Duality Analysis Of Dynamics Of Integrated Pest Management Spatial Model

A variety of landscapes determine that many habitats can be separated by rivers or mountains, so that broad ecological habitats may be fragmented into a series of isolated distinct patches. Moreover, in recent years, excessive exploitation activities from human have profoundly accelerate this process. Naturally habitat loss typically occurs concurrently with habitat fragmentation, thereby causing biodiversity loss worldwide. Within fragmented habitats, the growing pattern of population show unique characteristics, which is of great meaning to the protection of rare species and the implementation of pest controlling strategies in economical production.Among habitat patches with network structure, some populations of animals or plants tend to occur in community clysters with individuals mainly living in a certain patch. Sedentary populations with only small proportions of them able or willing to move to other patches are in contrast to highly migratory species which regularly move within and between patches. Fragmented habitat patches between which plants and animals can dispersal can be modeled as networks with varying degrees of connectivity. A predator-prey model with network structures is proposed for integrated pest management (IPM) with impulsive control actions. The model was analyzed using numerical methods to investigate how factors such as the impulsive period,the releasing constant of natural enemies and the mode of connections between the patches affect pest outbreak patterns and the success or failure of pest control.The concept of the cluster as defined by Holland and Hastings is used to describe variations in results ranging from global synchrony when all patches have identical fluctuations to ncluster solutions with all patches having different dynamics. Heterogeneity in the initial densities of either pest or natural enemy generally resulted in a variety of cluster oscillations. Surprisingly, if n>1, the clusters fall into two groups one with low amplitude fluctuations and the other with high amplitude fluctuations (i.e. duality in phase space), implying that control actions radically alter the system's characteristics by inducing duality and more complex dynamics. When the impulsive period is small enough, i.e. the control strategy is undertaken frequently, the pest can be eradicated. As the period increases, the pest's dynamics shift from a steady state to become chaotic distributions. Period-doubling bifurcation and periodic halving cascades occur as the releasing constant of the natural enemy increases. For the same ecological system with five differently connected networks, as the randomness of the connectedness increases, the transient duration becomes smaller and the probability of multicluster oscillations appearing becomes higher.In comparison with the results from impulsive controlling model without net-work structure, the model based on habitat network behave different phenomenon. Therefore, as the IPM strategies are carried out, the connectivity between net-worked habitat patches cannot be ignored. Moreover, the presentation of diverse cluster solutions suggest that pest population may have various outbreak pattern-s, which reminds the need for detailed scouting. Further, due to the difference of population dynamics on patch network, the impact of different dispersal modes on model dynamics should be well considered, while modelling the population with great mobility or obviously heterogenous distribution. Especially, connectivity of patches presents significant effect on the protection over endangered species. The higher the connectivity is, the easier to promote ecological communication between different population.