Complex Behavior Analysis of a Fractional-Order Land Dynamical Model with Holling-II Type Land Reclamation Rate on Time Delay

Wu, Li; Li, Zhouhong; Zhang, Yuan; Xie, Binggeng

doi:10.1155/2020/1053283

Cited by 4 publications

(6 citation statements)

References 45 publications

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“…Due to the need for both survival and population growth, more food is needed during population growth than during saturation, that is, the inherent growth rate of the population is a function of a time delay t-τ. Considering the coupling relationship between the population, forest and grass land, the production and living land, and unused land comprehensively, and only discussing the impact of population development on the time delay, the following fractional time delay human-land coupling dynamics model with a Holling-II functional response function can be obtained [30]:…”

Section: Human-land Coupling Model Constructionmentioning

confidence: 99%

“…Therefore, according to the calculation method of the basic regeneration number [47], the basic regeneration number of the model can be obtained after solving for the equilibrium point, R 0 = bd+ds ash = 18.8235 > 1, indicating that the land-use types' transformation is significant in the model. Through calculation, ω 0 = 0.002358, τ 0 = 728.403 [30]. An arbitrary τ value which is less than τ 0 was chosen arbitrarily, and MATLAB software was used for numerical simulation.…”

Section: Visual Output and Expression Of Human-land Coupling Relation...mentioning

confidence: 99%

“…From the point of the dynamic system, the existence of a time delay can induce the stability of the system to switch, resulting in complex dynamic behaviors such as periodic oscillation and chaos. Therefore, it is quite necessary to consider the dynamic properties of the land dynamics model with a time delay [30]. In addition, fractional order calculus is an arbitrary generalization of integer order calculus in order, and calculus is widely used in the study of complex dynamic systems, such as the regulation of various ecosystems [31,32], secure communication [33,34], system controls [35,36] and stability issues [37].…”

Section: Introductionmentioning

confidence: 99%

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Modeling Analysis on Coupling Mechanisms of Mountain–Basin Human–Land Systems: Take Yuxi City as an Example

Yang

Xie

2022

Land

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The result of a human–land relationship in geographical environment systems is a human–land coupling system, which is a comprehensive process of interaction and infiltration between human economic and social systems and the natural ecosystem. Based on the recognition that the human–land system is a nonlinear system coupled by multiple factors, a time delay fractional order dynamics model with a Holling-II-type transformation rate was constructed, the stability analysis of the system was carried out, the transformation times of different land classes were clarified, and the coupled dynamics model parameters of mountainous areas and basin areas were obtained by using the land-use change survey data and socio-economic statistical data in Yuxi City, respectively: the transformation parameter of the production and living land to the unused land in mountainous areas and basin areas (aM, 0.0486 and aB, 0.0126); the transformation parameter of unused land to production and living land in mountainous areas and basin areas (bM 0.0062 and bB, 0.0139); the transformation parameter of unused land to the forest and grass land in mountainous areas and basin areas (sM, 0.0051 and sB, 0.0028); the land area required to maintain the individual unit in mountainous areas and basin areas (hM, 0.0335 and hB, 0.0165); the average reclamation capacity in mountainous areas and basin areas (dM, 0.03 and dB, 0.05); the inherent growth rate of populations in mountainous areas and basin areas (rM, 0.0563 and rB, 0.151). Through analyzing the coupling mechanisms of human–land systems, the countermeasures for the difference between mountainous areas and basin areas in the future development are put forward. The mountainous area should reduce the conversion of forest and grass land to production and living land by reducing the average reclamation or development capacity, reducing the excessive interference of human beings on unused land, and speeding up its natural recovery and succession to forest and grass land. In addition to reducing the average reclamation or development capacity in basin areas, the reclamation or development rate of the idle land and degraded land should be increased, and the conversion of idle land and degraded land into productive and living land should be encouraged by certain scientific and technological means.

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Section: Human-land Coupling Model Constructionmentioning

confidence: 99%

Section: Visual Output and Expression Of Human-land Coupling Relation...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Modeling Analysis on Coupling Mechanisms of Mountain–Basin Human–Land Systems: Take Yuxi City as an Example

Yang

Xie

2022

Land

Self Cite

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“…[21]. The flatlands have a flat terrain, suitable for cultivation and construction, while the mountains have complex natural conditions, which make them difficult to use [22]; however, there is a co-evolutionary relationship in the process of land use evolution [23,24] because they are in the same region. Therefore, as two unique geographical spaces in the southwest mountainous area of China, how the mountains and flatlands play their respective roles in regional sustainable development according to their characteristics of land use evolution has become an important research topic [25].…”

Section: Introductionmentioning

confidence: 99%

A Comparative Study on Land Use/Land Cover Change and Topographic Gradient Effect between Mountains and Flatlands of Southwest China

Yang

et al. 2023

Land

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Topography plays an important role in restricting the formation of and change in land use/land cover (LULC) patterns. To compare the LULC change and topographic gradient effects between mountains and flatlands, the geo-informatic atlas, terrain position index, distribution index and diversity index were used to analyze the LULC patterns in Yuxi from 2000 to 2020. The results were as follows: (1) the temporal–spatial variation in LULC was obviously different. From 2000 to 2020, land use change in the flatlands was more severe than that in the mountains. The transfer amount of forestland in the mountains was the largest, with the transfer-out and transfer-in accounting for 48.53% and 31.05%. However, in the flatlands, the biggest changes were found in the transfer-out of cultivated land and the transfer-in of build-up land, which were 46.91% and 38.20%, respectively. The LULC types in the mountains changed dramatically from 2000 to 2010, while those in the flatlands changed dramatically from 2010 to 2020. (2) There were obvious differences in the topographic gradient effects. The dominant distributions of land use types in the low-terrain area were the same, but the dominance of build-up land in the flatlands and that of wetland in the mountains were the largest. In the mountains, the dominant distribution of grassland was in the medium-terrain position, while that of forestland was in the high position, and the opposite was found in the flatlands. In addition, the variation trend of the diversity index in the mountains was relatively simple, but the variation range was large, ranging from 0 to 1.677, and high diversity was mainly found in the medium- and high-terrain positions. However, the variation trend in the flatlands was complex, but only ranged from 0.918 to 1.994, and high diversity was found in the low-terrain positions. The differences in the LULC change and terrain gradient effects between the mountains and flatlands were mainly caused by natural, socio-economic and policy factors, which can provide a certain reference for differentiated land use policies for regional coordinated and sustainable development.

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“…Currently, in 2017, Simpson and Gumel [5] have designed a HIV model that incorporates pre-exposure prophylaxis (PrEP). Recently, in 2020, Akrami and Atabaigi [6] have analyzed about Hopf and forward bifurcation of an integer and fractional-order SIR epidemic model, followed by this in the same year Wu et al [7] have studied about the complex behavior analysis of a fractional-order land dynamical model with holling-II type land reclamation rate on time delay. In 2020, Shaikh et al [8] have designed a fractional order covid-19 model.…”

Section: Introductionmentioning

confidence: 99%

An Investigation on Analytical Properties of Delayed Fractional Order HIV Model: A Case Study

Pitchaimani¹,

Devi²

2021

Math.Biol.Bioinf.

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In this manuscript, we design a fractional order delay differential equation model for HIV transmission with the implementation of three distinct therapies for three different infectious stages. We investigate the positivity of solutions, analyze the stability properties, followed by Hopf bifurcation analysis. To probe the parameters that expedite the spread of infection, uncertainty and sensitivity analysis were performed. The numerical review was carried out to substantiate our theoretical results. Our proposed model parameters have been calibrated to fit yearly data from Afghanistan, Australia, France, Italy, Netherlands and New Zealand.

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Complex Behavior Analysis of a Fractional-Order Land Dynamical Model with Holling-II Type Land Reclamation Rate on Time Delay

Cited by 4 publications

References 45 publications

Modeling Analysis on Coupling Mechanisms of Mountain–Basin Human–Land Systems: Take Yuxi City as an Example

Modeling Analysis on Coupling Mechanisms of Mountain–Basin Human–Land Systems: Take Yuxi City as an Example

A Comparative Study on Land Use/Land Cover Change and Topographic Gradient Effect between Mountains and Flatlands of Southwest China

An Investigation on Analytical Properties of Delayed Fractional Order HIV Model: A Case Study

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