Bounded random fluctuations on the input flow in chemostat models with wall growth and non-monotonic kinetics

Caraballo, Tomás; López‐de‐la‐Cruz, Javier

doi:10.3934/math.2021239

Cited by 9 publications

(10 citation statements)

References 41 publications

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“…One may wonder about the choice of such a noise. Indeed, it has been shown to be a relevant way of modeling real random fluctuations in chemostat models (see, for instance [6,44,3,11,12,9,10], where the authors perturb different parameters in several chemostat models and other models in population dynamics).…”

Section: Fig 2: Diagram Of Two Chemostat Devices Connected By Fickian Diffussionmentioning

confidence: 99%

“…In this section we present a way to model bounded random fluctuations which has been proved to be very useful when modeling real random disturbances in biological models (see [3,9,10,12]) fitting the real devices.…”

Section: Modeling Random Bounded Fluctuationsmentioning

confidence: 99%

“…3 to observe how the random diffusion parameter behaves), the dynamics of the concentration of the species in both culture vessel seems to be almost deterministic even though the noise amplitude is not so small. Le us underline that, differently to disturbances on the input term Q as considered in [9,10,11,12], the noise acts on an internal term d of the dynamics.…”

Section: Numerical Simulationsmentioning

confidence: 99%

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Study of the dynamics of two chemostats connected by Fickian diffusion with bounded random fluctuations

2021

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This paper investigates the dynamics of a model of two chemostats connected by Fickian diffusion with bounded random fluctuations. We prove the existence and uniqueness of non-negative global solution as well as the existence of compact absorbing and attracting sets for the solutions of the corresponding random system. After that, we study the internal structure of the attracting set to obtain more detailed information about the long-time behavior of the state variables. In such a way, we provide conditions under which the extinction of the species cannot be avoided and conditions to ensure the persistence of the species, which is often the main goal pursued by practitioners. In addition, we illustrate the theoretical results with several numerical simulations.

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Section: Fig 2: Diagram Of Two Chemostat Devices Connected By Fickian Diffussionmentioning

confidence: 99%

Section: Modeling Random Bounded Fluctuationsmentioning

confidence: 99%

Section: Numerical Simulationsmentioning

confidence: 99%

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Study of the dynamics of two chemostats connected by Fickian diffusion with bounded random fluctuations

2021

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“…For this perturbations a condition as (5.10) is verify for the symbol space Ω instead of R × Ω. See also [25] where the authors study this type of perturbations.…”

Section: Applications To Differential Equationsmentioning

confidence: 99%

“…We also obtain stronger results on the continuity and topological structural stability of nonautonomous random attractors for the case when the random perturbations are uniformly bounded with respect to the random parameter, see Remark 5.4 and Remark 6.3 for more details. Moreover, see [9,25] for examples of this types of noises.…”

Section: Introductionmentioning

confidence: 99%

Continuity and topological structural stability for nonautonomous random attractors

Caraballo¹,

Carvalho²,

Langa³

et al. 2021

Preprint

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In this work, we study continuity and topological structural stability of attractors for nonautonomous random differential equations obtained by small bounded random perturbations of autonomous semilinear problems. First, we study existence and permanence of unstable sets of hyperbolic solutions. Then, we use this to establish lower semicontinuity of nonautonomous random attractors and to show that the gradient structure persists under nonautonomous random perturbations. Finally, we apply the abstract results in a stochastic differential equation and in a damped wave equation with a perturbation on the damping.

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Chemostat models with Monod and Haldane consumption functions and random environmental fluctuations

Caraballo

López‐de‐la‐Cruz

Caraballo‐Romero

2023

Math Methods in App Sciences

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In this paper, we study the asymptotic dynamics of two chemostat models with random environmental fluctuations modeled by means of real noise, where different consumption functions for the consumer species (Monod and Haldane) are taking into account. For each model, our main goal is to investigate the existence of deterministic attracting sets. This allows us to provide conditions under which the species become extinct or persist, which is the main goal in industrial setup. In addition, we depict different numerical simulations to support the theoretical results. Finally, we present some conclusions to sum up our contribution and we compare how the species behave depending on its consumption function.

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Bounded random fluctuations on the input flow in chemostat models with wall growth and non-monotonic kinetics

Cited by 9 publications

References 41 publications

Study of the dynamics of two chemostats connected by Fickian diffusion with bounded random fluctuations

Study of the dynamics of two chemostats connected by Fickian diffusion with bounded random fluctuations

Continuity and topological structural stability for nonautonomous random attractors

Chemostat models with Monod and Haldane consumption functions and random environmental fluctuations

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