Abstract In this paper, we establish an SIVR model with diffusion, spatially heterogeneous, latent infection, and incomplete immunity in the Neumann boundary condition. Firstly, threshold dynamic behavior of is proved by using operator semigroup method, well-posedness solution basic reproduction number $\Re _{0}$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>ℜ</mml:mi> <mml:mn>0</mml:mn> </mml:msub> </mml:math> are given. When _{0}&lt;1$ <mml:mo>&lt;</mml:mo>...

The dynamics of discrete SI epidemic model, which has been obtained by the forward Euler scheme, is investigated in detail. By using center manifold theorem and bifurcation interior<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mrow><mml:msubsup><mml:mrow><mml:mi>R</mml:mi></mml:mrow><mml:mrow><mml:mo>+</mml:mo></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msubsup></mml:mrow></mml:math>, specific conditions for existence flip Neimark-Sacker have derived....

Traditional research on the train control problem use determined model and method cannot deal with variable parameters in complex environment. This paper proposes a new approach by analyzing operation data reinforcement learning instead of using detailed model. Specifically, similarity-based sampling is introduced to sample segments data, which used predict running state train. With reward each segment for can be evaluated. Then, monte carlo applied select optimal solution decision. Finally,...

A discrete two-species competitive model is investigated. By using some preliminary lemmas and constructing a Lyapunov function, the existence uniformly asymptotic stability of positive almost periodic solutions system are derived. In addition, an example numerical simulations presented to illustrate substantiate results this paper.

This paper concerns with a reaction–diffusion susceptible-vaccinated-infectious-recovered model fixed latent period. The is formulated as non-local and time-delayed due to the fact that an individual infected by disease in one place may not stay at same space domain movement of human during incubation We then derive basic reproduction number ℜ0 spectral radius next infection operator show it serves threshold role predicting whether will spread. Further, explicit formula obtained when all...

A stage-structured prey–predator model with time delay and harve-sting is considered. Some novel sufficient conditions for the local stability of positive equilibria are obtained by Routh–Hurwitz criteria. Moreover, existence a Hopf bifurcation at coexistence equilibrium established. Finally, optimal harvesting problem formulated solved Pontryagin's maximum principle, an example given illustration.

This paper studies the model of host pathogen with saturation and spatial heterogeneity. In study infectious diseases, rate heterogeneity is an important factor affecting spread disease. First, since solution semiflow lacks compactness, we prove well-posedness by verifying smoothness semiflow. Then basic reproduction number $R_0$ determined, its threshold effect proved: when $R_0&lt;1$, system globally asymptotically at disease-free equilibrium; $R_0&gt;1$, give that not only uniformly...

We choose the delay as a variable parameter and investigate Lorentz-like system with delayed feedback by using Hopf bifurcation theory functional differential equations. The local stability of positive equilibrium existence bifurcations are obtained. After that direction periodic solutions bifurcating from is determined normal form center manifold theorem. In end, some numerical simulations employed to validate theoretical analysis. results show purpose controlling chaos can be achieved...

We discuss the dynamic behavior of a new Lorenz-like chaotic system with distributed delayed feedback by qualitative analysis and numerical simulations. It is verified that equilibria are locally asymptotically stable when<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mi>α</mml:mi><mml:mo>∈</mml:mo><mml:mo stretchy="false">(</mml:mo><mml:mn mathvariant="normal">0</mml:mn><mml:mo>,</mml:mo><mml:msub><mml:mrow><mml:mi>α</mml:mi></mml:mrow><mml:mrow><mml:mn...

This paper is concerned with chaos control and bifurcations of the Leslie–Gower type generalist predator model in a tri-trophic food web system time-delayed feedback control. First, distribution roots related characteristic equations analyzed by polynomial theorem, conditions to guarantee existence Hopf bifurcation are given choosing time delay as parameter. Then, explicit formula for direction stability periodic solutions bifurcating determined using normal form theory center manifold...

In this paper, we focus on the qualitative analysis of a parabolic–elliptic attraction–repulsion chemotaxis model with logistic source. Applying fixed point argument, [Formula: see text]-estimate technique and Moser’s iteration, derive that admits unique global solution provided initial cell mass satisfying text] for While text], there are no restrictions result still holds.

This note gives a supplement to the recent work of Wang and (2019) in sense that: (ⅰ) for critical case where $\Re_{0} = 1$, cholera-free steady state is globally asymptotically stable; (ⅱ) homogeneous case, positive constant steady-state stable with additional condition when $\Re_{0}>1$. Our first result achieved by proving local asymptotic stability global attractivity. second obtained Lyapunov function.