Nonlinear impulsive differential and integral inequalities with nonlocal jump conditions

Zheng, Zhaowen; Zhang, Yingjie; Shao, Jinghai

doi:10.1186/s13660-018-1762-3

Cited by 2 publications

(1 citation statement)

References 13 publications

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“…Jiang et al obtained the order-1 periodic solutions using the Poincaré map [18,19], and Chen developed the idea of successor functions to study the mathematical models with pulse state feedback control [20]. Due to its importance in applications, in recent years, systems of impulsive differential equations have attracted more and more attention and been applied to different areas from population dynamics to chemical regulator systems [21][22][23][24][25][26][27][28]. Due to the challenges in analysing these models, most of existing models only considered the population size without considering the population growth rate when proposing a control strategy [29,30].…”

Section: Introductionmentioning

confidence: 99%

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

Hou

Zhang

et al. 2021

Preprint

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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.

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Section: Introductionmentioning

confidence: 99%

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

Hou

Zhang

et al. 2021

Preprint

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Dynamic analysis of a phytoplankton-fish model with the impulsive feedback control depending on the fish density and its changing rate

Cheng

2023

MBE

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<abstract><p>This paper proposes and studies a comprehensive control model that considers fish population density and its current growth rate, providing new ideas for fishing strategies. First, we established a phytoplankton-fish model with state-impulse feedback control based on fish density and rate of change. Secondly, the complex phase sets and impulse sets of the model are divided into three cases, then the Poincar$ \acute{\mbox{e}} $ map of the model is defined and its complex dynamic properties are deeply studied. Furthermore, some necessary and sufficient conditions for the global stability of the fixed point (order-$ 1 $ limit cycle) have been provided even for the Poincar$ \acute{\mbox{e}} $ map. The existence conditions for periodic solutions of order-$ k $($ k \ge 2 $) are discussed, and the influence of dynamic thresholds on system dynamics is shown. Dynamic thresholds depend on fish density and rate of change, i.e., the form of control employed is more in line with the evolution of biological populations than in earlier studies. The analytical method presented in this paper also plays an important role in analyzing impulse models with complex phase sets or impulse sets.</p></abstract>

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Nonlinear impulsive differential and integral inequalities with nonlocal jump conditions

Cited by 2 publications

References 13 publications

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

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

Dynamic analysis of a phytoplankton-fish model with the impulsive feedback control depending on the fish density and its changing rate

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