Algae-herbivore interactions with Allee effect and chemical defense |
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| Affiliation: | 1. School of Science, Nanjing University of Science and Technology, Nanjing, Jiangsu 210094, China;2. School of Electrical and Electronic Engineering, Nanyang Technological University, Nanyang Avenue, 639798 Singapore;3. School of Automation, Nanjing University of Science and Technology, Nanjing, Jiangsu 210094, China |
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| Abstract: | Macroalgae exhibit a variety of characteristics that provide a degree of protection from herbivores. One characteristic is the production of chemicals that are toxic to herbivores. The toxic effect of macroalgae on herbivorous reef fish is studied by means of a spatiotemporal model of population dynamics with a nonmonotonic toxin-determined functional response of herbivores. It is assumed that the growth rate of macroalgae is mediated by Allee effect. We see that under certain conditions the system is uniformly persistent. Conditions for local stability of the system is obtained with weak and strong Allee effects. We observe that in presence of Allee effect on macroalgae, the system exhibits complex dynamics including Hopf bifurcation and saddle-node bifurcation. The obtained results show that the spatiotemporal system does not exhibit diffusion-driven instability. Computer simulations have been carried out to illustrate different analytical results. |
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| Keywords: | Allee effect Macroalgal toxicity Hopf bifurcation Saddle-node bifurcation |
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