Stability analysis of a fractional-order two-species facultative mutualism model with harvesting

Supajaidee, Nattakan; Moonchai, Sompop

doi:10.1186/s13662-017-1430-9

Cited by 13 publications

(10 citation statements)

References 40 publications

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“…We begin by introducing the definition of Caputo fractional derivative and stating related theorems (see [37][38][39][40][41]) that we will utilise to derive important results in this work.…”

Section: Preliminaries On the Caputo Fractional Calculusmentioning

confidence: 99%

A fractional-order Trypanosoma brucei rhodesiense model with vector saturation and temperature dependent parameters

et al. 2020

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Temperature is one of the integral environmental drivers that strongly affect the distribution and density of tsetse fly population. Precisely, ectotherm performance measures, such as development rate, survival probability and reproductive rate, increase from low values (even zero) at critical minimum temperature, peak at an optimum temperature and then decline to low levels (even zero) at a critical maximum temperature. In this study, a fractional-order Trypanosoma brucei rhodesiense model incorporating vector saturation and temperature dependent parameters is considered. The proposed model incorporates the interplay between vectors and two hosts, humans and animals. We computed the basic reproduction number and established results on the threshold dynamics. Meanwhile, we explored the effects of vector control and screening of infected host on long-term disease dynamics. We determine threshold levels essential to reducing the basic reproduction number to level below unity at various temperature levels. Our findings indicate that vector control and host screening could significantly control spread of the disease at different temperature levels.

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Section: Preliminaries On the Caputo Fractional Calculusmentioning

confidence: 99%

A fractional-order Trypanosoma brucei rhodesiense model with vector saturation and temperature dependent parameters

et al. 2020

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“…In this section, we derive the stability of the solutions obtained by the deterministic flow equations [47][48][49]. To simplify the problem, we consider the zero-temperature limit β → ∞.…”

Section: Stability Analysis Of the Equilibrium Solutionsmentioning

confidence: 99%

Dynamics of order parameters of nonstoquastic Hamiltonians in the adaptive quantum Monte Carlo method

2019

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We derive macroscopically deterministic flow equations with regard to the order parameters of the ferromagnetic p-spin model with infinite-range interactions. The p-spin model has a first-order phase transition for p > 2. In the case of p ≥ 5 ,the p-spin model with anti-ferromagnetic XX interaction has a second-order phase transition in a certain region. In this case, however, the model becomes a non-stoqustic Hamiltonian, resulting in a negative sign problem. To simulate the p-spin model with anti-ferromagnetic XX interaction, we utilize the adaptive quantum Monte Carlo method. By using this method, we can regard the effect of the anti-ferromagnetic XX interaction as fluctuations of the transverse magnetic field. A previous study (J.Inoue, J. Phys.Conf. Ser.233, 012010, 2010) derived deterministic flow equations of the order parameters in the quantum Monte Carlo method. In this study, we derive macroscopically deterministic flow equations for the magnetization and transverse magnetization from the master equation in the adaptive quantum Monte Carlo method. Under the Suzuki-Trotter decomposition, we consider the Glauber-type stochastic process. We solve these differential equations by using the Runge-Kutta method and verify that these results are consistent with the saddle-point solution of mean-field theory. Finally, we analyze the stability of the equilibrium solutions obtained by the differential equations.

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“…Fractional-order differential equation has been successfully used and applied to model many areas of science, engineering, and phenomena that cannot be formulated by other types of equations [10,16]. In [12,[16][17][18][19][20][21], authors have investigated the effects of the fractional order differential equation on a prey predator model as well as they also discussed the stability analysis of equilibrium points of fractional order model with and without harvest-ing, as well as the existence, uniqueness, and boundedness of the solutions that are proved.…”

Section: Introductionmentioning

confidence: 99%

Dynamical Behaviors of a Fractional-Order Three Dimensional Prey-Predator Model

Sh.

Al-Nassir

2021

Abstract and Applied Analysis

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In this paper, the dynamical behavior of a three-dimensional fractional-order prey-predator model is investigated with Holling type III functional response and constant rate harvesting. It is assumed that the middle predator species consumes only the prey species, and the top predator species consumes only the middle predator species. We also prove the boundedness, the non-negativity, the uniqueness, and the existence of the solutions of the proposed model. Then, all possible equilibria are determined, and the dynamical behaviors of the proposed model around the equilibrium points are investigated. Finally, numerical simulations results are presented to confirm the theoretical results and to give a better understanding of the dynamics of our proposed model.

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Stability analysis of a fractional-order two-species facultative mutualism model with harvesting

Cited by 13 publications

References 40 publications

A fractional-order Trypanosoma brucei rhodesiense model with vector saturation and temperature dependent parameters

A fractional-order Trypanosoma brucei rhodesiense model with vector saturation and temperature dependent parameters

Dynamics of order parameters of nonstoquastic Hamiltonians in the adaptive quantum Monte Carlo method

Dynamical Behaviors of a Fractional-Order Three Dimensional Prey-Predator Model

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