Asymptotic analysis of a spatially and size-structured population model with delayed birth process

Yan, Dongxue; Fu, Xianlong

doi:10.3934/cpaa.2016.15.637

Cited by 9 publications

(14 citation statements)

References 27 publications

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“…(Proof of Theorem 5.8). As in [26,35,36] we will apply Theorem 5.7 to prove this assertion. According to this theorem, we just have to show that the semigroup e t(A 0 ) 0 t≥0 is positive with ω ess A 0 0 < ω 0 A 0 0 and that λ 0 is a first order pole of R λ, A 0 0 with one dimensional eigenspace.…”

Section: Asynchronous Exponential Growthmentioning

confidence: 92%

“…This is an important characteristic of solutions of population equations both from the theoretical and application point of view. Some work on this issue can be found in, for example, [3,15,26,30,35,36]. In [35], particularly, we have explored the asynchronous exponential growth for a a spatially and size-structured population dynamics model.…”

Section: Asynchronous Exponential Growthmentioning

confidence: 99%

“…Some work on this issue can be found in, for example, [3,15,26,30,35,36]. In [35], particularly, we have explored the asynchronous exponential growth for a a spatially and size-structured population dynamics model. We shall use the similar technique as in [26,35,36] to investigate the asynchronous exponential growth for System (1.1).…”

Section: Asynchronous Exponential Growthmentioning

confidence: 99%

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Long-time behavior of a size-structured population model with diffusion and delayed birth process

Yan

2022

EECT

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This work focuses on the long time behavior for a size-dependent population system with diffusion and Riker type birth function. Some dynamical properties of the considered system is investigated by using C 0 -semigroup theory and spectral analysis arguments. Some sufficient conditions are obtained respectively for asymptotical stability, asynchronous exponential growth at the null equilibrium as well as Hopf bifurcation occurring at the positive steady state of the system. In the end several examples and their simulations are also provided to illustrate the achieved results.

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Section: Asynchronous Exponential Growthmentioning

confidence: 92%

Section: Asynchronous Exponential Growthmentioning

confidence: 99%

Section: Asynchronous Exponential Growthmentioning

confidence: 99%

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Long-time behavior of a size-structured population model with diffusion and delayed birth process

Yan

2022

EECT

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“…should be understood as the probability that an individual of size s reproduces after a time lag −τ starting from conception, here τ > 0 is a constant denoting the maximal time delay the birth process takes. Such a form of the delayed birth process was initialed by Pizzera [30] by taking into account the time which the birth process may take, and it has been adopted in many papers, such as in papers [18,19,37,38], to discuss the long-time behavior of the corresponding nonlinear systems and explore how the time lag influences the asymptotic behaviors of the considered systems.…”

mentioning

confidence: 99%

“…This is an important characteristic of solutions of population equations both from the theoretical and application point of view. In the past years there is much work on this topic, see for instance [5,31,37,38].…”

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confidence: 99%

Asymptotic behavior of a hierarchical size-structured population model

Yan¹,

Fu²

2018

Evolution Equations &Amp; Control Theory

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We study in this paper a hierarchical size-structured population dynamics model with environment feedback and delayed birth process. We are concerned with the asymptotic behavior, particularly on the effects of hierarchical structure and time lag on the long-time dynamics of the considered system. We formally linearize the system around a steady state and study the linearized system by C 0-semigroup framework and spectral analysis methods. Then we use the analytical results to establish the linearized stability, instability and asynchronous exponential growth conclusions under some conditions. Finally, some examples are presented and simulated to illustrate the obtained results.

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Controllability under positivity constraints of a size‐structured population model with delayed birth process

El Gantouh,

Fkirine,

Simpore

2023

Math Methods in App Sciences

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In this paper, we study the approximate controllability, under positivity constraints on the control and state, of a size‐structured population system with time‐delayed behavior. In this model, the birth term is non‐local in size and time, which describes the time‐delay in the recruitment process in newborn individuals population. Our control function is localized at birth and corresponds to a supply of newborn individuals. First, we establish the well‐posedness and positivity property of the model. Second, and more importantly, we derive necessary and sufficient conditions for approximate controllability under positivity constraints. The method relies on the feedback theory of infinite‐dimensional positive systems.

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Asymptotic analysis of a spatially and size-structured population model with delayed birth process

Cited by 9 publications

References 27 publications

Long-time behavior of a size-structured population model with diffusion and delayed birth process

Long-time behavior of a size-structured population model with diffusion and delayed birth process

Asymptotic behavior of a hierarchical size-structured population model

Controllability under positivity constraints of a size‐structured population model with delayed birth process

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