Abstract
Some mathematical models are suggested to describe the tritrofic interactions among plants, herbivores and their carnivorous enemies attracted by defensive volatiles of plants. For the interactions of Volterra type, it is proved that the threshold value for the persistence of herbivore and carnivore populations is not affected by the chemical attractions. Furthermore, the attraction to carnivores is beneficial to reduce the density of herbivores and increase the density of plants. If the interaction of plants and herbivores takes the Leslie type, the model admits the fold bifurcation that induces bistable positive equilibria. Numerical computations indicate that the response time of carnivores to defensive volatiles of plants induces periodic cycles and irregular fluctuations.
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