Dynamical analysis of an integrated pest management predator–prey model with weak Allee effect

Abstract

In this paper, a pest management predator-prey model with weak Allee effect on predator and state feedback impulsive control on prey is introduced and analysed, where the yield of predator released and intensity of pesticide sprayed are assumed to be linearly dependent on the selected pest control level. For the proposed model, the existence and stability of the order-1 periodic orbit of the control system are discussed. Meanwhile, with the aim of minimizing the input cost in practice, an optimization model is constructed to determine the optimal quantity of the predator released and the intensity of pesticide sprayed. The theoretical results and numerical simulations indicated that the number of pests can be limited to below an economic threshold and displays periodic variation under the proposed control strategy. In addition, it indicated in numerical simulations that an order-2 periodic orbit exists for some certain parameters.

Analisis dinamik model predator-prey tipe Gause dengan wabah penyakit pada prey

“…Selain karena adanya interaksi antara populasi, eksistensi dari suatu populasi juga dipengaruhi oleh adanya infeksi penyakit baik yang mewabah secara tertutup dalam suatu populasi ataupun menyebar lintas populasi. Wabah ini dapat diakibatkan oleh virus, bakteri, dan parasit [9][10][11][12][13][14]. Dalam artikel ini, dipelajari interaksi antara predator dan prey dengan wabah penyakit pada prey.…”

Predator-prey dynamics with Allee effect on predator species subject to intra-specific competition and nonlinear prey refuge

“…In the study of ecology, understanding the impact of Allee effect plays an important role because Allee effects can greatly increase the likelihood of local and global extinction. Accordingly, the most significant consequences of the Allee effect [9,10,27,33,34,36,40,44,45] for saving the endangered species and revealing the evolution process that has given improvement to extant biodiversity. Pal et al [25] have considered a delayed predator-prey model with strong Allee effect in prey population growth where the growth function is governed by multiplicative Allee effect on the prey population.…”

Stability and bifurcation in a single species logistic model with additive Allee effect and feedback control

“…In contrast, a population with weak Allee effect does not have such threshold. For more details on the Allee effect, please see [19][20][21]. Furthermore, Dennis [22] firstly deduced the additive Allee effect in the following equation:…”