A comprehensive study of the novel 4D hyperchaotic system with self-exited multistability and application in the voice encryption.

This paper describes a novel 4-D hyperchaotic system with a high level of complexity. It can produce chaotic, hyperchaotic, periodic, and quasi-periodic behaviors by adjusting its parameters. The study showed that the new system experienced the famous dynamical property of multistability. It can exhibit different coexisting attractors for the same parameter values. Furthermore, by using Lyapunov exponents, bifurcation diagram, equilibrium points' stability, dissipativity, and phase plots, the study was able to investigate the dynamical features of the proposed system. The mathematical model's feasibility is proved by applying the corresponding electronic circuit using Multisim software. The study also reveals an interesting and special feature of the system's offset boosting control. Therefore, the new 4D system is very desirable to use in Chaos-based applications due to its hyperchaotic behavior, multistability, offset boosting property, and easily implementable electronic circuit. Then, the study presents a voice encryption scheme that employs the characteristics of the proposed hyperchaotic system to encrypt a voice signal. The new encryption system is implemented on MATLAB (R2023) to simulate the research findings. Numerous tests are used to measure the efficiency of the developed encryption system against attacks, such as histogram analysis, percent residual deviation (PRD), signal-to-noise ratio (SNR), correlation coefficient (cc), key sensitivity, and NIST randomness test. The simulation findings show how effective our proposed encryption system is and how resilient it is to different cryptographic assaults.

The patterns of facial fractures in traumatic brain injury (TBI) patients using ordinal regression: a retrospective study of five years.

According to the World Health Organization (WHO), traumatic brain injury (TBI) will mainly contribute to disability and death by 2020. Facial fractures associated with TBI are a significant public health concern worldwide. The main etiological factors are road traffic accidents, violence, and falls. Neurological injury associated with facial fractures has been reported to be as high as 76%. Therefore, we retrospectively evaluated facial fracture patterns in patients with a traumatic brain injury in Hospital Universiti Sains Malaysia and evaluated their associations in our study. Ordinal regression was used to examine the facial fracture patterns in patients with traumatic brain injuries. The confounding variables were controlled using ordinal regression analysis, and probabilities of p < 0.1 were considered significant associations. The results found that zygomatic arch fracture -1.141 (95% CI, -2.487 to 0.204, p-value = 0.096), Le Fort II fracture -1.080 (95% CI, -2.138 to -0.022, p-value = 0.045), maxillary bone fracture 2.924 (95% CI, 1.784 to 4.063, p-value .001), nasal bone fracture 4.047 (95% CI, 1.243 to 6.851, p-value = 0.005), and mandibular bone fracture 1.501 (95% CI, 0.711 to 2.291, p-value .001) were the most common facial fracture types associated with traumatic brain injury (TBI). This study provides valuable data for creating prevention plans and gives a chance to discover the epidemiology, prevalence, and connection between TBI and facial fracture.

On three-term conjugate gradient method for optimization problems with applications on COVID-19 model and robotic motion control.

The three-term conjugate gradient (CG) algorithms are among the efficient variants of CG algorithms for solving optimization models. This is due to their simplicity and low memory requirements. On the other hand, the regression model is one of the statistical relationship models whose solution is obtained using one of the least square methods including the CG-like method. In this paper, we present a modification of a three-term conjugate gradient method for unconstrained optimization models and further establish the global convergence under inexact line search. The proposed method was extended to formulate a regression model for the novel coronavirus (COVID-19). The study considers the globally infected cases from January to October 2020 in parameterizing the model. Preliminary results have shown that the proposed method is promising and produces efficient regression model for COVID-19 pandemic. Also, the method was extended to solve a motion control problem involving a two-joint planar robot.

A new 10-D hyperchaotic system with coexisting attractors and high fractal dimension: Its dynamical analysis, synchronization and circuit design.

This work introduce a new high dimensional 10-D hyperchaotic system with high complexity and many of coexisting attractors. With the adjustment of its parameters and initial points, the novel system can generate periodic, quasi-periodic, chaotic, and hyperchaotic behaviours. For special values of parameters, we show that the proposed 10-D system has a very high Kaplan-Yorke fractal dimension, which can reach up to 9.067 indicating the very complexity of the 10-D system dynamics. In addition, the proposed system is shown to exhibit at least six varied attractors for the same values of parameters due to its multistability. Regions of multistability are identified by analysing the bifurcation diagrams of the proposed model versus its parameters and for six different values of initial points. Many of numerical plots are given to show the appearance of different dynamical behaviours and the existence of multiple coexisting attractors. The main problem with controlling chaos/hyperchaos systems is that they are not always fully synchronized. therefore, some powerful synchronization techniques should be considered. The synchronization between the high-dimensional 10-D system and a set of three low-dimensional chaotic and hyperchaotic systems is proposed. Ten control functions are designed using the active control method, ensuring synchronisation between the collection of systems and the 10-D hyperchaotic system. Finally, using Multisim 13.0 software to construct the new system's electronic circuit, the feasibility of the new system with its extremely complicated dynamics is verified. Therefore, the novel 10-D hyperchaotic system can be applied to different chaotic-based application due to its large dimension, complex dynamics, and simple circuit architecture.

Some novel mathematical analysis on the fractional-order 2019-nCoV dynamical model.

Since December 2019, the whole world has been facing the big challenge of Covid-19 or 2019-nCoV. Some nations have controlled or are controlling the spread of this virus strongly, but some countries are in big trouble because of their poor control strategies. Nowadays, mathematical models are very effective tools to simulate outbreaks of this virus. In this research, we analyze a fractional-order model of Covid-19 in terms of the Caputo fractional derivative. First, we generalize an integer-order model to a fractional sense, and then, we check the stability of equilibrium points. To check the dynamics of Covid-19, we plot several graphs on the time scale of daily and monthly cases. The main goal of this content is to show the effectiveness of fractional-order models as compared to integer-order dynamics.

Optimal control analysis of vector-host model with saturated treatment.

Vector-host infectious diseases remain a challenging issue and cause millions of deaths each year globally. In such outbreaks, many countries especially developing or underdevelopment faces a situation where the number of infected individuals is getting larger and the medical facilities are limited. In this paper, we construct an epidemic model to explore the transmission dynamics of vector-borne diseases with nonlinear saturated incidence rate and saturated treatment function. This type of incidence rate, as well as the saturated treatment function, is also known as the Holling type II form and describes the effect of delayed treatment. Initially, we formulate a mathematical model and then present the basic analysis of the model including the positivity and boundedness of the solution. The threshold quantity R 0 is presented and the stability analysis of the system is carried out for the model equilibria. The global stability results are shown using the Lyapunov function of Goh-Voltera type. The existence of backward bifurcation is discussed using the central manifold theory. Further, the global sensitivity analysis of the model is carried out using the Latin Hypercube sampling and the partial rank correlation coefficient techniques. Moreover, an optimal control problem is formulated and the necessary optimality conditions are investigated in order to eradicate the disease in a community. Four strategies are presented by choosing different set of controls combination for the disease minimization. Finally, the numerical simulations of each strategy are depicted to demonstrate the importance of suggesting control interventions on the disease dynamics and eradication.

Combating obesity through healthy eating behavior: a call for system dynamics optimization.

Poor eating behavior has been identified as one of the core contributory factors of the childhood obesity epidemic. The consequences of obesity on numerous aspects of life are thoroughly explored in the existing literature. For instance, evidence shows that obesity is linked to incidences of diseases such as heart disease, type-2 diabetes, and some cancers, as well as psychosocial problems. To respond to the increasing trends in the UK, in 2008 the government set a target to reverse the prevalence of obesity (POB) back to 2000 levels by 2020. This paper will outline the application of system dynamics (SD) optimization to simulate the effect of changes in the eating behavior of British children (aged 2 to 15 years) on weight and obesity. This study also will identify how long it will take to achieve the government's target. This paper proposed a simulation model called Intervention Childhood Obesity Dynamics (ICOD) by focusing the interrelations between various strands of knowledge in one complex human weight regulation system. The model offers distinct insights into the dynamics by capturing the complex interdependencies from the causal loop and feedback structure, with the intention to better understand how eating behaviors influence children's weight, body mass index (BMI), and POB measurement. This study proposed a set of equations that are revised from the original (baseline) equations. The new functions are constructed using a RAMP function of linear decrement in portion size and number of meal variables from 2013 until 2020 in order to achieve the 2020 desired target. Findings from the optimization analysis revealed that the 2020 target won't be achieved until 2026 at the earliest, six years late. Thus, the model suggested that a longer period may be needed to significantly reduce obesity in this population.