Modelling Environmental In uences on Wanderer Spiders in the Langhe Region (Piemonte { NW Italy)

Keywords: predator-prey model, equilibria, stochastic diferential equation, stochastic stability.

Abstract: We develop a mathematical model for understanding the e ect of wanderer
spiders as biological controllers of the insects infesting vineyards, thus accounting also for
the role played by residual wood and green patches as spiders habitat in the otherwise
homogeneuous landscape of the Langhe region. We then extend the deterministic model
allowing random
uctuations around the coexistence equilibrium. The stochastic stability
properties of the model are investigated both analytically and numerically.


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