Lacitignola Deborah, Diele Fasma, Marangi Carmela, Provenzale Antonello
Dipartimento di Ingegneria Elettrica e dell'Informazione, Università di Cassino e del Lazio Meridionale, via Di Biasio, Cassino I-03043, Italy.
Istituto per le Applicazioni del Calcolo M. Picone, CNR, Via Amendola 122, Bari I-70126, Italy.
Math Biosci. 2016 Oct;280:10-23. doi: 10.1016/j.mbs.2016.07.011. Epub 2016 Jul 27.
We apply the Z-control approach to a generalized predator-prey system and consider the specific case of indirect control of the prey population. We derive the associated Z-controlled model and investigate its properties from the point of view of the dynamical systems theory. The key role of the design parameter λ for the successful application of the method is stressed and related to specific dynamical properties of the Z-controlled model. Critical values of the design parameter are also found, delimiting the λ-range for the effectiveness of the Z-method. Analytical results are then numerically validated by the means of two ecological models: the classical Lotka-Volterra model and a model related to a case study of the wolf-wild boar dynamics in the Alta Murgia National Park. Investigations on these models also highlight how the Z-control method acts in respect to different dynamical regimes of the uncontrolled model.
我们将Z控制方法应用于广义捕食者 - 猎物系统，并考虑对猎物种群进行间接控制的具体情况。我们推导了相关的Z控制模型，并从动力系统理论的角度研究其性质。强调了设计参数λ对于该方法成功应用的关键作用，并将其与Z控制模型的特定动力学性质相关联。还找到了设计参数的临界值，划定了Z方法有效性的λ范围。然后通过两个生态模型对分析结果进行数值验证：经典的Lotka-Volterra模型和与阿尔塔穆尔贾国家公园狼 - 野猪动态案例研究相关的模型。对这些模型的研究还突出了Z控制方法在未受控制模型的不同动力学状态下的作用方式。
