Browsing by Author "Hu, Jie"

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    Extinction and permanence of the predator-prey system with general functional response and impulsive control
    (Elsevier, 2020-06-22) Liu, Juan; Hu, Jie; Yuen, Peter W. T.
    Traditional approach for modelling the evolution of populations in the predator-prey ecosystem has commonly been undertaken using specific impulsive response function, and this kind of modelling is applicable only for a specific ecosystem under certain environ- mental situations only. This paper attempts to fill the gap by modelling the predator-prey ecosystem using a ‘generalized’ impulsive response function for the first time. Different from previous research, the present work develops the modelling for an integrated pest management (IPM) especially when the stocking of predator (natural enemy) and the har- vesting of prey (pest) occur impulsively and at different instances of time. The paper firstly establishes the sufficient conditions for the local and the global stabilities of prey eradica- tion periodic solution by applying the Floquet theorem of the Impulsive different equation and small amplitude perturbation under a ‘generalized’ impulsive response function. Sub- sequently the sufficient condition for the permanence of the system is given through the comparison techniques. The corollaries of the theorems that are established by using the ‘general impulsive response function’ under the locally asymptotically stable condition are found to be in excellent agreement with those reported previously. Theoretical results that are obtained in this work is then validated by using a typical impulsive response func- tion (Holling type-II) as an example, and the outcome is shown to be consistent with the previously reported results. Finally, the implication of the developed theories for practical pest management is illustrated through numerical simulation. It is shown that the elim- ination of either the preys or the pest can be effectively deployed by making use of the theoretical model established in this work. The developed model is capable to predict the population evolutions of the predator-prey ecosystem to accommodate requirements such as: the combinations of the biological control, chemical control, any functional response function, the moderate impulsive period, the harvest rate for the prey and predator pa- rameter and the incremental stocking of the predator parameter
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    Modelling of a seasonally perturbed competitive three species impulsive system
    (AIMS press, 2022-01-21) Hu, Jie; Liu, Juan; Yuen, Peter W. T.; Li, Fuzhong; Deng, Linqiang
    The population of biological species in the ecosystem is known sensitive to the periodic fluctuations of seasonal change, food resources and climatic conditions. Research in the ecological management discipline conventionally models the behavior of such dynamic systems through specific impulsive response functions, but the results of such research are applicable only when the environments conform exactly to the conditions as defined by the specific response functions that have been implemented for specific scenarios. This means that the application of previous work may be somewhat limited. Moreover, the intra and inter competitions among species have been seldom studied for modelling the prey-predator ecosystem. To fill in the gaps this paper models the delicate balance of two-prey and one-predator system by addressing three main areas of: ⅰ) instead of using the specific impulse response this work models the ecosystem through a more general response function; ⅱ) to include the effects due to the competition between species and ⅲ) the system is subjected to the influences of seasonal factors. The seasonal factor has been implemented here in terms of periodic functions to represent the growth rates of predators. The sufficient condition for the local and global asymptotic stability of the prey-free periodic solution and the permanence of the system have been subsequently obtained by using the Comparison techniques and the Floquet theorems. Finally, the correctness of developed theories is verified by numerical simulation, and the corresponding biological explanation is given.
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    A seasonally competitive m-prey and n-predator impulsive system modeled by general functional response for integrated pest management
    (MDPI, 2022-07-29) Liu, Juan; Hu, Jie; Yuen, Peter W. T.; Li, Fuzhong
    Considering the harvesting of prey and stocking of predator impulsively at different fixed moments of time, this paper studies the dynamics of a seasonally competitive m-prey and n-predator impulsive system, which is focused more specifically in four areas as follows: (i) we emphasize the dynamics of m-prey and n-predator in the ecosystem with a view to understanding how the present work may be able to apply to real environment applications; (ii) this work uses the general functional response instead of using specific impulse responses; (iii) considering the intra- and inter-competitions between species and (iv) the system is subjected to the influences of seasonal factors which imposes direct impacts to the delicate balance of biological systems. By using the comparison techniques and the Floquet theorems, the sufficient conditions for the ecosystem permanence and the asymptotic stabilities of the global and local prey-free periodic solutions have been subsequently obtained. This work is concluded with an in-depth discussion of the biological significance of the results obtained in this research. The obtained results can provide theoretical support for protecting endangered species and to help maintain the ecological balance, especially when it is applied to practical pest management, such as rodent controls in the farmland.