| Abstract: |
| Plant-herbivore systems provide a natural laboratory for nonlinear dynamical phenomena arising from feedback, adaptation, and multi-scale interaction. In this paper, we develop and analyze a mathematical model for the intra- and inter-species dynamics governing the interaction between the wild tobacco plant (Nicotiana attenuata) and the tobacco hawk moth and its caterpillars (Manduca sexta). Hereby special attention is given to plant defense mechanisms, i.e., nicotine production, attack signals to other tabaco plants, and signals to predator insects, like big-eyed bugs (several species in the family Geocoris), that feed on the caterpillars of the tobacco hawk moth. The resulting model is studied by techniques from the theory of dynamical systems such that conditions for stability and bifurcations of mixed-species equilibria are determined and the phase space dynamics are classified. Simulations round-up the picture. The model and its mathematical analysis illustrate how biochemical defense pathways translate into ecological phase portraits and provide a case study in how adaptive biological feedback adds to the insights of classical predator-prey dynamics. |
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