Spatiotemporal dynamics in a toxin-producing predator–prey model with threshold harvesting

In this paper, we propose a toxin-producing predator–prey model with threshold harvesting and study spatiotemporal dynamics of the model under the homogeneous Neumann boundary conditions. At first, the persistence property of solutions to the system is investigated. Then the explicit requirements for the existence of nonconstant steady state solutions are derived by studying the relevant characteristic equation. These steady states occur from related constant steady states via steady state bifurcation. Throughout the analysis of the amplitude equations of Turing pattern by the multiple scale method, pattern formation can be found. Finally, we display  umerical simulations to verify the theoretical outcomes

Stability analysis for fractionalorder linear singular delay differential Systems,”

We investigate the delay-independently asymptotic stability of fractional-order linear singular delay differential systems. Based on the algebraic approach, the sufficient conditions are presented to ensure the asymptotic stability for any delay parameter. By applying the stability criteria, one can avoid solving the roots of transcendental equations. An example is also provided to illustrate the effectiveness and applicability of the theoretical results

Stability and bifurcation analysis for a single-species discrete model with stage structure

Abstract In this paper, a single-species discrete model with stage structure is investigated. By analyzing the corresponding characteristic equations, the local asymptotic stability of non-negative equilibrium points and the existence of flip bifurcation are discussed. Using the center manifold theory, the stability of the non-hyperbolic equilibrium point is obtained. Based on bifurcation theory, we obtain the direction and the stability of a flip bifurcation at the positive equilibrium with the birth rate as the bifurcation parameter. Finally, some numerical simulations, including phase portraits, chaotic bands with period windows, and Lyapunov exponent methods, are performed to validate the theoretical results, which extends the results in previous papers

HPR1000: Advanced Pressurized Water Reactor with Active and Passive Safety

HPR1000 is an advanced nuclear power plant (NPP) with the significant feature of an active and passive safety design philosophy, developed by the China National Nuclear Corporation. On one hand, it is an evolutionary design based on proven technology of the existing pressurized water reactor NPP; on the other hand, it incorporates advanced design features including a 177-fuel-assembly core loaded with CF3 fuel assemblies, active and passive safety systems, comprehensive severe accident prevention and mitigation measures, enhanced protection against external events, and improved emergency response capability. Extensive verification experiments and tests have been performed for critical innovative improvements on passive systems, the reactor core, and the main equipment. The design of HPR1000 fulfills the international utility requirements for advanced light water reactors and the latest nuclear safety requirements, and addresses the safety issues relevant to the Fukushima accident. Along with its outstanding safety and economy, HPR1000 provides an excellent and practicable solution for both domestic and international nuclear power markets

Asymptotic Stability of Caputo Type Fractional Neutral Dynamical Systems with Multiple Discrete Delays

We discuss the delay-independent asymptotic stability of Caputo type fractional-order neutral differential systems with multiple discrete delays. Based on the algebraic approach and matrix theory, the sufficient conditions are derived to ensure the asymptotic stability for all time-delay parameters. By applying the stability criteria, one can avoid solving the roots of transcendental equations. The results obtained are computationally flexible and convenient. Moreover, an example is provided to illustrate the effectiveness and applicability of the proposed theoretical results

Modeling Periodic HFMD with the Effect of Vaccination in Mainland China

Hand, foot, and mouth disease (HFMD), associated with more than 20 disease-causing enteroviruses, is one of the major public health problems in mainland China, and the unique vaccine available is for enterovirus 71 (EV71). In this paper, we propose a new epidemic model to investigate the effect of EV71 vaccination on the spread of HFMD with multiple pathogenic viruses in mainland China. In addition, suitable periodic transmission functions are designed, with a two-year period and taking into consideration the effects of opening and closing of schools. After defining the basic reproduction number R0, we prove that the disease-free equilibrium is globally asymptotically stable if R01. We use the model to simulate the HFMD reported data in mainland China from January 2008 to June 2019. The numerical experiments show that increasing the vaccinated rate can effectively control the spread of HFMD in mainland China, yet the disease does not become extinct. Moreover, if we can control the baseline contact rate of infectious individuals and the recovery rate of symptomatic infectious individuals under certain conditions, which can be achieved by improving protective measures and medical conditions, then the disease will be eliminated

Stability and Bifurcation Analysis of a Nonlinear Discrete Logistic Model with Delay

We consider a nonlinear discrete logistic model with delay. The characteristic equation of the linearized system at the positive equilibrium is a polynomial equation involving high order terms. We obtain the conditions ensuring the asymptotic stability of the positive equilibrium and the existence of Neimark-Sacker bifurcation, with respect to the parameter of the model. Based on the bifurcation theory, we discuss Neimark-Sacker bifurcation direction and the stability of bifurcated solutions. Finally, some numerical simulations are performed to illustrate the theoretical results