Optimal control and bifurcation analysis of a delayed fractional-order SIRS model with general incidence rate and delayed control

A fractional-order generalized SIRS model considering incubation period is established in this paper for the transmission of emerging pathogens. The corresponding Hopf bifurcation is discussed by selecting time delay as the bifurcation parameter. In order to control the occurrence of Hopf bifurcation and achieve better dynamic behaviors, a delayed feedback control is adopted to the model. Further, the delayed fractional-order optimal control problem (DFOCP) is proposed and discussed. The parameters of the proposed model are identified through the measurement data of coronavirus disease 2019 (COVID-19). Based on the results of parameter identification, the corresponding DFOCP with delayed control is numerically solved

Global dynamics for a class of reaction–diffusion multigroup SIR epidemic models with time fractional-order derivatives

This paper investigates the global dynamics for a class of multigroup SIR epidemic model with time fractional-order derivatives and reaction–diffusion. The fractional order considered in this paper is in (0; 1], which the propagation speed of this process is slower than Brownian motion leading to anomalous subdiffusion. Furthermore, the generalized incidence function is considered so that the data itself can flexibly determine the functional form of incidence rates in practice. Firstly, the existence, nonnegativity, and ultimate boundedness of the solution for the proposed system are studied. Moreover, the basic reproduction number R0 is calculated and shown as a threshold: the disease-free equilibrium point of the proposed system is globally asymptotically stable when R0 ≤ 1, while when R0 > 1, the proposed system is uniformly persistent, and the endemic equilibrium point is globally asymptotically stable. Finally, the theoretical results are verified by numerical simulation

Leader-Following Consensus of Fractional Nonlinear Multiagent Systems

The leader-following consensus of fractional nonlinear multiagent systems is investigated over an undirected fixed interaction graph. Mittag-Leffler stability and the fractional Lyapunov direct method are firstly introduced into the fractional multiagent systems. The sufficient conditions are given to guarantee that the leader-following consensus can be achieved in the systems with both single-integrator dynamics and double-integrator dynamics. Finally, the numerical simulations are given to verify the correctness of the presented theory

Leader-Following Formation Control for Discrete-Time Fractional Stochastic Multi-Agent Systems by Event-Triggered Strategy

Fractional differential equations, which are non-local and can better describe memory and genetic properties, are widely used to describe various physical, chemical, and biological phenomena. Therefore, the multi-agent systems based on discrete-time fractional stochastic models are established. First, some followers are selected for pinning control. In order to save resources and energy, an event-triggered based control mechanism is proposed. Second, under this control mechanism, sufficient conditions on the interaction graph and the fractional derivative order such that formation control can be achieved are given. Additionally, influenced by noise, the multi-agent system completes formation control in the mean square. In addition to that, these results are equally applicable to the discrete-time fractional formation problem without noise. Finally, the example of numerical simulation is given to prove the correctness of the results

Extinction Analysis of Stochastic Predator–Prey System with Stage Structure and Crowley–Martin Functional Response

In this paper, we researched some dynamical behaviors of a stochastic predator–prey system, which is considered under the combination of Crowley–Martin functional response and stage structure. First, we obtained the existence and uniqueness of the global positive solution of the system. Then, we studied the stochastically ultimate boundedness of the solution. Furthermore, we established two sufficient conditions, which are separately given to ensure the stochastic extinction of the prey and predator populations. In the end, we carried out the numerical simulations to explain some cases

Adaptive Pinning Synchronization of Fractional Complex Networks with Impulses and Reaction–Diffusion Terms

In this paper, a class of fractional complex networks with impulses and reaction−diffusion terms is introduced and studied. Meanwhile, a class of more general network structures is considered, which consists of an instant communication topology and a delayed communication topology. Based on the Lyapunov method and linear matrix inequality techniques, some sufficient criteria are obtained, ensuring adaptive pinning synchronization of the network under a designed adaptive control strategy. In addition, a pinning scheme is proposed, which shows that the nodes with delayed communication are good candidates for applying controllers. Finally, a numerical example is given to verify the validity of the main results

Global Synchronization of Reaction-Diffusion Fractional-Order Memristive Neural Networks with Time Delay and Unknown Parameters

This paper investigated the global synchronization of fractional-order memristive neural networks (FMNNs). To deal with the effect of reaction-diffusion and time delay, fractional partial and comparison theorem are introduced. Based on the set value mapping theory and Filippov solution, the activation function is extended to discontinuous case. Adaptive controllers with a compensator are designed owing to the existence of unknown parameters, with the help of Gronwall–Bellman inequality. Numerical simulation examples demonstrate the availability of the theoretical results

Seepage Performance of Fibre Bundle Drainage Pipes: Particle Flow Simulation and Laboratory Testing

Mining coal, oil and other energy will form much slope engineering, such as open-pit mine slope and oil depot slope. The groundwater seepage seriously affects the stability of these slope engineering projects. Drainage pipes are commonly used in slope engineering projects to reduce the risk of moisture decreasing soil stability. Such pipes are prone to blockage by soil accumulation after a period of operation, resulting in decreased drainage or complete failure. By installing fibre bundles in drainage pipes, drainage can be maintained under soil ingress. This paper conducted particle flow simulations of the influences of soil particles on the clogging of geotextile filters and drainage pipes under various influences and estimated their seepage rates. Higher water pressure, smaller flower hole intervals in the pipe, greater soil friction angles and smaller pipe inclination angles are less conducive to drainage. Under silting conditions, the seepage and drainage performance of a drainage pipe can be improved by installing a fibre bundle. Five types of fibre bundles were tested with plastic rope providing the best drainage effect. With plastic rope and cotton rope, the best drainage is achieved using uneven arrangements of fibre bundles. In contrast, nylon rope, hemp rope and polyester rope perform best when uniformly arranged. The greater the number of fibre bundles per unit cross-sectional area of pipe, the better the seepage conductivity. Seepage is also greater when the soil in the pipe has a higher sand content. These results provide a reference for the design and construction of more reliable drainage systems for slope engineering in wet areas