Design, Analysis and Comparison of a Nonstandard Computational Method for the Solution of a General Stochastic Fractional Epidemic Model

Malaria is a deadly human disease that is still a major cause of casualties worldwide. In this work, we consider the fractional-order system of malaria pestilence. Further, the essential traits of the model are investigated carefully. To this end, the stability of the model at equilibrium points is investigated by applying the Jacobian matrix technique. The contribution of the basic reproduction number, R0, in the infection dynamics and stability analysis is elucidated. The results indicate that the given system is locally asymptotically stable at the disease-free steady-state solution when R0<1. A similar result is obtained for the endemic equilibrium when R0>1. The underlying system shows global stability at both steady states. The fractional-order system is converted into a stochastic model. For a more realistic study of the disease dynamics, the non-parametric perturbation version of the stochastic epidemic model is developed and studied numerically. The general stochastic fractional Euler method, Runge–Kutta method, and a proposed numerical method are applied to solve the model. The standard techniques fail to preserve the positivity property of the continuous system. Meanwhile, the proposed stochastic fractional nonstandard finite-difference method preserves the positivity. For the boundedness of the nonstandard finite-difference scheme, a result is established. All the analytical results are verified by numerical simulations. A comparison of the numerical techniques is carried out graphically. The conclusions of the study are discussed as a closing note.

Local Dynamics of Logistic Equation with Delay and Diffusion

The behavior of all the solutions of the logistic equation with delay and diffusion in a sufficiently small positive neighborhood of the equilibrium state is studied. It is assumed that the Andronov–Hopf bifurcation conditions are met for the coefficients of the problem. Small perturbations of all coefficients are considered, including the delay coefficient and the coefficients of the boundary conditions. The conditions are studied when these perturbations depend on the spatial variable and when they are time-periodic functions. Equations on the central manifold are constructed as the main results. Their nonlocal dynamics determines the behavior of all the solutions of the original boundary value problem in a sufficiently small neighborhood of the equilibrium state. The ability to control the dynamics of the original problem using the phase change in the perturbing force is set. The numerical and analytical results regarding the dynamics of the system with parametric perturbation are obtained. The asymptotic formulas for the solutions of the original boundary value problem are given.

PP-PG: Combining Parameter Perturbation with Policy Gradient Methods for Effective and Efficient Explorations in Deep Reinforcement Learning

Efficient and stable exploration remains a key challenge for deep reinforcement learning (DRL) operating in high-dimensional action and state spaces. Recently, a more promising approach by combining the exploration in the action space with the exploration in the parameters space has been proposed to get the best of both methods. In this article, we propose a new iterative and close-loop framework by combining the evolutionary algorithm (EA), which does explorations in a gradient-free manner directly in the parameters space with an actor-critic, and the deep deterministic policy gradient (DDPG) reinforcement learning algorithm, which does explorations in a gradient-based manner in the action space to make these two methods cooperate in a more balanced and efficient way. In our framework, the policies represented by the EA population (the parametric perturbation part) can evolve in a guided manner by utilizing the gradient information provided by the DDPG and the policy gradient part (DDPG) is used only as a fine-tuning tool for the best individual in the EA population to improve the sample efficiency. In particular, we propose a criterion to determine the training steps required for the DDPG to ensure that useful gradient information can be generated from the EA generated samples and the DDPG and EA part can work together in a more balanced way during each generation. Furthermore, within the DDPG part, our algorithm can flexibly switch between fine-tuning the same previous RL-Actor and fine-tuning a new one generated by the EA according to different situations to further improve the efficiency. Experiments on a range of challenging continuous control benchmarks demonstrate that our algorithm outperforms related works and offers a satisfactory trade-off between stability and sample efficiency.

Bifurcation, routes to chaos, and synchronized chaos of electromagnetic valve train in camless engines

The main objects of this paper focus on the complex dynamics and chaos control of an electromagnetic valve train (EMV). A variety of periodic solutions and nonlinear phenomena can be expressed using various numerical techniques such as time responses, phase portraits, Poincaré maps, and frequency spectra. The effects of varying the system parameters can be observed in the bifurcation diagram. It shows that this system can undergo a cascade of period-doubling bifurcations prior to the onset of chaos. Lyapunov exponents and Lyapunov dimensions are employed to confirm chaotic behavior for EMV. A proposed continuous feedback control method based on synchronization characteristics eliminated chaotic oscillations. Numerical simulations are utilized to verify the feasibility and efficiency of the proposed control technique. Finally, some robustness analysis of parametric perturbation on EMV system with synchronization control is confirmed by Lyapunov stability theory and numerical simulations.

Towards non-linear inverse problem for atmospheric source term determination

&lt;div&gt;The basic linear inverse problem of atmospheric release can be formulated as &lt;strong&gt;y&lt;/strong&gt; = M &lt;strong&gt;x&lt;/strong&gt; + &lt;strong&gt;e&lt;/strong&gt; , where &lt;strong&gt;y&lt;/strong&gt; is the measurement vector which is typically in the form of gamma dose rates or concentrations, M is the source-receptor-sensitivity (SRS) matrix, &lt;strong&gt;x&lt;/strong&gt; is the unknown source term to be estimated, and &lt;strong&gt;e&lt;/strong&gt; is the model residue. The SRS matrix M is computed using an atmospheric transport model coupled with meteorological reanalyses. The inverse problem is typically ill-conditioned due to number of uncertainties, hence, the estimation of the source term is not straightforward and additional information, e.g. in the form of regularization or the prior source term, is often needed. Besides, traditional techniques rely on assumption that the SRS matrix is correct which is not realistic due to the number of approximations made during its computation. Therefore, we propose relaxation of the inverse model using introduction of the term &amp;#916;&lt;sub&gt;M&lt;/sub&gt; such as &lt;strong&gt;y&lt;/strong&gt; = ( M+ &amp;#916;&lt;sub&gt;M&lt;/sub&gt; ) &lt;strong&gt;x&lt;/strong&gt; + &lt;strong&gt;e&lt;/strong&gt; leading to non-linear inverse problem formulation, where &amp;#916;&lt;sub&gt;M&lt;/sub&gt; can be, as an example, parametric perturbation of the SRS matrix M in the spatial or temporal domain. We estimate parameters of this perturbation together with solving the inverse problem using variational Bayes procedure. The method will be validated on synthetic dataset as well as demonstrated on real case scenario such as the controlled tracer experiment ETEX or episode of ruthenium-106 release over the Europe on the fall of 2017.&lt;/div&gt;

A Novel Sliding Mode Control with Low-Pass Filter for Nonlinear Handling Chain System in Container Ports

Nonlinearities in a container port handling chain include mainly nonnegative arrive rate of container cargoes, limited container handling completion rate, and nonnegative unsatisfied freight requirement constraints. The nonlinearity influences the operation resources availability and consequently the planned container port handling strategies. Developments presented in this work are devoted to a novel design of sliding mode control with low-pass filter (SMC-LPF) to nonlinear handling chain system (HCS) in container ports. The SMC-LPF can effectively reduce unsatisfied freight requirement of the HCS and make chattering decrease significantly. To illustrate the effectiveness and accuracy of the proposed SMC-LPF, an application to a real container port in China is outlined. The performances of the SMC-LPF for the nonlinear HCS in container ports outperform those of the traditional method, particle swarm optimization algorithm, and slide mode control under simulations with a unit step signal and a sinusoidal signal with offset as the freight requirements. The contributions herein demonstrate the proposed control strategy in weakening chattering, reducing the unsatisfied freight requirements to 0 as close as possible in the HCS, maximizing the operation resilience and robustness of port and shipping supply chain against parametric perturbation, external disturbances, and fluctuant handling abilities.

A Study on Neutral-Point Potential in Three-Level NPC Converters

This paper proposes an accurate mathematical model of three-level neutral-point-clamped (NPC) converters that can accurately represent the midpoint potential drift of the DC link with parameter perturbation. The mathematical relationships between the fluctuation in neutral-point voltage, the parametric perturbation, and the capacitance error are obtained as mathematical expressions in this model. The expressions can be used to quantitatively analyze the reason for the neutral-point voltage imbalance and balancing effect based on a zero-sequence voltage injection. The injected zero-sequence voltage, which can be used to balance the DC-side voltages with the combined action of active current, can be easily obtained from the proposed model. A balancing control under four-quadrant operation modes is proposed by considering the active current to verify the effectiveness of this model. Both the simulation and experiment results validate the excellent performance of the proposed model compared to the conventional model.