Periodic Solution for a Stochastic Non-autonomous Predator-Prey Model with Holling II Functional Response

Zu, Li; Jiang, Daqing; O’Regan, Donal

doi:10.1007/s10440-018-0205-y

Cited by 11 publications

(5 citation statements)

References 36 publications

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“…Hence, we believe a nonlinear transmission rate can better manifest the law of the spreading between S(t) and I(t), and the interactive process is consistent with Holling II functional response function. In regard of this, we introduce the Holling II functional response function [37][38][39][40] to the classical DK rumor spreading model. The model is given by All parameters in model (1) are assumed positive and are summarized in the following list:…”

Section: Near-optimal Control Of a Stochastic Rumor Spreading Modelmentioning

confidence: 99%

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Near-optimal control of a stochastic rumor spreading model with Holling II functional response function and imprecise parameters*

Huo¹,

Chen²

2021

Chinese Phys. B

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In recent years, rumor spreading has caused widespread public panic and affected the whole social harmony and stability. Consequently, how to control the rumor spreading effectively and reduce its negative influence urgently needs people to pay much attention. In this paper, we mainly study the near-optimal control of a stochastic rumor spreading model with Holling II functional response function and imprecise parameters. Firstly, the science knowledge propagation and the refutation mechanism as the control strategies are introduced into a stochastic rumor spreading model. Then, some sufficient and necessary conditions for the near-optimal control of the stochastic rumor spreading model are discussed respectively. Finally, through some numerical simulations, the validity and availability of theoretical analysis is verified. Meanwhile, it shows the significance and effectiveness of the proposed control strategies on controlling rumor spreading, and demonstrates the influence of stochastic disturbance and imprecise parameters on the process of rumor spreading.

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Section: Near-optimal Control Of a Stochastic Rumor Spreading Modelmentioning

confidence: 99%

“…By Hypothesis (H2), we get the Hamiltonian function His differentiable in u(t), and Eq. (38) shows that there exists a…”

Section: Sufficient Conditions For Near-optimal Controlsmentioning

confidence: 99%

Near-optimal control of a stochastic rumor spreading model with Holling II functional response function and imprecise parameters*

Huo¹,

Chen²

2021

Chinese Phys. B

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“…In addition, the Hopf bifurcation method has been followed in [7] to study a delayed density-dependent predator-prey system with Beddington-DeAngelis functional response. The periodic dynamic in the solutions has been shown to exist as a consequence of stochastic disturbance for a Holling II functional response [8]. Similar stability and bifurcation methods have been used in [9] for a predator-prey model subject to the Allee effect with a discrete-time Holling type-IV functional response.…”

Section: Introductionmentioning

confidence: 95%

Regularity, Asymptotic Solutions and Travelling Waves Analysis in a Porous Medium System to Model the Interaction between Invasive and Invaded Species

et al. 2022

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This work provides an analytical approach to characterize and determine solutions to a porous medium system of equations with views in applications to invasive-invaded biological dynamics. Firstly, the existence and uniqueness of solutions are proved. Afterwards, profiles of solutions are obtained making use of the self-similar structure that permits showing the existence of a diffusive front. The solutions are then studied within the Travelling Waves (TW) domain showing the existence of potential and exponential profiles in the stable connection that converges to the stationary solutions in which the invasive species predominates. The TW profiles are shown to exist based on the geometry perturbation theory together with an analytical-topological argument in the phase plane. The finding of an exponential decaying rate (related with the advection and diffusion parameters) in the invaded species TW is not trivial in the nonlinear diffusion case and reflects the existence of a TW trajectory governed by the invaded species runaway (in the direction of the advection) and the diffusion (acting in a finite speed front or support).

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“…In addition, the Hopf bifurcation method has been followed in [19] to study a delayed density-dependent predator-prey system with Beddington-DeAngelis functional response. The periodic dynamic in the solutions has been shown to exist as a consequences of stochastic disturbance for a Holling II functional response [34]. Similar stability and bifurcation methods have been used in [24] for a predator-prey model subject to the Allee effect with a discrete-time Holling type-IV functional response.…”

Section: Introductionmentioning

confidence: 96%

Invasive-invaded system of non-Lipschitz porous medium equations with advection

Palencia

2021

Int. J. Biomath.

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This work provides analytical results towards applications in the field of invasive-invaded systems modeled with nonlinear diffusion and with advection. The results focus on showing regularity, existence and uniqueness of weak solutions using the condition of a nonlinear slightly positive parabolic operator and the reaction-absorption monotone properties. The coupling in the reaction-absorption terms, that characterizes the species interaction, impedes the formulation of a global comparison principle that is shown to exist locally. Additionally, this work provides analytical solutions obtained as selfsimilar minimal and maximal profiles. A propagating diffusive front is shown to exist until the invaded specie notes the existence of the invasive. When the desertion of the invaded starts, the diffusive front vanishes globally and the nonlinear diffusion concentrates only on the propagating tail which exhibits finite speed. Finally, the invaded specie is shown to exhibit an exponential decay along a characteristic curve. Such exponential decay is not trivial in the nonlinear diffusion case and confirms that the invasive continues to feed on the invaded during the desertion.

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Periodic Solution for a Stochastic Non-autonomous Predator-Prey Model with Holling II Functional Response

Cited by 11 publications

References 36 publications

Near-optimal control of a stochastic rumor spreading model with Holling II functional response function and imprecise parameters*

Near-optimal control of a stochastic rumor spreading model with Holling II functional response function and imprecise parameters*

Regularity, Asymptotic Solutions and Travelling Waves Analysis in a Porous Medium System to Model the Interaction between Invasive and Invaded Species

Invasive-invaded system of non-Lipschitz porous medium equations with advection

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