Dynamic Analysis of a Phytoplankton-Fish Model with the Impulsive Feedback Control Depending on the Fish Density and Its Changing Rate

This paper proposes a comprehensive fishing strategy that takes into consideration the population density of fish and its current growth rate, which provides new ideas for fishing strategies. Firstly, we establish a phytoplankton-fish model with the impulsive feedback control depending on the density and rate of change of the fish. Secondly, the complex phase and impulse sets of this model are divided into three cases, then the Poincar´e map for the model is defined, and analyzed the properties of Poincar´e map. In addition, the sufficient and necessary conditions for the global asymptotic stability of the order-1 periodic solution and existence condition of order- k ( k ≥ 2) periodic solution are discussed. The action threshold depends on the density and rate of change of the fish, which is reasonable than earlier studies. The analysis method proposed in this paper also plays an important role in the analysis of impulse models with complex phase sets or impulse sets.

The transverse electric plasmonic modes in a negative refractive index black phosphorene waveguide structure

We consider the transverse electric (TE) plasmonic modes supported by black phosphorene (BP) in a parallel waveguide structure with left-handed material (LHM) instead of the conventional right-handed dielectric material. The existence condition of the TE BP surface plasmon polariton (SPP) is $\mathrm{Im}\sigma>0$. When an electric field is polarized along one of the two orthogonal crystal axes, the anisotropic symmetric and anti-symmetric plasmonic modes depend on the incident optical energy, the chemical potential, and the distance between two BP sheets can be observed. The symmetric mode has a more extensive effective refractive index, which possesses stronger field confinement. With a decreasing distance $d$ between two BP sheets, the coupling strength between the two separate BPSPP waves increases. When $d$ is small enough, the anti-symmetric mode root does not exist. LHMs can be used to realize a TE BPSPP mode to enhance the localization of the BPSPP, which is a practical method in optoelectronic devices based on black phosphorene.

Schistosomiasis Model Incorporating Snail Predator as Biological Control Agent

Schistosomiasis is a parasitic disease caused by the schistosoma worm. A snail can act as the intermediate host for the parasite. Snail-population control is considered to be an effective way to control schistosomiasis spread. In this paper, we discuss the schistosomiasis model incorporating a snail predator as a biological control agent. We prove that the solutions of the model are non-negative and bounded. The existence condition of equilibrium points is investigated. We determine the basic reproduction number when the predator goes to extinction and when the predator survives. The local stability condition of disease-free equilibrium point is proved using linearization, and the Lienard–Chipart and Routh–Hurwitz criteria. We use center-manifold theory to prove the local stability condition of the endemic equilibrium points. Furthermore, we constructed a Lyapunov function to investigate the global stability condition of the disease-free equilibrium points. To support the analytical results, we presented some numerical simulation results. Our findings suggest that a snail predator as a biological control agent can reduce schistosomiasis prevalence. Moreover, the snail-predator birth rate plays an essential role in controlling schistosomiasis spread.

The effect of prey refuge on the dynamics of three species food web system

In this paper, a mathematical model is proposed to study the effect of prey refuge on the dynamics of three species food web system. The food web comprises of a single prey and two competing predators. The two predators predate their prey following Holling type II functional response. In this work we discussed boundedness of the system, existence condition of the equilibrium points and the Jacobean matrix is obtained by linearization techniques. The local stability of the equilibrium points was discussed by using Routh-Hurwitz criteria and the global stability of the equilibrium points by constructing suitable Lyapunov function. Numerical simulation is conducted to support the analytical result. Finally, the effect of prey refuge on the dynamics of one prey two predator was discussed based on the analytical and numerical simulation results. From the numerical simulations, it is found that the dynamical system is persistent for a small value of the refuge constant. However, an increase in the refuge constant leads to the extinction of one of the predator species.

H∞ Constrained Pareto Suboptimal Strategy for Stochastic LPV Time-Delay Systems

Not only in control problems, but also in dynamic games, several sources of performance degradation, such as model variation, deterministic and stochastic uncertainties and state delays, need to be considered. In this paper, we present an [Formula: see text] constrained Pareto suboptimal strategy for stochastic linear parameter-varying (LPV) time-delay systems involving multiple decision makers. The goal of developing the [Formula: see text] constrained Pareto suboptimal strategy set is to construct a memoryless state feedback strategy set, so that the closed-loop stochastic LPV system is stochastically mean-square stable. In the paper, the existence condition of the extended bounded real lemma is first established via linear matrix inequalities (LMIs). Then, a quadratic cost bound for cost performance is derived. Based on these preliminary results, sufficient conditions for the existence of such a strategy set under the [Formula: see text] constraint are derived by using cross-coupled bilinear matrix inequalities (BMIs). To determine the strategy set, a viscosity iterative scheme based on the LMIs is established to avoid the processing of BMIs. Finally, two numerical examples are presented to demonstrate the reliability and usefulness of the proposed method.

The Yellow Active Queue Management Algorithm in ICN Routers Based on the Monitoring of Bandwidth Competition

Deploying the active queue management (AQM) algorithm on a router is an effective way to avoid packet loss caused by congestion. In an information-centric network (ICN), routers not only play a role of packets forwarding but are also content service providers. Congestion in ICN routers can be further summarized as the competition between the external forwarding traffic and the internal cache response traffic for limited bandwidth resources. This indicates that the traditional AQM needs to be redesigned to adapt to ICN. In this paper, we first demonstrated mathematically that allocating more bandwidth for the upstream forwarding flow could improve the quality of service (QoS) of the whole network. Secondly, we propose a novel AQM algorithm, YELLOW, which predicts the bandwidth competition event and adjusts the input rate of request and the marking probability adaptively. Afterwards, we model YELLOW through the totally asymmetric simple exclusion process (TASEP) and deduce the approximate solution of the existence condition for each stationary phase. Finally, we evaluated the performance of YELLOW by NS-3 simulator, and verified the accuracy of modeling results by Monte Carlo. The simulation results showed that the queue of YELLOW could converge to the expected value, and the significant gains of the router with low packet loss rate, robustness and high throughput.

Investigation on dynamics of an impulsive predator–prey system with generalized Holling type IV functional response and anti-predator behavior

In the present article, we propose and analyze a new mathematical model for a predator–prey system including the following terms: a Monod–Haldane functional response (a generalized Holling type IV), a term describing the anti-predator behavior of prey populations and one for an impulsive control strategy. In particular, we establish the existence condition under which the system has a locally asymptotically stable prey-eradication periodic solution. Violating such a condition, the system turns out to be permanent. Employing bifurcation theory, some conditions, under which the existence and stability of a positive periodic solution of the system occur but its prey-eradication periodic solution becomes unstable, are provided. Furthermore, numerical simulations for the proposed model are given to confirm the obtained theoretical results.

Actuator Fault Tolerant Control of Variable Cycle Engine Using Sliding Mode Control Scheme

This paper presents a fault tolerant control (FTC) design for the actuator faults in a variable cycle engine (VCE). Ensured by the multiple variable geometries structure of VCE, the design is realized by distributing the control effort among the unfaulty actuators with the “functional redundancy” idea. The FTC design consists of two parts: the fault reconstruction part and the fault tolerant control part, which use a sliding mode observer (SMO) and a sliding mode control (SMC) scheme respectively. Considering the inaccuracy of the fault reconstruction result, the proposed design requires only inaccurate fault information. The stability of the closed-loop control system is proved and the existence condition for the proposed control law is analyzed. This work also reveals its relation to the sliding mode control allocation design and the adaptive SMC design. An application case is then studied for tolerating the loss of effectiveness fault of the nozzle area actuator. Results show that the FTC design is able to tolerate the fault and achieves the same control goal as in the fault-free situation. Finally, a hardware-in-the-loop test is carried out to verify the design in a real-time distributed control system, which demonstrates its use from the engineering perspective.