Dynamics analysis of a predator–prey model with nonmonotonic functional response and impulsive control

Li, Wenjie; Zhang, Ying; Huang, Lihong

doi:10.1016/j.matcom.2022.09.002

Cited by 10 publications

(3 citation statements)

References 39 publications

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“…From the above discuss, we know that the point Q is located above P , that is, Eq. ( 33) holds, which contradicts to (31). Then we know that there does no closed orbit containing pseudo-equilibrium E p and domain X sl .…”

Section: The Dulac Function Is Given Asmentioning

confidence: 89%

Global dynamics and bifurcations of Filippov SIR epidemic model with general nonlinear transmission and discontinuous control

Alsaedi³

et al. 2023

Preprint

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This paper investigates the global dynamic behavior and bifurcations of a classical nonlinear transmission SIR epidemic model with discontinuous threshold strategy. Different from previous results, we not only consider the general nonlinear transmission, but also adopt the discontinuity control. First, the positivity and boundedness of the model are given. Second, by employing Lyapunov LaSalle approach and using Green Theorem, we perform the globally stable the three types of equilibria of the system. We analytically show the orbit can tend to the disease-free equilibrium point, the endemic equilibrium point or the sliding equilibrium point in discontinuous surfaces of the system. In addition, we also analyze the sliding bifurcations of the model when consider the special transmission. Finally, some numerical simulations are worked out to confirm the results obtained in this paper.

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Section: The Dulac Function Is Given Asmentioning

confidence: 89%

Global dynamics and bifurcations of Filippov SIR epidemic model with general nonlinear transmission and discontinuous control

Alsaedi³

et al. 2023

Preprint

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show abstract

“…The established epidemic mathematical systems have played a significant role in the prediction and control of infectious diseases. Many control strategies have been developed for different control objectives, including harvesting control [ 2 – 4 ], threshold control [ 5 , 6 ] and impulsive control [ 7 , 8 ]. It is known that the disease transmission is often accompanied by a diffusion process in practical cases.…”

Section: Introductionmentioning

confidence: 99%

Dynamics of a diffusion epidemic SIRI system in heterogeneous environment

Zhang

et al. 2023

Z. Angew. Math. Phys.

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This paper studies the dynamical behaviors of a diffusion epidemic SIRI system with distinct dispersal rates. The overall solution of the system is derived by using theory and the Young’s inequality. The uniformly boundedness of the solution is obtained for the system. The asymptotic smoothness of the semi-flow and the existence of the global attractor are discussed. Moreover, the basic reproduction number is defined in a spatially uniform environment and the threshold dynamical behaviors are obtained for extinction or continuous persistence of disease. When the spread rate of the susceptible individuals or the infected individuals is close to zero, the asymptotic profiles of the system are studied. This can help us to better understand the dynamic characteristics of the model in a bounded space domain with zero flux boundary conditions.

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“…The complexity of non-linear systems can increase when their evolution is described by sudden changes, that is, impulses, [10,11,12,13,14], especially when they are state-dependent [15,16,17].…”

Section: Introductionmentioning

confidence: 99%

First-order periodic coupled systems with generalized impulse conditions

Perestrelo,

Minhós

2023

Preprint

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We present some existence and localization results for periodic solutions of impulsive first-order coupled non-linear systems of two equations, without requiring periodicity for the nonlinearities. The arguments are based on Schauder’s Fixed Point Theorem together with the upper and lower solution method, where the upper and lower solutions are not necessarily well-ordered. In addition, results on equi-regulated functions are required for the impulsive analysis. An application to a Wilson-Cowan system of two strongly coupled neurons illustrates one of the main results.

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Dynamics analysis of a predator–prey model with nonmonotonic functional response and impulsive control

Cited by 10 publications

References 39 publications

Global dynamics and bifurcations of Filippov SIR epidemic model with general nonlinear transmission and discontinuous control

Global dynamics and bifurcations of Filippov SIR epidemic model with general nonlinear transmission and discontinuous control

Dynamics of a diffusion epidemic SIRI system in heterogeneous environment

First-order periodic coupled systems with generalized impulse conditions

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