bubble oscillating in an incompressible liquid while driven by a dual-frequency force consisting of high-frequency, amplitude-modulated, weak, acoustic waves. The complex equation of the Rayleigh-Plesset bubble oscillator model was expressed as the dynamics of a classical particle in a potential well of the Li´enard type, thus allowing us to use both numerical and analytic approaches to investigate the occurrence of VR. We provide clear evidence that an acoustically-driven bubble oscillates in a time-dependent single or double- well potential whose properties are determined by the density of the liquid and its surface tension. We show both theoretically and numerically that, besides the VR effect facilitated by the variation of the parameters on which the high-frequency depends, amplitude modulation, the properties of the liquid in which the gas bubble oscillates contribute significantly to the occurrence of VR. In addition, we discuss the observation of multiple resonances and their origin for the double-well case, as well as their connection to the low frequency, weak, acoustic force field

Vibrational resonances in driven oscillators with position-dependent mass

The vibrational resonance (VR) phenomenon has received a great deal of research attention over the two decades since its introduction. The wide range of theoretical and experimental results obtained has, however, been confined to VR in systems with constant mass. We now extend the VR formalism to encompass systems with position-dependent mass (PDM).We consider a generalized classical counterpart of the quantum mechanical nonlinear oscillator with PDM. By developing a theoretical framework fordetermining the response amplitude of PDMsystems, we examine and analyse their VR phenomenona, obtain conditions for the occurrence of resonances, show that the role played by PDM can be both inductive and contributory, and suggest that PDM effects could usefully be explored to maximise the efficiency of devices being operated in VRmodes. Our analysis suggests new directions for the investigation of VR in a general class of PDM systems

Global burden of 288 causes of death and life expectancy decomposition in 204 countries and territories and 811 subnational locations, 1990–2021: a systematic analysis for the Global Burden of Disease Study 2021

BACKGROUND Regular, detailed reporting on population health by underlying cause of death is fundamental for public health decision making. Cause-specific estimates of mortality and the subsequent effects on life expectancy worldwide are valuable metrics to gauge progress in reducing mortality rates. These estimates are particularly important following large-scale mortality spikes, such as the COVID-19 pandemic. When systematically analysed, mortality rates and life expectancy allow comparisons of the consequences of causes of death globally and over time, providing a nuanced understanding of the effect of these causes on global populations. METHODS The Global Burden of Diseases, Injuries, and Risk Factors Study (GBD) 2021 cause-of-death analysis estimated mortality and years of life lost (YLLs) from 288 causes of death by age-sex-location-year in 204 countries and territories and 811 subnational locations for each year from 1990 until 2021. The analysis used 56 604 data sources, including data from vital registration and verbal autopsy as well as surveys, censuses, surveillance systems, and cancer registries, among others. As with previous GBD rounds, cause-specific death rates for most causes were estimated using the Cause of Death Ensemble model-a modelling tool developed for GBD to assess the out-of-sample predictive validity of different statistical models and covariate permutations and combine those results to produce cause-specific mortality estimates-with alternative strategies adapted to model causes with insufficient data, substantial changes in reporting over the study period, or unusual epidemiology. YLLs were computed as the product of the number of deaths for each cause-age-sex-location-year and the standard life expectancy at each age. As part of the modelling process, uncertainty intervals (UIs) were generated using the 2·5th and 97·5th percentiles from a 1000-draw distribution for each metric. We decomposed life expectancy by cause of death, location, and year to show cause-specific effects on life expectancy from 1990 to 2021. We also used the coefficient of variation and the fraction of population affected by 90% of deaths to highlight concentrations of mortality. Findings are reported in counts and age-standardised rates. Methodological improvements for cause-of-death estimates in GBD 2021 include the expansion of under-5-years age group to include four new age groups, enhanced methods to account for stochastic variation of sparse data, and the inclusion of COVID-19 and other pandemic-related mortality-which includes excess mortality associated with the pandemic, excluding COVID-19, lower respiratory infections, measles, malaria, and pertussis. For this analysis, 199 new country-years of vital registration cause-of-death data, 5 country-years of surveillance data, 21 country-years of verbal autopsy data, and 94 country-years of other data types were added to those used in previous GBD rounds. FINDINGS The leading causes of age-standardised deaths globally were the same in 2019 as they were in 1990; in descending order, these were, ischaemic heart disease, stroke, chronic obstructive pulmonary disease, and lower respiratory infections. In 2021, however, COVID-19 replaced stroke as the second-leading age-standardised cause of death, with 94·0 deaths (95% UI 89·2-100·0) per 100 000 population. The COVID-19 pandemic shifted the rankings of the leading five causes, lowering stroke to the third-leading and chronic obstructive pulmonary disease to the fourth-leading position. In 2021, the highest age-standardised death rates from COVID-19 occurred in sub-Saharan Africa (271·0 deaths [250·1-290·7] per 100 000 population) and Latin America and the Caribbean (195·4 deaths [182·1-211·4] per 100 000 population). The lowest age-standardised death rates from COVID-19 were in the high-income super-region (48·1 deaths [47·4-48·8] per 100 000 population) and southeast Asia, east Asia, and Oceania (23·2 deaths [16·3-37·2] per 100 000 population). Globally, life expectancy steadily improved between 1990 and 2019 for 18 of the 22 investigated causes. Decomposition of global and regional life expectancy showed the positive effect that reductions in deaths from enteric infections, lower respiratory infections, stroke, and neonatal deaths, among others have contributed to improved survival over the study period. However, a net reduction of 1·6 years occurred in global life expectancy between 2019 and 2021, primarily due to increased death rates from COVID-19 and other pandemic-related mortality. Life expectancy was highly variable between super-regions over the study period, with southeast Asia, east Asia, and Oceania gaining 8·3 years (6·7-9·9) overall, while having the smallest reduction in life expectancy due to COVID-19 (0·4 years). The largest reduction in life expectancy due to COVID-19 occurred in Latin America and the Caribbean (3·6 years). Additionally, 53 of the 288 causes of death were highly concentrated in locations with less than 50% of the global population as of 2021, and these causes of death became progressively more concentrated since 1990, when only 44 causes showed this pattern. The concentration phenomenon is discussed heuristically with respect to enteric and lower respiratory infections, malaria, HIV/AIDS, neonatal disorders, tuberculosis, and measles. INTERPRETATION Long-standing gains in life expectancy and reductions in many of the leading causes of death have been disrupted by the COVID-19 pandemic, the adverse effects of which were spread unevenly among populations. Despite the pandemic, there has been continued progress in combatting several notable causes of death, leading to improved global life expectancy over the study period. Each of the seven GBD super-regions showed an overall improvement from 1990 and 2021, obscuring the negative effect in the years of the pandemic. Additionally, our findings regarding regional variation in causes of death driving increases in life expectancy hold clear policy utility. Analyses of shifting mortality trends reveal that several causes, once widespread globally, are now increasingly concentrated geographically. These changes in mortality concentration, alongside further investigation of changing risks, interventions, and relevant policy, present an important opportunity to deepen our understanding of mortality-reduction strategies. Examining patterns in mortality concentration might reveal areas where successful public health interventions have been implemented. Translating these successes to locations where certain causes of death remain entrenched can inform policies that work to improve life expectancy for people everywhere. FUNDING Bill & Melinda Gates Foundation