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J. Comput. Nonlinear Dynam. 2019;14(7):071001-071001-14. doi:10.1115/1.4043001.

A classic susceptible–infected–recovered (SIR) model with nonlinear state-dependent feedback control is proposed and investigated in which integrated control measures, including vaccination, treatment and isolation, are applied once the number of the susceptible population reaches a threshold level. The interventions are density dependent due to limitations on the availability of resources. The existence and global stability of the disease-free periodic solution (DFPS) are addressed, and the threshold condition is provided, which can be used to define the control reproduction number Rc for the model with state-dependent feedback control. The DFPS may also be globally stable even if the basic reproduction number R0 of the SIR model is larger than one. To show that the threshold dynamics are determined by the Rc, we employ bifurcation theories of the discrete one-parameter family of maps, which are determined by the Poincaré map of the proposed model, and the main results indicate that under certain conditions, a stable or unstable interior periodic solution could be generated through transcritical, pitchfork, and backward bifurcations. A biphasic vaccination rate (or threshold level) could result in an inverted U-shape (or U-shape) curve, which reveals some important issues related to disease control and vaccine design in bioengineering including vaccine coverage, efficiency, and vaccine production. Moreover, the nonlinear state-dependent feedback control could result in novel dynamics including various bifurcations.

Commentary by Dr. Valentin Fuster
J. Comput. Nonlinear Dynam. 2019;14(7):071002-071002-9. doi:10.1115/1.4043003.

Systems with hidden attractors have been the hot research topic of recent years because of their striking features. Fractional-order systems with hidden attractors are newly introduced and barely investigated. In this paper, a new 4D fractional-order chaotic system with hidden attractors is proposed. The abundant and complex hidden dynamical behaviors are studied by nonlinear theory, numerical simulation, and circuit realization. As the main mode of electrical behavior in many neuroendocrine cells, bursting oscillations (BOs) exist in this system. This complicated phenomenon is seldom found in the chaotic systems, especially in the fractional-order chaotic systems without equilibrium points. With the view of practical application, the spectral entropy (SE) algorithm is chosen to estimate the complexity of this fractional-order system for selecting more appropriate parameters. Interestingly, there is a state variable correlated with offset boosting that can adjust the amplitude of the variable conveniently. In addition, the circuit of this fractional-order chaotic system is designed and verified by analog as well as hardware circuit. All the results are very consistent with those of numerical simulation.

Commentary by Dr. Valentin Fuster
J. Comput. Nonlinear Dynam. 2019;14(7):071003-071003-16. doi:10.1115/1.4043084.

The Army's mission is to develop, integrate, and sustain the right technology solution for all manned and unmanned ground vehicles, and mobility is a key requirement for all ground vehicles. Mobility focuses on ground vehicles' capabilities that enable them to be deployable worldwide, operationally mobile in all environments, and protected from symmetrical and asymmetrical threats. In order for military ground vehicles to operate in any combat zone, mobility on off-road terrains should be extensively investigated. Mobility on off-road terrains is poorly understood because of the empirical and semi-empirical height-field based methods which are often used for predicting vehicle mobility, such as Bekker–Wong type models. Those methods do not capture the three-dimensional soil deformation/flow as well as the soil's nonlinear behavior. The discrete element method (DEM) in which soil is modeled using discrete particles was identified as a high-fidelity method that can capture the deformation of the soil and its nonlinear behavior. In this paper, a simulation study is undertaken to understand the influence of DEM soil model parameters on vehicle mobility. A typical wheeled vehicle model was built in ivress/dis software and simulated over different cohesive and noncohesive soils modeled using DEM, with a particular emphasis on weak soils (with both low friction angle and low cohesion). Some characteristics of these soils were varied, namely, the interparticle cohesion, the interparticle friction, the particle size, and the particle mass. The mobility measures, including vehicle speed, wheel sinkage, wheel slip, and tractive force were evaluated using the model and correlated to the DEM soil model parameters. This study shows that the vehicle speed increases with cohesion, friction, soil density, and particle size while wheel sinkage, wheel slip, and tractive force decrease with those parameters. The combined influence of those parameters is more complex. Extensive studies of those and other soil parameters need to be carried out in the future to understand their effect on vehicle mobility.

Commentary by Dr. Valentin Fuster

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